Multi-resolution Time-Series Transformer for Long-term Forecasting

Abstract: The performance of transformers for time-series forecasting has improved significantly. Recent architectures learn complex temporal patterns by segmenting a time-series into patches and using the patches as tokens. The patch size controls the ability of transformers to learn the temporal patterns at different frequencies: shorter patches are effective for learning localized, high-frequency patterns, whereas mining long-term seasonalities and trends requires longer patches. Inspired by this observation, we propose a novel framework, Multi-resolution Time-Series Transformer (MTST), which consists of a multi-branch architecture for simultaneous modeling of diverse temporal patterns at different resolutions. In contrast to many existing time-series transformers, we employ relative positional encoding, which is better suited for extracting periodic components at different scales. Extensive experiments on several real-world datasets demonstrate the effectiveness of MTST in comparison to state-of-the-art forecasting techniques.

Yitian Zhang
Liheng Ma
Soumyasundar Pal
Yingxue Zhang
Mark Coates

International Conference on Artificial Intelligence and Statistics


Deep Double Descent for Time Series Forecasting: Avoiding Undertrained Models

Abstract: Deep learning models, particularly Transformers, have achieved impressive results in various domains, including time series forecasting. While existing time series literature primarily focuses on model architecture modifications and data augmentation techniques, this paper explores the training schema of deep learning models for time series; how models are trained regardless of their architecture. We perform extensive experiments to investigate the occurrence of deep double descent in several Transformer models trained on public time series data sets. We demonstrate epoch-wise deep double descent and that overfitting can be reverted using more epochs. Leveraging these findings, we achieve state-of-the-art results for long sequence time series forecasting in nearly 70% of the 72 benchmarks tested. This suggests that many models in the literature may possess untapped potential. Additionally, we introduce a taxonomy for classifying training schema modifications, covering data augmentation, model inputs, model targets, time series per model, and computational budget.

Valentino Assandri
Sam Heshmati
Burhaneddin Yaman
Anton Iakovlev
Ariel Emiliano Repetur


A Systematic Review for Transformer-based Long-term Series Forecasting

Abstract: The emergence of deep learning has yielded noteworthy advancements in time series forecasting (TSF). Transformer architectures, in particular, have witnessed broad utilization and adoption in TSF tasks. Transformers have proven to be the most successful solution to extract the semantic correlations among the elements within a long sequence. Various variants have enabled transformer architecture to effectively handle long-term time series forecasting (LTSF) tasks. In this article, we first present a comprehensive overview of transformer architectures and their subsequent enhancements developed to address various LTSF tasks. Then, we summarize the publicly available LTSF datasets and relevant evaluation metrics. Furthermore, we provide valuable insights into the best practices and techniques for effectively training transformers in the context of time-series analysis. Lastly, we propose potential research directions in this rapidly evolving field.

Liyilei Su
Xumin Zuo
Rui Li
Xin Wang
Heng Zhao
Bingding Huang


Graph Deep Learning for Time Series Forecasting

Abstract: Graph deep learning methods have become popular tools to process collections of correlated time series. Unlike traditional multivariate forecasting methods, graph-based predictors leverage pairwise relationships by conditioning forecasts on graphs spanning the time series collection. The conditioning takes the form of architectural inductive biases on the forecasting architecture, resulting in a family of models called spatiotemporal graph neural networks. These biases allow for training global forecasting models on large collections of time series while localizing predictions w.r.t. each element in the set (nodes) by accounting for correlations among them (edges). Recent advances in graph neural networks and deep learning for time series forecasting make the adoption of such processing framework appealing and timely. However, most studies focus on refining existing architectures by exploiting modern deep-learning practices. Conversely, foundational and methodological aspects have not been subject to systematic investigation. To fill this void, this tutorial paper aims to introduce a comprehensive methodological framework formalizing the forecasting problem and providing design principles for graph-based predictors, as well as methods to assess their performance. In addition, together with an overview of the field, we provide design guidelines and best practices, as well as an in-depth discussion of open challenges and future directions.

Andrea Cini
Ivan Marisca
Daniele Zambon
Cesare Alippi


Mid-Long Term Daily Electricity Consumption Forecasting Based on Piecewise Linear Regression and Dilated Causal CNN

Abstract: Daily electricity consumption forecasting is a classical problem. Existing forecasting algorithms tend to have decreased accuracy on special dates like holidays. This study decomposes the daily electricity consumption series into three components: trend, seasonal, and residual, and constructs a two-stage prediction method using piecewise linear regression as a filter and Dilated Causal CNN as a predictor. The specific steps involve setting breakpoints on the time axis and fitting the piecewise linear regression model with one-hot encoded information such as month, weekday, and holidays. For the challenging prediction of the Spring Festival, distance is introduced as a variable using a third-degree polynomial form in the model. The residual sequence obtained in the previous step is modeled using Dilated Causal CNN, and the final prediction of daily electricity consumption is the sum of the two-stage predictions. Experimental results demonstrate that this method achieves higher accuracy compared to existing approaches.

Zhou Lan
Ben Liu
Yi Feng
Danhuang Dong
Peng Zhang


Pyramidal Hidden Markov Model For Multivariate Time Series Forecasting

Abstract: The Hidden Markov Model (HMM) can predict the future value of a time series based on its current and previous values, making it a powerful algorithm for handling various types of time series. Numerous studies have explored the improvement of HMM using advanced techniques, leading to the development of several variations of HMM. Despite these studies indicating the increased competitiveness of HMM compared to other advanced algorithms, few have recognized the significance and impact of incorporating multistep stochastic states into its performance. In this work, we propose a Pyramidal Hidden Markov Model (PHMM) that can capture multiple multistep stochastic states. Initially, a multistep HMM is designed for extracting short multistep stochastic states. Next, a novel time series forecasting structure is proposed based on PHMM, which utilizes pyramid-like stacking to adaptively identify long multistep stochastic states. By employing these two schemes, our model can effectively handle non-stationary and noisy data, while also establishing long-term dependencies for more accurate and comprehensive forecasting. The experimental results on diverse multivariate time series datasets convincingly demonstrate the superior performance of our proposed PHMM compared to its competitive peers in time series forecasting.


A decoder-only foundation model for time-series forecasting

Abstract: Motivated by recent advances in large language models for Natural Language Processing (NLP), we design a time-series foundation model for forecasting whose out-of-the-box zero-shot performance on a variety of public datasets comes close to the accuracy of state-of-the-art supervised forecasting models for each individual dataset. Our model is based on pretraining a patched-decoder style attention model on a large time-series corpus, and can work well across different forecasting history lengths, prediction lengths and temporal granularities.

Abhimanyu Das
Weihao Kong
Rajat Sen
Yichen Zhou

International Conference on Machine Learning


Lag-Llama: Towards Foundation Models for Probabilistic Time Series Forecasting

Abstract: Over the past years, foundation models have caused a paradigm shift in machine learning due to their unprecedented capabilities for zero-shot and few-shot generalization. However, despite the success of foundation models in modalities such as natural language processing and computer vision, the development of foundation models for time series forecasting has lagged behind. We present Lag-Llama, a general-purpose foundation model for univariate probabilistic time series forecasting based on a decoder-only transformer architecture that uses lags as covariates. Lag-Llama is pretrained on a large corpus of diverse time series data from several domains, and demonstrates strong zero-shot generalization capabilities compared to a wide range of forecasting models on downstream datasets across domains. Moreover, when fine-tuned on relatively small fractions of such previously unseen datasets, Lag-Llama achieves state-of-the-art performance, outperforming prior deep learning approaches, emerging as the best general-purpose model on average. Lag-Llama serves as a strong contender to the current state-of-art in time series forecasting and paves the way for future advancements in foundation models tailored to time series data.

Kashif Rasul
Arjun Ashok
Andrew Robert Williams
Hena Ghonia
Rishika Bhagwatkar
Arian Khorasani
Mohammad Javad Darvishi Bayazi
George Adamopoulos
Roland Riachi
Nadhir Hassen
Marin Biloš
Sahil Garg
Anderson Schneider
Nicolas Chapados
Alexandre Drouin
Valentina Zantedeschi
Yuriy Nevmyvaka
Irina Rish


Counterfactual Explanations for Time Series Forecasting

Abstract: Among recent developments in time series forecasting methods, deep forecasting models have gained popularity as they can utilize hidden feature patterns in time series to improve forecasting performance. Nevertheless, the majority of current deep forecasting models are opaque, hence making it challenging to interpret the results. While counterfactual explanations have been extensively employed as a post-hoc approach for explaining classification models, their application to forecasting models still remains underexplored. In this paper, we formulate the novel problem of counterfactual generation for time series forecasting, and propose an algorithm, called ForecastCF, that solves the problem by applying gradient-based perturbations to the original time series. ForecastCF guides the perturbations by applying constraints to the forecasted values to obtain desired prediction outcomes. We experimentally evaluate ForecastCF using four state-of-the-art deep model architectures and compare to two baselines. Our results show that ForecastCF outperforms the baseline in terms of counterfactual validity and data manifold closeness. Overall, our findings suggest that ForecastCF can generate meaningful and relevant counterfactual explanations for various forecasting tasks.

Zhendong Wang
Ioanna Miliou
Isak Samsten
Panagiotis Papapetrou


iTransformer: Inverted Transformers Are Effective for Time Series Forecasting

Abstract: The recent boom of linear forecasting models questions the ongoing passion for architectural modifications of Transformer-based forecasters. These forecasters leverage Transformers to model the global dependencies over temporal tokens of time series, with each token formed by multiple variates of the same timestamp. However, Transformers are challenged in forecasting series with larger lookback windows due to performance degradation and computation explosion. Besides, the embedding for each temporal token fuses multiple variates that represent potential delayed events and distinct physical measurements, which may fail in learning variate-centric representations and result in meaningless attention maps. In this work, we reflect on the competent duties of Transformer components and repurpose the Transformer architecture without any modification to the basic components. We propose iTransformer that simply applies the attention and feed-forward network on the inverted dimensions. Specifically, the time points of individual series are embedded into variate tokens which are utilized by the attention mechanism to capture multivariate correlations; meanwhile, the feed-forward network is applied for each variate token to learn nonlinear representations. The iTransformer model achieves state-of-the-art on challenging real-world datasets, which further empowers the Transformer family with promoted performance, generalization ability across different variates, and better utilization of arbitrary lookback windows, making it a nice alternative as the fundamental backbone of time series forecasting. Code is available at this repository: https://github.com/thuml/iTransformer.

