PAX-TS: Model-agnostic multi-granular explanations for time series forecasting via localized perturbations

TL;DR

PAX-TS introduces a model-agnostic post-hoc XAI method for time series forecasting that uses localized input perturbations to generate multi-granular explanations, including time-step importance, temporal dependencies, and cross-channel correlations. By perturbing inputs with Gaussian-smoothed perturbations, applying summary-statistic and trend adjustments, and computing change ratios to forecast properties, it constructs a faithful explanation matrix that can be analyzed locally or globally. Across seven forecasting algorithms and ten datasets, PAX-TS identifies six temporal-dependency classes and demonstrates that explanations align with model performance, while enabling cross-channel visualization; it also compares favorably to ShapTime and TS-MULE in granularity and fidelity, with runtime considerations suitable for practical use. The work highlights practical questions end-users ask, offering scalable, interpretable insights into how inputs drive forecasts and how inter-series channels interact, thereby enhancing trust and decision-making in real-time forecasting settings.

Abstract

Time series forecasting has seen considerable improvement during the last years, with transformer models and large language models driving advancements of the state of the art. Modern forecasting models are generally opaque and do not provide explanations for their forecasts, while well-known post-hoc explainability methods like LIME are not suitable for the forecasting context. We propose PAX-TS, a model-agnostic post-hoc algorithm to explain time series forecasting models and their forecasts. Our method is based on localized input perturbations and results in multi-granular explanations. Further, it is able to characterize cross-channel correlations for multivariate time series forecasts. We clearly outline the algorithmic procedure behind PAX-TS, demonstrate it on a benchmark with 7 algorithms and 10 diverse datasets, compare it with two other state-of-the-art explanation algorithms, and present the different explanation types of the method. We found that the explanations of high-performing and low-performing algorithms differ on the same datasets, highlighting that the explanations of PAX-TS effectively capture a model's behavior. Based on time step correlation matrices resulting from the benchmark, we identify 6 classes of patterns that repeatedly occur across different datasets and algorithms. We found that the patterns are indicators of performance, with noticeable differences in forecasting error between the classes. Lastly, we outline a multivariate example where PAX-TS demonstrates how the forecasting model takes cross-channel correlations into account. With PAX-TS, time series forecasting models' mechanisms can be illustrated in different levels of detail, and its explanations can be used to answer practical questions on forecasts.

Figures (9)

• Figure 1: Forecasting with localized perturbations, the basis for PAX-TS. The figure shows a perturbation of the global minimum of a sample from CIF and the respective forecasts.
• Figure 2: Time step importance of MultiPatchFormer on a sample of the CIF dataset with relation to the maximum of the forecast.
• Figure 3: Time step correlation on the Rain dataset, where MultiPatchFormer achieves high accuracy, while SegRNN performs poorly. The different temporal dependency patterns show that MultiPatchFormer is able to capture dependencies in the data.
• Figure 4: Cross-channel correlations of iTransformer on the ETTh1 dataset, showing strong relations from channel 5 to channel 0, and from channel 5 to channel 2.
• Figure 5: High-level input importance explanations of state-of-the art XAI methods for forecasting.