Autorelevance: function and other relevance measures in univariate series

Understanding the temporal relevance of each variable in a univariate series is one of the most subtle and strategic challenges of predictive modeling. In the realm of custom software and artificial intelligence for businesses, having metrics that accurately indicate which historical lags influence future projections not only improves accuracy but also allows data teams to design lighter and more explainable architectures. Recently, approaches have emerged that combine dummy variables with Shapley values to quantify the importance of each time lag, giving rise to concepts such as the autorelevance function and partial autorelevance. These tools make it possible to decompose the individual contribution of each previous step in the forecast, overcoming the limitations of traditional metrics based on coefficients or correlations. By applying these methods, artificial intelligence models—from seasonal ARMA to recurrent neural networks—reveal dependency patterns that often go unnoticed. For a company that develops custom applications, integrating this perspective into its prediction engines represents a qualitative leap in decision-making. At Q2B STUDIO, where we offer AWS and Azure cloud services and business intelligence solutions with Power BI, we understand that model interpretability is as critical as its performance. The autorelevance function, by measuring the marginal contribution of each lag within a cooperative framework (such as Shapley games), facilitates the selection of optimal time windows and the detection of hidden seasonalities. This is especially useful when implementing AI agents to automate forecasting processes in production environments. Furthermore, the proposed technique of replacing missing features in coalitions using a one-step forecast—instead of using mean values or zeros—avoids biases and preserves temporal dynamics. Our team applies these principles in cybersecurity and AI projects for businesses where prediction traceability is a regulatory requirement. By combining these methods with scalable cloud platforms, we achieve systems that not only predict but also explain their reasoning. Partial relevance, for its part, allows isolating the direct effect of a lag while controlling for intermediate ones, which is invaluable for causality analysis. Ultimately, the adoption of these importance measures positions organizations at the forefront of temporal analysis, and at Q2B STUDIO we offer the technical capabilities and knowledge to implement them in custom applications and robust artificial intelligence solutions.