Yong Liu
Tengge Hu
Haoran Zhang
Haixu Wu
Shiyu Wang
Lintao Ma
Mingsheng Long

International Conference on Learning Representations


Introducing the Attribution Stability Indicator: a Measure for Time Series XAI Attributions

Abstract: Given the increasing amount and general complexity of time series data in domains such as finance, weather forecasting, and healthcare, there is a growing need for state-of-the-art performance models that can provide interpretable insights into underlying patterns and relationships. Attribution techniques enable the extraction of explanations from time series models to gain insights but are hard to evaluate for their robustness and trustworthiness. We propose the Attribution Stability Indicator (ASI), a measure to incorporate robustness and trustworthiness as properties of attribution techniques for time series into account. We extend a perturbation analysis with correlations of the original time series to the perturbed instance and the attributions to include wanted properties in the measure. We demonstrate the wanted properties based on an analysis of the attributions in a dimension-reduced space and the ASI scores distribution over three whole time series classification datasets.


Toward a Foundation Model for Time Series Data

Abstract: A foundation model is a machine learning model trained on a large and diverse set of data, typically using self-supervised learning-based pre-training techniques, that can be adapted to various downstream tasks. However, current research on time series pre-training has mostly focused on models pre-trained solely on data from a single domain, resulting in a lack of knowledge about other types of time series. However, current research on time series pre-training has predominantly focused on models trained exclusively on data from a single domain. As a result, these models possess domain-specific knowledge that may not be easily transferable to time series from other domains. In this paper, we aim to develop an effective time series foundation model by leveraging unlabeled samples from multiple domains. To achieve this, we repurposed the publicly available UCR Archive and evaluated four existing self-supervised learning-based pre-training methods, along with a novel method, on the datasets. We tested these methods using four popular neural network architectures for time series to understand how the pre-training methods interact with different network designs. Our experimental results show that pre-training improves downstream classification tasks by enhancing the convergence of the fine-tuning process. Furthermore, we found that the proposed pre-training method, when combined with the Transformer model, outperforms the alternatives.

Chin-Chia Michael Yeh
Xin Dai
Huiyuan Chen
Yan Zheng
Yujie Fan
Audrey Der
Vivian Lai
Zhongfang Zhuang
Junpeng Wang
Liang Wang
Wei Zhang

International Conference on Information and Knowledge Management


Time-LLM: Time Series Forecasting by Reprogramming Large Language Models

Abstract: Time series forecasting holds significant importance in many real-world dynamic systems and has been extensively studied. Unlike natural language process (NLP) and computer vision (CV), where a single large model can tackle multiple tasks, models for time series forecasting are often specialized, necessitating distinct designs for different tasks and applications. While pre-trained foundation models have made impressive strides in NLP and CV, their development in time series domains has been constrained by data sparsity. Recent studies have revealed that large language models (LLMs) possess robust pattern recognition and reasoning abilities over complex sequences of tokens. However, the challenge remains in effectively aligning the modalities of time series data and natural language to leverage these capabilities. In this work, we present Time-LLM, a reprogramming framework to repurpose LLMs for general time series forecasting with the backbone language models kept intact. We begin by reprogramming the input time series with text prototypes before feeding it into the frozen LLM to align the two modalities. To augment the LLM's ability to reason with time series data, we propose Prompt-as-Prefix (PaP), which enriches the input context and directs the transformation of reprogrammed input patches. The transformed time series patches from the LLM are finally projected to obtain the forecasts. Our comprehensive evaluations demonstrate that Time-LLM is a powerful time series learner that outperforms state-of-the-art, specialized forecasting models. Moreover, Time-LLM excels in both few-shot and zero-shot learning scenarios.

Ming Jin
Shiyu Wang
Lintao Ma
Zhixuan Chu
James Y. Zhang
Xiaoming Shi
Pin-Yu Chen
Yuxuan Liang
Yuan-Fang Li
Shirui Pan
Qingsong Wen


Modality-aware Transformer for Financial Time series Forecasting

Abstract: Time series forecasting presents a significant challenge, particularly when its accuracy relies on external data sources rather than solely on historical values. This issue is prevalent in the financial sector, where the future behavior of time series is often intricately linked to information derived from various textual reports and a multitude of economic indicators. In practice, the key challenge lies in constructing a reliable time series forecasting model capable of harnessing data from diverse sources and extracting valuable insights to predict the target time series accurately. In this work, we tackle this challenging problem and introduce a novel multimodal transformer-based model named the \textit{Modality-aware Transformer}. Our model excels in exploring the power of both categorical text and numerical timeseries to forecast the target time series effectively while providing insights through its neural attention mechanism. To achieve this, we develop feature-level attention layers that encourage the model to focus on the most relevant features within each data modality. By incorporating the proposed feature-level attention, we develop a novel Intra-modal multi-head attention (MHA), Inter-modal MHA and Target-modal MHA in a way that both feature and temporal attentions are incorporated in MHAs. This enables the MHAs to generate temporal attentions with consideration of modality and feature importance which leads to more informative embeddings. The proposed modality-aware structure enables the model to effectively exploit information within each modality as well as foster cross-modal understanding. Our extensive experiments on financial datasets demonstrate that Modality-aware Transformer outperforms existing methods, offering a novel and practical solution to the complex challenges of multi-modal financial time series forecasting.

Hajar Emami
Xuan-Hong Dang
Yousaf Shah
Petros Zerfos

International Conference on AI in Finance


Jais and Jais-chat: Arabic-Centric Foundation and Instruction-Tuned Open Generative Large Language Models

Abstract: We introduce Jais and Jais-chat, new state-of-the-art Arabic-centric foundation and instruction-tuned open generative large language models (LLMs). The models are based on the GPT-3 decoder-only architecture and are pretrained on a mixture of Arabic and English texts, including source code in various programming languages. With 13 billion parameters, they demonstrate better knowledge and reasoning capabilities in Arabic than any existing open Arabic and multilingual models by a sizable margin, based on extensive evaluation. Moreover, the models are competitive in English compared to English-centric open models of similar size, despite being trained on much less English data. We provide a detailed description of the training, the tuning, the safety alignment, and the evaluation of the models. We release two open versions of the model -- the foundation Jais model, and an instruction-tuned Jais-chat variant -- with the aim of promoting research on Arabic LLMs. Available at https://huggingface.co/inception-mbzuai/jais-13b-chat

Neha Sengupta
Sunil Kumar Sahu
Bokang Jia
Satheesh Katipomu
Haonan Li
Fajri Koto
William Marshall
Gurpreet Gosal
Cynthia Liu
Zhiming Chen
Osama Mohammed Afzal
Samta Kamboj
Onkar Pandit
Rahul Pal
Lalit Pradhan
Zain Muhammad Mujahid
Massa Baali
Xudong Han
Sondos Mahmoud Bsharat
Alham Fikri Aji
Zhiqiang Shen
Zhengzhong Liu
Natalia Vassilieva
Joel Hestness
Andy Hock
Andrew Feldman
Jonathan Lee
Andrew Jackson
Hector Xuguang Ren
Preslav Nakov
Timothy Baldwin
Eric Xing


Hierarchical Time Series Forecasting with Bayesian Modeling

Abstract: We encounter time series data in many domains such as finance, physics, business, and weather. One of the main tasks of time series analysis, one that helps to take informed decisions under uncertainty, is forecasting. Time series are often hierarchically structured, e.g., a company sales might be broken down into different regions, and each region into different stores. In some cases the number of series in the hierarchy is too big to fit in a single model to produce forecasts in relevant time, and a decentralized approach is beneficial. One way to do this is to train independent forecasting models for each series and for some summary statistics series implied by the hierarchy (e.g. the sum of all series) and to pass those models to a reconciliation algorithm to improve those forecasts by sharing information between the series. In this work we focus on the reconciliation step, and propose a method to do so from a Bayesian perspective - Bayesian forecast reconciliation. We also define the common case of linear Gaussian reconciliation, where the forecasts are Gaussian and the hierarchy has linear structure, and show that we can compute reconciliation in closed form. We evaluate these methods on synthetic and real data sets, and compare them to other work in this field.


Multi-scale Transformer Pyramid Networks for Multivariate Time Series Forecasting

Abstract: Multivariate Time Series (MTS) forecasting involves modeling temporal dependencies within historical records. Transformers have demonstrated remarkable performance in MTS forecasting due to their capability to capture long-term dependencies. However, prior work has been confined to modeling temporal dependencies at either a fixed scale or multiple scales that exponentially increase (most with base 2). This limitation hinders their effectiveness in capturing diverse seasonalities, such as hourly and daily patterns. In this paper, we introduce a dimension invariant embedding technique that captures short-term temporal dependencies and projects MTS data into a higher-dimensional space, while preserving the dimensions of time steps and variables in MTS data. Furthermore, we present a novel Multi-scale Transformer Pyramid Network (MTPNet), specifically designed to effectively capture temporal dependencies at multiple unconstrained scales. The predictions are inferred from multi-scale latent representations obtained from transformers at various scales. Extensive experiments on nine benchmark datasets demonstrate that the proposed MTPNet outperforms recent state-of-the-art methods.

