Global Explanations for Multivariate Time Series Forecasting Models via $K$-Order Markov Approximations

A Necessary Step Beyond Static XAI for Time Series

The research paper introduced by this Arxiv preprint tackles a critical blind spot in explainable AI (XAI): the inability of most existing methods to properly handle multivariate time series forecasting. The core innovation is a framework that uses $K$-order Markov approximations to generate global explanations—meaning explanations that describe model behavior across the entire dataset, not just for a single prediction.

The problem the authors identify is fundamental. Most popular XAI techniques, such as SHAP or LIME, were designed for tabular or image data. When applied to time series, they implicitly treat each timestamp as an independent feature. This is a severe misstep. In a time series, the value at time t is inherently dependent on values at t-1, t-2, and so on. Ignoring this temporal dependency produces explanations that are statistically invalid and practically misleading. For example, an explanation might suggest that a reading from three hours ago had no influence, when in reality it set the entire context for the current forecast.

The proposed solution—using a $K$-order Markov approximation—is a mathematically principled way to capture these temporal dependencies without incurring the computational cost of modeling the full, infinitely long history. By assuming that the future depends only on the last $K$ time steps, the method creates a tractable, interpretable model of the forecasting model's internal logic. This allows for the generation of global explanations that reveal which lagged features and which time steps are consistently important across the entire forecasting horizon.

Why This Matters for AI Practitioners

For anyone deploying forecasting models in production—whether for supply chain demand, energy load balancing, or financial risk—this work addresses a practical pain point. Regulators and business stakeholders increasingly demand not just accurate forecasts, but understandable ones. A model that predicts a spike in electricity demand is useless if you cannot explain why it predicts that spike, especially if the explanation points to a sensor reading from a specific hour.

Current practice often involves using feature importance scores that are averaged over time, which washes out the dynamic nature of temporal influence. This new approach offers a way to produce explanations that are faithful to the model's actual temporal reasoning. It moves the field from "here is what the model looked at" (static feature attribution) to "here is when and how the model used that information" (temporal attribution).

Implications for the Field

This research signals a maturation of XAI. The field is moving beyond one-size-fits-all methods toward domain-specific solutions that respect the structure of the data. For time series, this means abandoning the independence assumption. The $K$-order Markov approach is elegant because it is both theoretically sound and computationally feasible. It does not require retraining the forecasting model; it works as a post-hoc explanation layer.

However, the practical utility will depend on how well the method scales to very high-dimensional time series (e.g., thousands of sensors) and how sensitive the explanations are to the choice of $K$. A $K$ that is too small will miss long-range dependencies; one that is too large will reintroduce complexity.

Key Takeaways

• Core innovation: The paper introduces a global explanation framework for multivariate time series forecasting that uses $K$-order Markov approximations to respect temporal dependencies, unlike static XAI methods that treat timestamps as independent.
• Why it matters: It provides a principled way to generate explanations that are faithful to the temporal structure of forecasting models, addressing a major gap in current XAI practice.
• For practitioners: This method enables more trustworthy and auditable forecasting systems, which is critical for regulated industries and high-stakes operational decisions.
• Next frontier: The approach's scalability to high-dimensional data and the sensitivity of explanations to the Markov order ($K$) will determine its real-world adoption.