level: technical
a new methodology measures how much each past observation matters for predictions in univariate time series models. it works with any forecasting model, including seasonal arma and recurrent neural networks. the approach combines ghost variables, shapley values, and additive importance measures to create two new tools: the auto-relevance function and the partial auto-relevance function. these functions assign importance scores to each lag, showing which past time steps the model relies on most.
the method also introduces a way to handle missing features when using coalition-based importance calculations. instead of removing a lag entirely, it replaces it with a one-step forecast from the same model. this keeps the data structure intact and avoids unrealistic gaps. tests on simulated and real data show the measures correctly identify the expected lag patterns in nearly all cases. the framework is designed specifically for time series, where observations are ordered and dependent.
the results confirm that the auto-relevance and partial auto-relevance functions can reveal the internal lag structure of forecasting models. this helps practitioners understand model behavior without needing to know the model's inner workings. the approach is model-agnostic, so it applies to both classical statistical models and modern neural networks. it provides a consistent way to compare how different models use past information.
why it matters: it gives data scientists a reliable way to explain which past time steps drive forecasts, improving model transparency and trust in time series applications.