Yifan Zhang
Rui Wu
Sergiu M. Dascalu
Frederick C. Harris


PETformer: Long-term Time Series Forecasting via Placeholder-enhanced Transformer

Abstract: Recently, the superiority of Transformer for long-term time series forecasting (LTSF) tasks has been challenged, particularly since recent work has shown that simple models can outperform numerous Transformer-based approaches. This suggests that a notable gap remains in fully leveraging the potential of Transformer in LTSF tasks. Consequently, this study investigates key issues when applying Transformer to LTSF, encompassing aspects of temporal continuity, information density, and multi-channel relationships. We introduce the Placeholder-enhanced Technique (PET) to enhance the computational efficiency and predictive accuracy of Transformer in LTSF tasks. Furthermore, we delve into the impact of larger patch strategies and channel interaction strategies on Transformer's performance, specifically Long Sub-sequence Division (LSD) and Multi-channel Separation and Interaction (MSI). These strategies collectively constitute a novel model termed PETformer. Extensive experiments have demonstrated that PETformer achieves state-of-the-art performance on eight commonly used public datasets for LTSF, surpassing all existing models. The insights and enhancement methodologies presented in this paper serve as valuable reference points and sources of inspiration for future research endeavors.

Shengsheng Lin
Weiwei Lin
Wentai Wu
Songbo Wang
Yongxiang Wang

IEEE Transactions on Emerging Topics in Computational Intelligence


Conformal PID Control for Time Series Prediction

Abstract: We study the problem of uncertainty quantification for time series prediction, with the goal of providing easy-to-use algorithms with formal guarantees. The algorithms we present build upon ideas from conformal prediction and control theory, are able to prospectively model conformal scores in an online setting, and adapt to the presence of systematic errors due to seasonality, trends, and general distribution shifts. Our theory both simplifies and strengthens existing analyses in online conformal prediction. Experiments on 4-week-ahead forecasting of statewide COVID-19 death counts in the U.S. show an improvement in coverage over the ensemble forecaster used in official CDC communications. We also run experiments on predicting electricity demand, market returns, and temperature using autoregressive, Theta, Prophet, and Transformer models. We provide an extendable codebase for testing our methods and for the integration of new algorithms, data sets, and forecasting rules.

Anastasios N. Angelopoulos
Emmanuel J. Candes
Ryan J. Tibshirani

Computer Science
Engineering
Mathematics


Differential Evolution Algorithm based Hyper-Parameters Selection of Transformer Neural Network Model for Load Forecasting

Abstract: Accurate load forecasting plays a vital role in numerous sectors, but accurately capturing the complex dynamics of dynamic power systems remains a challenge for traditional statistical models. For these reasons, time-series models (ARIMA) and deep-learning models (ANN, LSTM, GRU, etc.) are commonly deployed and often experience higher success. In this paper, we analyze the efficacy of the recently developed Transformer-based Neural Network model in Load forecasting. Transformer models have the potential to improve Load forecasting because of their ability to learn long-range dependencies derived from their Attention Mechanism. We apply several metaheuristics namely Differential Evolution to find the optimal hyperparameters of the Transformer-based Neural Network to produce accurate forecasts. Differential Evolution provides scalable, robust, global solutions to non-differentiable, multi-objective, or constrained optimization problems. Our work compares the proposed Transformer based Neural Network model integrated with different metaheuristic algorithms by their performance in Load forecasting based on numerical metrics such as Mean Squared Error (MSE) and Mean Absolute Percentage Error (MAPE). Our findings demonstrate the potential of metaheuristic-enhanced Transformer-based Neural Network models in Load forecasting accuracy and provide optimal hyperparameters for each model.

Anuvab Sen
Arul Rhik Mazumder
Udayon Sen

IEEE Symposium Series on Computational Intelligence


Predict, Refine, Synthesize: Self-Guiding Diffusion Models for Probabilistic Time Series Forecasting

Abstract: Diffusion models have achieved state-of-the-art performance in generative modeling tasks across various domains. Prior works on time series diffusion models have primarily focused on developing conditional models tailored to specific forecasting or imputation tasks. In this work, we explore the potential of task-agnostic, unconditional diffusion models for several time series applications. We propose TSDiff, an unconditionally-trained diffusion model for time series. Our proposed self-guidance mechanism enables conditioning TSDiff for downstream tasks during inference, without requiring auxiliary networks or altering the training procedure. We demonstrate the effectiveness of our method on three different time series tasks: forecasting, refinement, and synthetic data generation. First, we show that TSDiff is competitive with several task-specific conditional forecasting methods (predict). Second, we leverage the learned implicit probability density of TSDiff to iteratively refine the predictions of base forecasters with reduced computational overhead over reverse diffusion (refine). Notably, the generative performance of the model remains intact -- downstream forecasters trained on synthetic samples from TSDiff outperform forecasters that are trained on samples from other state-of-the-art generative time series models, occasionally even outperforming models trained on real data (synthesize).

Marcel Kollovieh
Abdul Fatir Ansari
Michael Bohlke-Schneider
Jasper Zschiegner
Hao Wang
Yuyang Wang


GBT: Two-stage transformer framework for non-stationary time series forecasting

Abstract: This paper shows that time series forecasting Transformer (TSFT) suffers from severe over-fitting problem caused by improper initialization method of unknown decoder inputs, esp. when handling non-stationary time series. Based on this observation, we propose GBT, a novel two-stage Transformer framework with Good Beginning. It decouples the prediction process of TSFT into two stages, including Auto-Regression stage and Self-Regression stage to tackle the problem of different statistical properties between input and prediction sequences.Prediction results of Auto-Regression stage serve as a Good Beginning, i.e., a better initialization for inputs of Self-Regression stage. We also propose Error Score Modification module to further enhance the forecasting capability of the Self-Regression stage in GBT. Extensive experiments on seven benchmark datasets demonstrate that GBT outperforms SOTA TSFTs (FEDformer, Pyraformer, ETSformer, etc.) and many other forecasting models (SCINet, N-HiTS, etc.) with only canonical attention and convolution while owning less time and space complexity. It is also general enough to couple with these models to strengthen their forecasting capability. The source code is available at: https://github.com/OrigamiSL/GBT


Autoregressive with Slack Time Series Model for Forecasting a Partially-Observed Dynamical Time Series

Abstract: This study delves into the domain of dynamical systems, specifically the forecasting of dynamical time series defined through an evolution function. Traditional approaches in this area predict the future behavior of dynamical systems by inferring the evolution function. However, these methods may confront obstacles due to the presence of missing variables, which are usually attributed to challenges in measurement and a partial understanding of the system of interest. To overcome this obstacle, we introduce the autoregressive with slack time series (ARS) model, that simultaneously estimates the evolution function and imputes missing variables as a slack time series. Assuming time-invariance and linearity in the (underlying) entire dynamical time series, our experiments demonstrate the ARS model's capability to forecast future time series. From a theoretical perspective, we prove that a 2-dimensional time-invariant and linear system can be reconstructed by utilizing observations from a single, partially observed dimension of the system.

Akifumi Okuno
Yuya Morishita
Yoh-ichi Mototake


What Constitutes Good Contrastive Learning in Time-Series Forecasting?

Abstract: In recent years, the introduction of self-supervised contrastive learning (SSCL) has demonstrated remarkable improvements in representation learning across various domains, including natural language processing and computer vision. By leveraging the inherent benefits of self-supervision, SSCL enables the pre-training of representation models using vast amounts of unlabeled data. Despite these advances, there remains a significant gap in understanding the impact of different SSCL strategies on time series forecasting performance, as well as the specific benefits that SSCL can bring. This paper aims to address these gaps by conducting a comprehensive analysis of the effectiveness of various training variables, including different SSCL algorithms, learning strategies, model architectures, and their interplay. Additionally, to gain deeper insights into the improvements brought about by SSCL in the context of time-series forecasting, a qualitative analysis of the empirical receptive field is performed. Through our experiments, we demonstrate that the end-to-end training of a Transformer model using the Mean Squared Error (MSE) loss and SSCL emerges as the most effective approach in time series forecasting. Notably, the incorporation of the contrastive objective enables the model to prioritize more pertinent information for forecasting, such as scale and periodic relationships. These findings contribute to a better understanding of the benefits of SSCL in time series forecasting and provide valuable insights for future research in this area. Our codes are available at https://github.com/chiyuzhang94/contrastive_learning_time-series_e2e.

Chiyu Zhang
Qi Yan
Lili Meng
Tristan Sylvain


Transformer Training Strategies for Forecasting Multiple Load Time Series

Abstract: In the smart grid of the future, accurate load forecasts on the level of individual clients can help to balance supply and demand locally and to prevent grid outages. While the number of monitored clients will increase with the ongoing smart meter rollout, the amount of data per client will always be limited. We evaluate whether a Transformer load forecasting model benefits from a transfer learning strategy, where a global univariate model is trained on the load time series from multiple clients. In experiments with two datasets containing load time series from several hundred clients, we find that the global training strategy is superior to the multivariate and local training strategies used in related work. On average, the global training strategy results in 21.8% and 12.8% lower forecasting errors than the two other strategies, measured across forecasting horizons from one day to one month into the future. A comparison to linear models, multi-layer perceptrons and LSTMs shows that Transformers are effective for load forecasting when they are trained with the global training strategy.

