Foundation models have recently emerged as a promising approach for time series analysis, adapting transformer architectures originally designed for natural language processing to handle continuous temporal data. While these models demonstrate strong performance across various time series tasks, their handling of multivariate time series, particularly inter-channel dependencies, remains underexplored. In this paper, we present a comprehensive analysis of current foundation models for time series, including tokenization-based, patch-based, and shape-based approaches, focusing on their mechanisms and data representations for capturing relationships between channels. Our analysis shows that even though these models have advanced architectures, they mostly process channels independently, which may prevent them from fully capturing cross-channel patterns. We examine this limitation across different model families and discuss its implications for multivariate time series analysis. Our empirical evaluation shows that foundation models perform well on simpler tasks but exhibit diminished effectiveness as channel dependencies increase, with specialized time series methods consistently outperforming them on complex datasets. These findings highlight the critical need for channel-aware architectures and more effective strategies for modeling inter-channel relationships in foundation models.

Attribution methods are essential for interpreting time series predictive models by quantifying the relevance of each time step for the prediction. State-of-the-art methods are often based on SHAP, an attribution method developed for tabular data. However, this has several challenges. First, SHAP is expensive to compute, especially for long time series, hence to speed it up it is usually approximated. Second, the impact of the background selection for emulating data ‘missingness’, essential to compute SHAP, remains understudied. Third, SHAP and more generally attribution methods for time series regression are notably lacking. In this paper, we address these limitations and propose TSHAP, a novel SHAP-based attribution method for time series classification and regression. TSHAP leverages a sliding window to group temporal data, enabling the efficient computation of exact SHAP values for each group. We further develop a methodology for the principled selection of background data. We evaluate TSHAP’s performance and robustness using comprehensive experiments on synthetic and real-world time series datasets.

Explanation for Multivariate Time Series Classification (MTSC) is an important topic that is under explored. There are very few quantitative evaluation methodologies and even fewer examples of actionable explanation, where the explanation methods are shown to objectively improve specific computational tasks on time series data. In this paper we focus on analyzing InterpretTime, a recent evaluation methodology for attribution methods applied to MTSC. We showcase some significant weaknesses of the original methodology and propose ideas to improve both its accuracy and efficiency. Unlike related work, we go beyond evaluation and also showcase the actionability of the produced explainer ranking, by using the best attribution methods for the task of channel selection in MTSC. We find that perturbation-based methods such as SHAP and Feature Ablation work well across a set of datasets, classifiers and tasks and outperform gradient-based methods. We apply the best ranked explainers to channel selection for MTSC and show significant data size reduction and improved classifier accuracy.

Abstract Time series classification is a task which deals with temporal sequences, a prevalent data type common in domains such as human activity recognition, sports analytics and general sensing. In this area, interest in explanability has been growing as explanation is key to understand the data and the model better. Recently, a great variety of techniques (e.g., LIME, SHAP, CAM) have been proposed and adapted for time series to provide explanation in the form of saliency maps, where the importance of each data point in the time series is quantified with a numerical value. However, the saliency maps can and often disagree, so it is unclear which one to use. This paper provides a novel framework to quantitatively evaluate and rank explanation methods for time series classification. We show how to robustly evaluate the informativeness of a given explanation method (i.e., relevance for the classification task), and how to compare explanations side-by-side. The goal is to recommend the best explainer for a given time series classification dataset. We propose AMEE, a Model-Agnostic Explanation Evaluation framework, for recommending saliency-based explanations for time series classification. In this approach, data perturbation is added to the input time series guided by each explanation. Our results show that perturbing discriminative parts of the time series leads to significant changes in classification accuracy, which can be used to evaluate each explanation. To be robust to different types of perturbations and different types of classifiers, we aggregate the accuracy loss across perturbations and classifiers. This novel approach allows us to recommend the best explainer among a set of different explainers, including random and oracle explainers. We provide a quantitative and qualitative analysis for synthetic datasets, a variety of time-series datasets, as well as a real-world case study with known expert ground truth.

Accuracy is a key focus of current work in time series classification. However, speed and data reduction are equally important in many applications, especially when the data scale and storage requirements rapidly increase. Current multivariate time series classification (MTSC) algorithms need hundreds of compute hours to complete training and prediction. This is due to the nature of multivariate time series data which grows with the number of time series, their length and the number of channels. In many applications, not all the channels are useful for the classification task, hence we require methods that can efficiently select useful channels and thus save computational resources. We propose and evaluate two methods for channel selection. Our techniques work by representing each class by a prototype time series and performing channel selection based on the prototype distance between classes. The main hypothesis is that useful channels enable better separation between classes; hence, channels with a larger distance between class prototypes are more useful. On the UEA MTSC benchmark, we show that these techniques achieve significant data reduction and classifier speedup for similar levels of classification accuracy. Channel selection is applied as a pre-processing step before training state-of-the-art MTSC algorithms and saves about 70% of computation time and data storage with preserved accuracy. Furthermore, our methods enable efficient classifiers, such as ROCKET, to achieve better accuracy than using no selection or greedy forward channel selection. To further study the impact of our techniques, we present experiments on classifying synthetic multivariate time series datasets with more than 100 channels, as well as a real-world case study on a dataset with 50 channels. In both cases, our channel selection methods result in significant data reduction with preserved or improved accuracy.

Existing approaches to time series classification can be grouped into shape-based (numeric) and structure-based (symbolic). Shape-based techniques use the raw numeric time series with Euclidean or Dynamic Time Warping distance and a 1-Nearest Neighbor classifier. They are accurate, but computationally intensive. Structure-based methods discretize the raw data into symbolic representations, then extract features for classifiers. Recent symbolic methods have outperformed numeric ones regarding both accuracy and efficiency. Most approaches employ a bag-of-symbolic-words representation, but typically the word-length is fixed across all time series, an issue identified as a major weakness in the literature. Also, there are no prior attempts to use efficient sequence learning techniques to go beyond single words, to features based on variable-length sequences of words or symbols. We study an efficient linear classification approach, SEQL, originally designed for classification of symbolic sequences. SEQL learns discriminative subsequences from training data by exploiting the all-subsequence space using greedy gradient descent. We explore different discretization approaches, from none at all to increasing smoothing of the original data, and study the effect of these transformations on the accuracy of SEQL classifiers. We propose two adaptations of SEQL for time series data, SAX-VSEQL, can deal with X-axis offsets by learning variable-length symbolic words, and SAX-VFSEQL, can deal with X-axis and Y-axis offsets, by learning fuzzy variable-length symbolic words. Our models are linear classifiers in rich feature spaces. Their predictions are based on the most discriminative subsequences learned during training, and can be investigated for interpreting the classification decision.