Matthias Hertel
Maximilian Beichter
Benedikt Heidrich
Oliver Neumann
Benjamin Schäfer
Ralf Mikut
Veit Hagenmeyer


TSMixer: Lightweight MLP-Mixer Model for Multivariate Time Series Forecasting

Abstract: Transformers have gained popularity in time series forecasting for their ability to capture long-sequence interactions. However, their high memory and computing requirements pose a critical bottleneck for long-term forecasting. To address this, we propose TSMixer, a lightweight neural architecture exclusively composed of multi-layer perceptron (MLP) modules for multivariate forecasting and representation learning on patched time series. Inspired by MLP-Mixer's success in computer vision, we adapt it for time series, addressing challenges and introducing validated components for enhanced accuracy. This includes a novel design paradigm of attaching online reconciliation heads to the MLP-Mixer backbone, for explicitly modeling the time-series properties such as hierarchy and channel-correlations. We also propose a novel Hybrid channel modeling and infusion of a simple gating approach to effectively handle noisy channel interactions and generalization across diverse datasets. By incorporating these lightweight components, we significantly enhance the learning capability of simple MLP structures, outperforming complex Transformer models with minimal computing usage. Moreover, TSMixer's modular design enables compatibility with both supervised and masked self-supervised learning methods, making it a promising building block for time-series Foundation Models. TSMixer outperforms state-of-the-art MLP and Transformer models in forecasting by a considerable margin of 8-60%. It also outperforms the latest strong benchmarks of Patch-Transformer models (by 1-2%) with a significant reduction in memory and runtime (2-3X). The source code of our model is officially released as PatchTSMixer in the HuggingFace. Model: https://huggingface.co/docs/transformers/main/en/model_doc/patchtsmixer Examples: https://github.com/ibm/tsfm/#notebooks-links

Vijay Ekambaram
Arindam Jati
Nam Nguyen
Phanwadee Sinthong
Jayant Kalagnanam


Self-Interpretable Time Series Prediction with Counterfactual Explanations

Abstract: Interpretable time series prediction is crucial for safety-critical areas such as healthcare and autonomous driving. Most existing methods focus on interpreting predictions by assigning important scores to segments of time series. In this paper, we take a different and more challenging route and aim at developing a self-interpretable model, dubbed Counterfactual Time Series (CounTS), which generates counterfactual and actionable explanations for time series predictions. Specifically, we formalize the problem of time series counterfactual explanations, establish associated evaluation protocols, and propose a variational Bayesian deep learning model equipped with counterfactual inference capability of time series abduction, action, and prediction. Compared with state-of-the-art baselines, our self-interpretable model can generate better counterfactual explanations while maintaining comparable prediction accuracy.


Client: Cross-variable Linear Integrated Enhanced Transformer for Multivariate Long-Term Time Series Forecasting

Abstract: Long-term time series forecasting (LTSF) is a crucial aspect of modern society, playing a pivotal role in facilitating long-term planning and developing early warning systems. While many Transformer-based models have recently been introduced for LTSF, a doubt have been raised regarding the effectiveness of attention modules in capturing cross-time dependencies. In this study, we design a mask-series experiment to validate this assumption and subsequently propose the "Cross-variable Linear Integrated ENhanced Transformer for Multivariate Long-Term Time Series Forecasting" (Client), an advanced model that outperforms both traditional Transformer-based models and linear models. Client employs linear modules to learn trend information and attention modules to capture cross-variable dependencies. Meanwhile, it simplifies the embedding and position encoding layers and replaces the decoder module with a projection layer. Essentially, Client incorporates non-linearity and cross-variable dependencies, which sets it apart from conventional linear models and Transformer-based models. Extensive experiments with nine real-world datasets have confirmed the SOTA performance of Client with the least computation time and memory consumption compared with the previous Transformer-based models. Our code is available at https://github.com/daxin007/Client.


Adaptive Sparsity Level during Training for Efficient Time Series Forecasting with Transformers

Abstract: Efficient time series forecasting has become critical for real-world applications, particularly with deep neural networks (DNNs). Efficiency in DNNs can be achieved through sparse connectivity and reducing the model size. However, finding the sparsity level automatically during training remains challenging due to the heterogeneity in the loss-sparsity tradeoffs across the datasets. In this paper, we propose \enquote{\textbf{P}runing with \textbf{A}daptive \textbf{S}parsity \textbf{L}evel} (\textbf{PALS}), to automatically seek a decent balance between loss and sparsity, all without the need for a predefined sparsity level. PALS draws inspiration from sparse training and during-training methods. It introduces the novel "expand" mechanism in training sparse neural networks, allowing the model to dynamically shrink, expand, or remain stable to find a proper sparsity level. In this paper, we focus on achieving efficiency in transformers known for their excellent time series forecasting performance but high computational cost. Nevertheless, PALS can be applied directly to any DNN. To this aim, we demonstrate its effectiveness also on the DLinear model. Experimental results on six benchmark datasets and five state-of-the-art (SOTA) transformer variants show that PALS substantially reduces model size while maintaining comparable performance to the dense model. More interestingly, PALS even outperforms the dense model, in \textcolor{blue}{12} and \textcolor{blue}{14} cases out of 30 cases in terms of MSE and MAE loss, respectively, while reducing \textcolor{blue}{65\%} parameter count and \textcolor{blue}{63\%} FLOPs on average. Our code and supplementary material are available on Github\footnote{\tiny \url{https://github.com/zahraatashgahi/PALS}}.

Zahra Atashgahi
Mykola Pechenizkiy
Raymond Veldhuis
Decebal Constantin Mocanu


Stecformer: Spatio-temporal Encoding Cascaded Transformer for Multivariate Long-term Time Series Forecasting

Abstract: Multivariate long-term time series forecasting is of great application across many domains, such as energy consumption and weather forecasting. With the development of transformer-based methods, the performance of multivariate long-term time series forecasting has been significantly improved, however, the study of spatial features extracting in transformer-based model is rare and the consistency of different prediction periods is unsatisfactory due to the large span. In this work, we propose a complete solution to address these problems in terms of feature extraction and target prediction. For extraction, we design an efficient spatio-temporal encoding extractor including a semi-adaptive graph to acquire sufficient spatio-temporal information. For prediction, we propose a Cascaded Decoding Predictor (CDP) to strengthen the correlation between different intervals, which can also be utilized as a generic component to improve the performance of transformer-based methods. The proposed method, termed as Spatio-temporal Encoding Cascaded Transformer (Stecformer), achieving a notable gap over the baseline model and is comparable with the state-of-the-art performance of transformer-based methods on five benchmark datasets. We hope our attempt will serve as a regular configuration in multivariate long-term time series forecasting in the future.


CARD: Channel Aligned Robust Blend Transformer for Time Series Forecasting

Abstract: Recent studies have demonstrated the great power of Transformer models for time series forecasting. One of the key elements that lead to the transformer's success is the channel-independent (CI) strategy to improve the training robustness. However, the ignorance of the correlation among different channels in CI would limit the model's forecasting capacity. In this work, we design a special Transformer, i.e., Channel Aligned Robust Blend Transformer (CARD for short), that addresses key shortcomings of CI type Transformer in time series forecasting. First, CARD introduces a channel-aligned attention structure that allows it to capture both temporal correlations among signals and dynamical dependence among multiple variables over time. Second, in order to efficiently utilize the multi-scale knowledge, we design a token blend module to generate tokens with different resolutions. Third, we introduce a robust loss function for time series forecasting to alleviate the potential overfitting issue. This new loss function weights the importance of forecasting over a finite horizon based on prediction uncertainties. Our evaluation of multiple long-term and short-term forecasting datasets demonstrates that CARD significantly outperforms state-of-the-art time series forecasting methods. The code is available at the following repository:https://github.com/wxie9/CARD

Wang Xue
Tian Zhou
Qingsong Wen
Jinyang Gao
Bolin Ding
Rong Jin


Revisiting Long-term Time Series Forecasting: An Investigation on Linear Mapping

Abstract: Introduction: Long-term time series forecasting (LTSF) has gained significant attention in recent years. While various specialized designs exist for capturing temporal dependency, recent studies have shown that even a single linear layer can achieve competitive performance. This paper investigates the intrinsic effectiveness of recent LTSF approaches and reveals the critical role of affine mapping. Materials and methods: We conduct comprehensive experiments on both simulated and real-world datasets to analyze the components of state-of-the-art models. A theoretical analysis is provided to explain the working mechanisms of affine mapping in periodic signal forecasting. We evaluate the impact of reversible normalization and input horizon extension on model robustness. Results: We find that (1) affine mapping dominates forecasting performance across commonly utilized benchmarks, with models learning similar transition matrices from input to output; (2) affine mapping effectively captures periodic patterns but struggles with non-periodic signals or time series with varying periods across channels; (3) reversible normalization significantly enhances trend forecasting by transforming non-periodic trends into periodic-like patterns; (4) increasing input horizon improves performance on multi-channel data with different periods. Code is available at: \url{https://github.com/plumprc/RTSF}. Conclusions: Our findings provide theoretical and experimental insights into the working mechanisms of LTSF models, highlighting both the strengths and limitations of linear approaches. The results suggest that future model development should focus on handling cross-channel period variations and non-periodic components.

Li, Zhe, Shiyi Qi, Yiduo Li, and Zenglin Xu. Revisiting Long-Term Time Series Forecasting: an Investigation on Affine Mapping. Academia AI and Applications 2, no. 2 (2026)


pTSE: A Multi-model Ensemble Method for Probabilistic Time Series Forecasting

Abstract: Various probabilistic time series forecasting models have sprung up and shown remarkably good performance. However, the choice of model highly relies on the characteristics of the input time series and the fixed distribution that the model is based on. Due to the fact that the probability distributions cannot be averaged over different models straightforwardly, the current time series model ensemble methods cannot be directly applied to improve the robustness and accuracy of forecasting. To address this issue, we propose pTSE, a multi-model distribution ensemble method for probabilistic forecasting based on Hidden Markov Model (HMM). pTSE only takes off-the-shelf outputs from member models without requiring further information about each model. Besides, we provide a complete theoretical analysis of pTSE to prove that the empirical distribution of time series subject to an HMM will converge to the stationary distribution almost surely. Experiments on benchmarks show the superiority of pTSE overall member models and competitive ensemble methods.

Yunyi Zhou
Zhixuan Chu
Yijia Ruan
Ge Jin
Yuchen Huang
Sheng Li

International Joint Conference on Artificial Intelligence


Differential Convolutional Fuzzy Time Series Forecasting

Abstract: Fuzzy time series forecasting (FTSF) is a typical forecasting method with wide application. Traditional FTSF is regarded as an expert system which leads to loss of the ability to recognize undefined features. The mentioned is the main reason for poor forecasting with FTSF. To solve the problem, the proposed model Differential Fuzzy Convolutional Neural Network (DFCNN) utilizes a convolution neural network to re-implement FTSF with learnable ability. DFCNN is capable of recognizing potential information and improving forecasting accuracy. Thanks to the learnable ability of the neural network, the length of fuzzy rules established in FTSF is expended to an arbitrary length that the expert is not able to handle by the expert system. At the same time, FTSF usually cannot achieve satisfactory performance of non-stationary time series due to the trend of non-stationary time series. The trend of non-stationary time series causes the fuzzy set established by FTSF to be invalid and causes the forecasting to fail. DFCNN utilizes the Difference algorithm to weaken the non-stationary of time series so that DFCNN can forecast the non-stationary time series with a low error that FTSF cannot forecast in satisfactory performance. After the mass of experiments, DFCNN has an excellent prediction effect, which is ahead of the existing FTSF and common time series forecasting algorithms. Finally, DFCNN provides further ideas for improving FTSF and holds continued research value.

Tianxiang Zhan
Yuanpeng He
Yong Deng
Zhen Li


Financial Time Series Forecasting using CNN and Transformer

Abstract: Time series forecasting is important across various domains for decision-making. In particular, financial time series such as stock prices can be hard to predict as it is difficult to model short-term and long-term temporal dependencies between data points. Convolutional Neural Networks (CNN) are good at capturing local patterns for modeling short-term dependencies. However, CNNs cannot learn long-term dependencies due to the limited receptive field. Transformers on the other hand are capable of learning global context and long-term dependencies. In this paper, we propose to harness the power of CNNs and Transformers to model both short-term and long-term dependencies within a time series, and forecast if the price would go up, down or remain the same (flat) in the future. In our experiments, we demonstrated the success of the proposed method in comparison to commonly adopted statistical and deep learning methods on forecasting intraday stock price change of S&P 500 constituents.

Zhen Zeng
Rachneet Kaur
Suchetha Siddagangappa
Saba Rahimi
Tucker Balch
Manuela Veloso


Clustering Multivariate Time Series using Energy Distance

Abstract: A novel methodology is proposed for clustering multivariate time series data using energy distance defined in Székely and Rizzo (2013). Specifically, a dissimilarity matrix is formed using the energy distance statistic to measure separation between the finite dimensional distributions for the component time series. Once the pairwise dissimilarity matrix is calculated, a hierarchical clustering method is then applied to obtain the dendrogram. This procedure is completely nonparametric as the dissimilarities between stationary distributions are directly calculated without making any model assumptions. In order to justify this procedure, asymptotic properties of the energy distance estimates are derived for general stationary and ergodic time series. The method is illustrated in a simulation study for various component time series that are either linear or nonlinear. Finally the methodology is applied to two examples; one involves GDP of selected countries and the other is population size of various states in the U.S.A. in the years 1900 -1999.

Richard A. Davis
Leon Fernandes
Konstantinos Fokianos


TsSHAP: Robust model agnostic feature-based explainability for time series forecasting

Abstract: A trustworthy machine learning model should be accurate as well as explainable. Understanding why a model makes a certain decision defines the notion of explainability. While various flavors of explainability have been well-studied in supervised learning paradigms like classification and regression, literature on explainability for time series forecasting is relatively scarce. In this paper, we propose a feature-based explainability algorithm, TsSHAP, that can explain the forecast of any black-box forecasting model. The method is agnostic of the forecasting model and can provide explanations for a forecast in terms of interpretable features defined by the user a prior. The explanations are in terms of the SHAP values obtained by applying the TreeSHAP algorithm on a surrogate model that learns a mapping between the interpretable feature space and the forecast of the black-box model. Moreover, we formalize the notion of local, semi-local, and global explanations in the context of time series forecasting, which can be useful in several scenarios. We validate the efficacy and robustness of TsSHAP through extensive experiments on multiple datasets.

Vikas C. Raykar
Arindam Jati
Sumanta Mukherjee
Nupur Aggarwal
Kanthi Sarpatwar
Giridhar Ganapavarapu
Roman Vaculin


Hybrid Variational Autoencoder for Time Series Forecasting

Abstract: Variational autoencoders (VAE) are powerful generative models that learn the latent representations of input data as random variables. Recent studies show that VAE can flexibly learn the complex temporal dynamics of time series and achieve more promising forecasting results than deterministic models. However, a major limitation of existing works is that they fail to jointly learn the local patterns (e.g., seasonality and trend) and temporal dynamics of time series for forecasting. Accordingly, we propose a novel hybrid variational autoencoder (HyVAE) to integrate the learning of local patterns and temporal dynamics by variational inference for time series forecasting. Experimental results on four real-world datasets show that the proposed HyVAE achieves better forecasting results than various counterpart methods, as well as two HyVAE variants that only learn the local patterns or temporal dynamics of time series, respectively.

Borui Cai
Shuiqiao Yang
Longxiang Gao
Yong Xiang


Interpretable Water Level Forecaster with Spatiotemporal Causal Attention Mechanisms

Abstract: Accurate forecasting of river water levels is vital for effectively managing traffic flow and mitigating the risks associated with natural disasters. This task presents challenges due to the intricate factors influencing the flow of a river. Recent advances in machine learning have introduced numerous effective forecasting methods. However, these methods lack interpretability due to their complex structure, resulting in limited reliability. Addressing this issue, this study proposes a deep learning model that quantifies interpretability, with an emphasis on water level forecasting. This model focuses on generating quantitative interpretability measurements, which align with the common knowledge embedded in the input data. This is facilitated by the utilization of a transformer architecture that is purposefully designed with masking, incorporating a multi-layer network that captures spatiotemporal causation. We perform a comparative analysis on the Han River dataset obtained from Seoul, South Korea, from 2016 to 2021. The results illustrate that our approach offers enhanced interpretability consistent with common knowledge, outperforming competing methods and also enhances robustness against distribution shift.

Sungchul Hong
Yunjin Choi
Jong-June Jeon


A comparative assessment of deep learning models for day-ahead load forecasting: Investigating key accuracy drivers

Abstract: Short-term load forecasting (STLF) is vital for the effective and economic operation of power grids and energy markets. However, the non-linearity and non-stationarity of electricity demand as well as its dependency on various external factors renders STLF a challenging task. To that end, several deep learning models have been proposed in the literature for STLF, reporting promising results. In order to evaluate the accuracy of said models in day-ahead forecasting settings, in this paper we focus on the national net aggregated STLF of Portugal and conduct a comparative study considering a set of indicative, well-established deep autoregressive models, namely multi-layer perceptrons (MLP), long short-term memory networks (LSTM), neural basis expansion coefficient analysis (N-BEATS), temporal convolutional networks (TCN), and temporal fusion transformers (TFT). Moreover, we identify factors that significantly affect the demand and investigate their impact on the accuracy of each model. Our results suggest that N-BEATS consistently outperforms the rest of the examined models. MLP follows, providing further evidence towards the use of feed-forward networks over relatively more sophisticated architectures. Finally, certain calendar and weather features like the hour of the day and the temperature are identified as key accuracy drivers, providing insights regarding the forecasting approach that should be used per case.

Sotiris Pelekis
Ioannis-Konstantinos Seisopoulos
Evangelos Spiliotis
Theodosios Pountridis
Evangelos Karakolis
Spiros Mouzakitis
Dimitris Askounis


Creating Probabilistic Forecasts from Arbitrary Deterministic Forecasts using Conditional Invertible Neural Networks

Abstract: In various applications, probabilistic forecasts are required to quantify the inherent uncertainty associated with the forecast. However, numerous modern forecasting methods are still designed to create deterministic forecasts. Transforming these deterministic forecasts into probabilistic forecasts is often challenging and based on numerous assumptions that may not hold in real-world situations. Therefore, the present article proposes a novel approach for creating probabilistic forecasts from arbitrary deterministic forecasts. In order to implement this approach, we use a conditional Invertible Neural Network (cINN). More specifically, we apply a cINN to learn the underlying distribution of the data and then combine the uncertainty from this distribution with an arbitrary deterministic forecast to generate accurate probabilistic forecasts. Our approach enables the simple creation of probabilistic forecasts without complicated statistical loss functions or further assumptions. Besides showing the mathematical validity of our approach, we empirically show that our approach noticeably outperforms traditional methods for including uncertainty in deterministic forecasts and generally outperforms state-of-the-art probabilistic forecasting benchmarks.

Kaleb Phipps
Benedikt Heidrich
Marian Turowski
Moritz Wittig
Ralf Mikut
Veit Hagenmeyer


Towards Better Long-range Time Series Forecasting using Generative Forecasting

Abstract: Long-range time series forecasting is usually based on one of two existing forecasting strategies: Direct Forecasting and Iterative Forecasting, where the former provides low bias, high variance forecasts and the latter leads to low variance, high bias forecasts. In this paper, we propose a new forecasting strategy called Generative Forecasting (GenF), which generates synthetic data for the next few time steps and then makes long-range forecasts based on generated and observed data. We theoretically prove that GenF is able to better balance the forecasting variance and bias, leading to a much smaller forecasting error. We implement GenF via three components: (i) a novel conditional Wasserstein Generative Adversarial Network (GAN) based generator for synthetic time series data generation, called CWGAN-TS. (ii) a transformer based predictor, which makes long-range predictions using both generated and observed data. (iii) an information theoretic clustering algorithm to improve the training of both the CWGAN-TS and the transformer based predictor. The experimental results on five public datasets demonstrate that GenF significantly outperforms a diverse range of state-of-the-art benchmarks and classical approaches. Specifically, we find a 5% - 11% improvement in predictive performance (mean absolute error) while having a 15% - 50% reduction in parameters compared to the benchmarks. Lastly, we conduct an ablation study to further explore and demonstrate the effectiveness of the components comprising GenF.


A K-variate Time Series Is Worth K Words: Evolution of the Vanilla Transformer Architecture for Long-term Multivariate Time Series Forecasting

Abstract: Multivariate time series forecasting (MTSF) is a fundamental problem in numerous real-world applications. Recently, Transformer has become the de facto solution for MTSF, especially for the long-term cases. However, except for the one forward operation, the basic configurations in existing MTSF Transformer architectures were barely carefully verified. In this study, we point out that the current tokenization strategy in MTSF Transformer architectures ignores the token uniformity inductive bias of Transformers. Therefore, the vanilla MTSF transformer struggles to capture details in time series and presents inferior performance. Based on this observation, we make a series of evolution on the basic architecture of the vanilla MTSF transformer. We vary the flawed tokenization strategy, along with the decoder structure and embeddings. Surprisingly, the evolved simple transformer architecture is highly effective, which successfully avoids the over-smoothing phenomena in the vanilla MTSF transformer, achieves a more detailed and accurate prediction, and even substantially outperforms the state-of-the-art Transformers that are well-designed for MTSF.

Zanwei Zhou
Ruizhe Zhong
Chen Yang
Yan Wang
Xiaokang Yang
Wei Shen


Hierarchical Proxy Modeling for Improved HPO in Time Series Forecasting

Abstract: Selecting the right set of hyperparameters is crucial in time series forecasting. The classical temporal cross-validation framework for hyperparameter optimization (HPO) often leads to poor test performance because of a possible mismatch between validation and test periods. To address this test-validation mismatch, we propose a novel technique, H-Pro to drive HPO via test proxies by exploiting data hierarchies often associated with time series datasets. Since higher-level aggregated time series often show less irregularity and better predictability as compared to the lowest-level time series which can be sparse and intermittent, we optimize the hyperparameters of the lowest-level base-forecaster by leveraging the proxy forecasts for the test period generated from the forecasters at higher levels. H-Pro can be applied on any off-the-shelf machine learning model to perform HPO. We validate the efficacy of our technique with extensive empirical evaluation on five publicly available hierarchical forecasting datasets. Our approach outperforms existing state-of-the-art methods in Tourism, Wiki, and Traffic datasets, and achieves competitive result in Tourism-L dataset, without any model-specific enhancements. Moreover, our method outperforms the winning method of the M5 forecast accuracy competition.

Arindam Jati
Vijay Ekambaram
Shaonli Pal
Brian Quanz
Wesley M. Gifford
Pavithra Harsha
Stuart Siegel
Sumanta Mukherjee
Chandra Narayanaswami


A Time Series is Worth 64 Words: Long-term Forecasting with Transformers

Abstract: We propose an efficient design of Transformer-based models for multivariate time series forecasting and self-supervised representation learning. It is based on two key components: (i) segmentation of time series into subseries-level patches which are served as input tokens to Transformer; (ii) channel-independence where each channel contains a single univariate time series that shares the same embedding and Transformer weights across all the series. Patching design naturally has three-fold benefit: local semantic information is retained in the embedding; computation and memory usage of the attention maps are quadratically reduced given the same look-back window; and the model can attend longer history. Our channel-independent patch time series Transformer (PatchTST) can improve the long-term forecasting accuracy significantly when compared with that of SOTA Transformer-based models. We also apply our model to self-supervised pre-training tasks and attain excellent fine-tuning performance, which outperforms supervised training on large datasets. Transferring of masked pre-trained representation on one dataset to others also produces SOTA forecasting accuracy. Code is available at: https://github.com/yuqinie98/PatchTST.

Yuqi Nie
Nam H. Nguyen
Phanwadee Sinthong
Jayant Kalagnanam


Probabilistic Decomposition Transformer for Time Series Forecasting

Abstract: Time series forecasting is crucial for many fields, such as disaster warning, weather prediction, and energy consumption. The Transformer-based models are considered to have revolutionized the field of sequence modeling. However, the complex temporal patterns of the time series hinder the model from mining reliable temporal dependencies. Furthermore, the autoregressive form of the Transformer introduces cumulative errors in the inference step. In this paper, we propose the probabilistic decomposition Transformer model that combines the Transformer with a conditional generative model, which provides hierarchical and interpretable probabilistic forecasts for intricate time series. The Transformer is employed to learn temporal patterns and implement primary probabilistic forecasts, while the conditional generative model is used to achieve non-autoregressive hierarchical probabilistic forecasts by introducing latent space feature representations. In addition, the conditional generative model reconstructs typical features of the series, such as seasonality and trend terms, from probability distributions in the latent space to enable complex pattern separation and provide interpretable forecasts. Extensive experiments on several datasets demonstrate the effectiveness and robustness of the proposed model, indicating that it compares favorably with the state of the art.

Junlong Tong
Liping Xie
Wankou Yang
Kanjian Zhang


Retrieval Based Time Series Forecasting

Abstract: Time series data appears in a variety of applications such as smart transportation and environmental monitoring. One of the fundamental problems for time series analysis is time series forecasting. Despite the success of recent deep time series forecasting methods, they require sufficient observation of historical values to make accurate forecasting. In other words, the ratio of the output length (or forecasting horizon) to the sum of the input and output lengths should be low enough (e.g., 0.3). As the ratio increases (e.g., to 0.8), the uncertainty for the forecasting accuracy increases significantly. In this paper, we show both theoretically and empirically that the uncertainty could be effectively reduced by retrieving relevant time series as references. In the theoretical analysis, we first quantify the uncertainty and show its connections to the Mean Squared Error (MSE). Then we prove that models with references are easier to learn than models without references since the retrieved references could reduce the uncertainty. To empirically demonstrate the effectiveness of the retrieval based time series forecasting models, we introduce a simple yet effective two-stage method, called ReTime consisting of a relational retrieval and a content synthesis. We also show that ReTime can be easily adapted to the spatial-temporal time series and time series imputation settings. Finally, we evaluate ReTime on real-world datasets to demonstrate its effectiveness.

Baoyu Jing
Si Zhang
Yada Zhu
Bin Peng
Kaiyu Guan
Andrew Margenot
Hanghang Tong


PromptCast: A New Prompt-based Learning Paradigm for Time Series Forecasting

Abstract: This paper presents a new perspective on time series forecasting. In existing time series forecasting methods, the models take a sequence of numerical values as input and yield numerical values as output. The existing SOTA models are largely based on the Transformer architecture, modified with multiple encoding mechanisms to incorporate the context and semantics around the historical data. Inspired by the successes of pre-trained language foundation models, we pose a question about whether these models can also be adapted to solve time-series forecasting. Thus, we propose a new forecasting paradigm: prompt-based time series forecasting (PromptCast). In this novel task, the numerical input and output are transformed into prompts and the forecasting task is framed in a sentence-to-sentence manner, making it possible to directly apply language models for forecasting purposes. To support and facilitate the research of this task, we also present a large-scale dataset (PISA) that includes three real-world forecasting scenarios. We evaluate different SOTA numerical-based forecasting methods and language generation models. The benchmark results with various forecasting settings demonstrate the proposed PromptCast with language generation models is a promising research direction. Additionally, in comparison to conventional numerical-based forecasting, PromptCast shows a much better generalization ability under the zero-shot setting.

IEEE Transactions on Knowledge and Data Engineering


W-Transformers : A Wavelet-based Transformer Framework for Univariate Time Series Forecasting

Abstract: Deep learning utilizing transformers has recently achieved a lot of success in many vital areas such as natural language processing, computer vision, anomaly detection, and recommendation systems, among many others. Among several merits of transformers, the ability to capture long-range temporal dependencies and interactions is desirable for time series forecasting, leading to its progress in various time series applications. In this paper, we build a transformer model for non-stationary time series. The problem is challenging yet crucially important. We present a novel framework for univariate time series representation learning based on the wavelet-based transformer encoder architecture and call it W-Transformer. The proposed W-Transformers utilize a maximal overlap discrete wavelet transformation (MODWT) to the time series data and build local transformers on the decomposed datasets to vividly capture the nonstationarity and long-range nonlinear dependencies in the time series. Evaluating our framework on several publicly available benchmark time series datasets from various domains and with diverse characteristics, we demonstrate that it performs, on average, significantly better than the baseline forecasters for short-term and long-term forecasting, even for datasets that consist of only a few hundred training samples.

Lena Sasal
Tanujit Chakraborty
Abdenour Hadid

Computer Science
Physics
Mathematics
Economics
Engineering

International Conference on Machine Learning and Applications


Persistence Initialization: A novel adaptation of the Transformer architecture for Time Series Forecasting

Abstract: Time series forecasting is an important problem, with many real world applications. Ensembles of deep neural networks have recently achieved impressive forecasting accuracy, but such large ensembles are impractical in many real world settings. Transformer models been successfully applied to a diverse set of challenging problems. We propose a novel adaptation of the original Transformer architecture focusing on the task of time series forecasting, called Persistence Initialization. The model is initialized as a naive persistence model by using a multiplicative gating mechanism combined with a residual skip connection. We use a decoder Transformer with ReZero normalization and Rotary positional encodings, but the adaptation is applicable to any auto-regressive neural network model. We evaluate our proposed architecture on the challenging M4 dataset, achieving competitive performance compared to ensemble based methods. We also compare against existing recently proposed Transformer models for time series forecasting, showing superior performance on the M4 dataset. Extensive ablation studies show that Persistence Initialization leads to better performance and faster convergence. As the size of the model increases, only the models with our proposed adaptation gain in performance. We also perform an additional ablation study to determine the importance of the choice of normalization and positional encoding, and find both the use of Rotary encodings and ReZero normalization to be essential for good forecasting performance.

Espen Haugsdal
Erlend Aune
Massimiliano Ruocco


Identifying and Overcoming Transformation Bias in Forecasting Models

Abstract: Log and square root transformations of target variable are routinely used in forecasting models to predict future sales. These transformations often lead to better performing models. However, they also introduce a systematic negative bias (under-forecasting). In this paper, we demonstrate the existence of this bias, dive deep into its root cause and introduce two methods to correct for the bias. We conclude that the proposed bias correction methods improve model performance (by up to 50%) and make a case for incorporating bias correction in modeling workflow. We also experiment with `Tweedie' family of cost functions which circumvents the transformation bias issue by modeling directly on sales. We conclude that Tweedie regression gives the best performance so far when modeling on sales making it a strong alternative to working with a transformed target variable.


Expressing Multivariate Time Series as Graphs with Time Series Attention Transformer

Abstract: A reliable and efficient representation of multivariate time series is crucial in various downstream machine learning tasks. In multivariate time series forecasting, each variable depends on its historical values and there are inter-dependencies among variables as well. Models have to be designed to capture both intra- and inter-relationships among the time series. To move towards this goal, we propose the Time Series Attention Transformer (TSAT) for multivariate time series representation learning. Using TSAT, we represent both temporal information and inter-dependencies of multivariate time series in terms of edge-enhanced dynamic graphs. The intra-series correlations are represented by nodes in a dynamic graph; a self-attention mechanism is modified to capture the inter-series correlations by using the super-empirical mode decomposition (SMD) module. We applied the embedded dynamic graphs to times series forecasting problems, including two real-world datasets and two benchmark datasets. Extensive experiments show that TSAT clearly outerperforms six state-of-the-art baseline methods in various forecasting horizons. We further visualize the embedded dynamic graphs to illustrate the graph representation power of TSAT. We share our code at https://github.com/RadiantResearch/TSAT.

William T. Ng
K. Siu
Albert C. Cheung
Michael K. Ng


SDWPF: A Dataset for Spatial Dynamic Wind Power Forecasting Challenge at KDD Cup 2022

Abstract: The variability of wind power supply can present substantial challenges to incorporating wind power into a grid system. Thus, Wind Power Forecasting (WPF) has been widely recognized as one of the most critical issues in wind power integration and operation. There has been an explosion of studies on wind power forecasting problems in the past decades. Nevertheless, how to well handle the WPF problem is still challenging, since high prediction accuracy is always demanded to ensure grid stability and security of supply. We present a unique Spatial Dynamic Wind Power Forecasting dataset: SDWPF, which includes the spatial distribution of wind turbines, as well as the dynamic context factors. Whereas, most of the existing datasets have only a small number of wind turbines without knowing the locations and context information of wind turbines at a fine-grained time scale. By contrast, SDWPF provides the wind power data of 134 wind turbines from a wind farm over half a year with their relative positions and internal statuses. We use this dataset to launch the Baidu KDD Cup 2022 to examine the limit of current WPF solutions. The dataset is released at https://aistudio.baidu.com/aistudio/competition/detail/152/0/datasets.

Jingbo Zhou
Xinjiang Lu
Yixiong Xiao
Jiantao Su
Junfu Lyu
Yanjun Ma
Dejing Dou


LETS-GZSL: A Latent Embedding Model for Time Series Generalized Zero Shot Learning

Abstract: One of the recent developments in deep learning is generalized zero-shot learning (GZSL), which aims to recognize objects from both seen and unseen classes, when only the labeled examples from seen classes are provided. Over the past couple of years, GZSL has picked up traction and several models have been proposed to solve this problem. Whereas an extensive amount of research on GZSL has been carried out in fields such as computer vision and natural language processing, no such research has been carried out to deal with time series data. GZSL is used for applications such as detecting abnormalities from ECG and EEG data and identifying unseen classes from sensor, spectrograph and other devices' data. In this regard, we propose a Latent Embedding for Time Series - GZSL (LETS-GZSL) model that can solve the problem of GZSL for time series classification (TSC). We utilize an embedding-based approach and combine it with attribute vectors to predict the final class labels. We report our results on the widely popular UCR archive datasets. Our framework is able to achieve a harmonic mean value of at least 55% on most of the datasets except when the number of unseen classes is greater than 3 or the amount of data is very low (less than 100 training examples).

Sathvik Bhaskarpandit
Priyanka Gupta
Manik Gupta


Respecting Time Series Properties Makes Deep Time Series Forecasting Perfect

Abstract: How to handle time features shall be the core question of any time series forecasting model. Ironically, it is often ignored or misunderstood by deep-learning based models, even those baselines which are state-of-the-art. This behavior makes their inefficient, untenable and unstable. In this paper, we rigorously analyze three prevalent but deficient/unfounded deep time series forecasting mechanisms or methods from the view of time series properties, including normalization methods, multivariate forecasting and input sequence length. Corresponding corollaries and solutions are given on both empirical and theoretical basis. We thereby propose a novel time series forecasting network, i.e. RTNet, on the basis of aforementioned analysis. It is general enough to be combined with both supervised and self-supervised forecasting format. Thanks to the core idea of respecting time series properties, no matter in which forecasting format, RTNet shows obviously superior forecasting performances compared with dozens of other SOTA time series forecasting baselines in three real-world benchmark datasets. By and large, it even occupies less time complexity and memory usage while acquiring better forecasting accuracy. The source code is available at https://github.com/OrigamiSL/RTNet.


MQRetNN: Multi-Horizon Time Series Forecasting with Retrieval Augmentation

Abstract: Multi-horizon probabilistic time series forecasting has wide applicability to real-world tasks such as demand forecasting. Recent work in neural time-series forecasting mainly focus on the use of Seq2Seq architectures. For example, MQTransformer - an improvement of MQCNN - has shown the state-of-the-art performance in probabilistic demand forecasting. In this paper, we consider incorporating cross-entity information to enhance model performance by adding a cross-entity attention mechanism along with a retrieval mechanism to select which entities to attend over. We demonstrate how our new neural architecture, MQRetNN, leverages the encoded contexts from a pretrained baseline model on the entire population to improve forecasting accuracy. Using MQCNN as the baseline model (due to computational constraints, we do not use MQTransformer), we first show on a small demand forecasting dataset that it is possible to achieve ~3% improvement in test loss by adding a cross-entity attention mechanism where each entity attends to all others in the population. We then evaluate the model with our proposed retrieval methods - as a means of approximating an attention over a large population - on a large-scale demand forecasting application with over 2 million products and observe ~1% performance gain over the MQCNN baseline.


Learning Deep Time-index Models for Time Series Forecasting

Abstract: Deep learning has been actively applied to time series forecasting, leading to a deluge of new methods, belonging to the class of historical-value models. Yet, despite the attractive properties of time-index models, such as being able to model the continuous nature of underlying time series dynamics, little attention has been given to them. Indeed, while naive deep time-index models are far more expressive than the manually predefined function representations of classical time-index models, they are inadequate for forecasting, being unable to generalize to unseen time steps due to the lack of inductive bias. In this paper, we propose DeepTime, a meta-optimization framework to learn deep time-index models which overcome these limitations, yielding an efficient and accurate forecasting model. Extensive experiments on real world datasets in the long sequence time-series forecasting setting demonstrate that our approach achieves competitive results with state-of-the-art methods, and is highly efficient. Code is available at https://github.com/salesforce/DeepTime.

Gerald Woo
Chenghao Liu
Doyen Sahoo
Akshat Kumar
Steven Hoi


Dateformer: Time-modeling Transformer for Longer-term Series Forecasting

Abstract: Transformers have demonstrated impressive strength in long-term series forecasting. Existing prediction research mostly focused on mapping past short sub-series (lookback window) to future series (forecast window). The longer training dataset time series will be discarded, once training is completed. Models can merely rely on lookback window information for inference, which impedes models from analyzing time series from a global perspective. And these windows used by Transformers are quite narrow because they must model each time-step therein. Under this point-wise processing style, broadening windows will rapidly exhaust their model capacity. This, for fine-grained time series, leads to a bottleneck in information input and prediction output, which is mortal to long-term series forecasting. To overcome the barrier, we propose a brand-new methodology to utilize Transformer for time series forecasting. Specifically, we split time series into patches by day and reform point-wise to patch-wise processing, which considerably enhances the information input and output of Transformers. To further help models leverage the whole training set's global information during inference, we distill the information, store it in time representations, and replace series with time representations as the main modeling entities. Our designed time-modeling Transformer -- Dateformer yields state-of-the-art accuracy on 7 real-world datasets with a 33.6\% relative improvement and extends the maximum forecast range to half-year.

Julong Young
Junhui Chen
Feihu Huang
Jian Peng


LASSO Principal Component Averaging -- a fully automated approach for point forecast pooling

Abstract: This paper develops a novel, fully automated forecast averaging scheme, which combines LASSO estimation method with Principal Component Averaging (PCA). LASSO-PCA (LPCA) explores a pool of predictions based on a single model but calibrated to windows of different sizes. It uses information criteria to select tuning parameters and hence reduces the impact of researchers' at hock decisions. The method is applied to average predictions of hourly day-ahead electricity prices over 650 point forecasts obtained with various lengths of calibration windows. It is evaluated on four European and American markets with almost two and a half year of out-of-sample period and compared to other semi- and fully automated methods, such as simple mean, AW/WAW, LASSO and PCA. The results indicate that the LASSO averaging is very efficient in terms of forecast error reduction, whereas PCA method is robust to the selection of the specification parameter. LPCA inherits the advantages of both methods and outperforms other approaches in terms of MAE, remaining insensitive the the choice of a tuning parameter.

Bartosz Uniejewski
Katarzyna Maciejowska


DRAformer: Differentially Reconstructed Attention Transformer for Time-Series Forecasting

Abstract: Time-series forecasting plays an important role in many real-world scenarios, such as equipment life cycle forecasting, weather forecasting, and traffic flow forecasting. It can be observed from recent research that a variety of transformer-based models have shown remarkable results in time-series forecasting. However, there are still some issues that limit the ability of transformer-based models on time-series forecasting tasks: (i) learning directly on raw data is susceptible to noise due to its complex and unstable feature representation; (ii) the self-attention mechanisms pay insufficient attention to changing features and temporal dependencies. In order to solve these two problems, we propose a transformer-based differentially reconstructed attention model DRAformer. Specifically, DRAformer has the following innovations: (i) learning against differenced sequences, which preserves clear and stable sequence features by differencing and highlights the changing properties of sequences; (ii) the reconstructed attention: integrated distance attention exhibits sequential distance through a learnable Gaussian kernel, distributed difference attention calculates distribution difference by mapping the difference sequence to the adaptive feature space, and the combination of the two effectively focuses on the sequences with prominent associations; (iii) the reconstructed decoder input, which extracts sequence features by integrating variation information and temporal correlations, thereby obtaining a more comprehensive sequence representation. Extensive experiments on four large-scale datasets demonstrate that DRAformer outperforms state-of-the-art baselines.

Benhan Li
Shengdong Du
Tianrui Li
Jie Hu
Zhen Jia


Scaleformer: Iterative Multi-scale Refining Transformers for Time Series Forecasting

Abstract: The performance of time series forecasting has recently been greatly improved by the introduction of transformers. In this paper, we propose a general multi-scale framework that can be applied to the state-of-the-art transformer-based time series forecasting models (FEDformer, Autoformer, etc.). By iteratively refining a forecasted time series at multiple scales with shared weights, introducing architecture adaptations, and a specially-designed normalization scheme, we are able to achieve significant performance improvements, from 5.5% to 38.5% across datasets and transformer architectures, with minimal additional computational overhead. Via detailed ablation studies, we demonstrate the effectiveness of each of our contributions across the architecture and methodology. Furthermore, our experiments on various public datasets demonstrate that the proposed improvements outperform their corresponding baseline counterparts. Our code is publicly available in https://github.com/BorealisAI/scaleformer.

Amin Shabani
Amir Abdi
Lili Meng
Tristan Sylvain


Time series aggregation for optimization: One-size-fits-all?

Abstract: One of the fundamental problems of using optimization models that use different time series as data input, is the trade-off between model accuracy and computational tractability. To overcome the computational intractability of these full optimization models, the dimension of input data and model size is commonly reduced through time series aggregation (TSA) methods. However, traditional TSA methods often apply a one-size-fits-all approach based on the common belief that the clusters that best approximate the input data also lead to the aggregated model that best approximates the full model, while the metric that really matters - the resulting output error in optimization results - is not well addressed. In this paper, we plan to challenge this belief and show that output-error based TSA methods with theoretical underpinnings have unprecedented potential of computational efficiency and accuracy.


Non-stationary Transformers: Exploring the Stationarity in Time Series Forecasting

Abstract: Transformers have shown great power in time series forecasting due to their global-range modeling ability. However, their performance can degenerate terribly on non-stationary real-world data in which the joint distribution changes over time. Previous studies primarily adopt stationarization to attenuate the non-stationarity of original series for better predictability. But the stationarized series deprived of inherent non-stationarity can be less instructive for real-world bursty events forecasting. This problem, termed over-stationarization in this paper, leads Transformers to generate indistinguishable temporal attentions for different series and impedes the predictive capability of deep models. To tackle the dilemma between series predictability and model capability, we propose Non-stationary Transformers as a generic framework with two interdependent modules: Series Stationarization and De-stationary Attention. Concretely, Series Stationarization unifies the statistics of each input and converts the output with restored statistics for better predictability. To address the over-stationarization problem, De-stationary Attention is devised to recover the intrinsic non-stationary information into temporal dependencies by approximating distinguishable attentions learned from raw series. Our Non-stationary Transformers framework consistently boosts mainstream Transformers by a large margin, which reduces MSE by 49.43% on Transformer, 47.34% on Informer, and 46.89% on Reformer, making them the state-of-the-art in time series forecasting. Code is available at this repository: https://github.com/thuml/Nonstationary_Transformers.

Yong Liu
Haixu Wu
Jianmin Wang
Mingsheng Long


Are Transformers Effective for Time Series Forecasting?

Abstract: Recently, there has been a surge of Transformer-based solutions for the long-term time series forecasting (LTSF) task. Despite the growing performance over the past few years, we question the validity of this line of research in this work. Specifically, Transformers is arguably the most successful solution to extract the semantic correlations among the elements in a long sequence. However, in time series modeling, we are to extract the temporal relations in an ordered set of continuous points. While employing positional encoding and using tokens to embed sub-series in Transformers facilitate preserving some ordering information, the nature of the \emph{permutation-invariant} self-attention mechanism inevitably results in temporal information loss. To validate our claim, we introduce a set of embarrassingly simple one-layer linear models named LTSF-Linear for comparison. Experimental results on nine real-life datasets show that LTSF-Linear surprisingly outperforms existing sophisticated Transformer-based LTSF models in all cases, and often by a large margin. Moreover, we conduct comprehensive empirical studies to explore the impacts of various design elements of LTSF models on their temporal relation extraction capability. We hope this surprising finding opens up new research directions for the LTSF task. We also advocate revisiting the validity of Transformer-based solutions for other time series analysis tasks (e.g., anomaly detection) in the future. Code is available at: \url{https://github.com/cure-lab/LTSF-Linear}.

Ailing Zeng
Muxi Chen
Lei Zhang
Qiang Xu

AAAI Conference on Artificial Intelligence


Wind energy forecasting with missing values within a fully conditional specification framework

Abstract: Wind power forecasting is essential to power system operation and electricity markets. As abundant data became available thanks to the deployment of measurement infrastructures and the democratization of meteorological modelling, extensive data-driven approaches have been developed within both point and probabilistic forecasting frameworks. These models usually assume that the dataset at hand is complete and overlook missing value issues that often occur in practice. In contrast to that common approach, we rigorously consider here the wind power forecasting problem in the presence of missing values, by jointly accommodating imputation and forecasting tasks. Our approach allows inferring the joint distribution of input features and target variables at the model estimation stage based on incomplete observations only. We place emphasis on a fully conditional specification method owing to its desirable properties, e.g., being assumption-free when it comes to these joint distributions. Then, at the operational forecasting stage, with available features at hand, one can issue forecasts by implicitly imputing all missing entries. The approach is applicable to both point and probabilistic forecasting, while yielding competitive forecast quality within both simulation and real-world case studies. It confirms that by using a powerful universal imputation method like fully conditional specification, the proposed approach is superior to the common approach, especially in the context of probabilistic forecasting.

Honglin Wen
Pierre Pinson
Jie Gu
Zhijian Jin

Mathematics
Computer Science
Engineering


Robust Probabilistic Time Series Forecasting

Abstract: Probabilistic time series forecasting has played critical role in decision-making processes due to its capability to quantify uncertainties. Deep forecasting models, however, could be prone to input perturbations, and the notion of such perturbations, together with that of robustness, has not even been completely established in the regime of probabilistic forecasting. In this work, we propose a framework for robust probabilistic time series forecasting. First, we generalize the concept of adversarial input perturbations, based on which we formulate the concept of robustness in terms of bounded Wasserstein deviation. Then we extend the randomized smoothing technique to attain robust probabilistic forecasters with theoretical robustness certificates against certain classes of adversarial perturbations. Lastly, extensive experiments demonstrate that our methods are empirically effective in enhancing the forecast quality under additive adversarial attacks and forecast consistency under supplement of noisy observations.

TaeHo Yoon
Youngsuk Park
Ernest K. Ryu
Yuyang Wang


A Differential Attention Fusion Model Based on Transformer for Time Series Forecasting

Abstract: Time series forecasting is widely used in the fields of equipment life cycle forecasting, weather forecasting, traffic flow forecasting, and other fields. Recently, some scholars have tried to apply Transformer to time series forecasting because of its powerful parallel training ability. However, the existing Transformer methods do not pay enough attention to the small time segments that play a decisive role in prediction, making it insensitive to small changes that affect the trend of time series, and it is difficult to effectively learn continuous time-dependent features. To solve this problem, we propose a differential attention fusion model based on Transformer, which designs the differential layer, neighbor attention, sliding fusion mechanism, and residual layer on the basis of classical Transformer architecture. Specifically, the differences of adjacent time points are extracted and focused by difference and neighbor attention. The sliding fusion mechanism fuses various features of each time point so that the data can participate in encoding and decoding without losing important information. The residual layer including convolution and LSTM further learns the dependence between time points and enables our model to carry out deeper training. A large number of experiments on three datasets show that the prediction results produced by our method are favorably comparable to the state-of-the-art.


Preformer: Predictive Transformer with Multi-Scale Segment-wise Correlations for Long-Term Time Series Forecasting

Abstract: Transformer-based methods have shown great potential in long-term time series forecasting. However, most of these methods adopt the standard point-wise self-attention mechanism, which not only becomes intractable for long-term forecasting since its complexity increases quadratically with the length of time series, but also cannot explicitly capture the predictive dependencies from contexts since the corresponding key and value are transformed from the same point. This paper proposes a predictive Transformer-based model called {\em Preformer}. Preformer introduces a novel efficient {\em Multi-Scale Segment-Correlation} mechanism that divides time series into segments and utilizes segment-wise correlation-based attention for encoding time series. A multi-scale structure is developed to aggregate dependencies at different temporal scales and facilitate the selection of segment length. Preformer further designs a predictive paradigm for decoding, where the key and value come from two successive segments rather than the same segment. In this way, if a key segment has a high correlation score with the query segment, its successive segment contributes more to the prediction of the query segment. Extensive experiments demonstrate that our Preformer outperforms other Transformer-based methods.

IEEE International Conference on Acoustics, Speech, and Signal Processing