An interpretable multi-scaled agent hierarchy for time series prediction

Abstract

The traditional time series analysis treats the time series as a dynamic system of sequential entries, leading to complex models and a lack of interpretability. Time series, however, can be understood simply as a composition of correlated information hierarchies in various time scales. Rising from this perspective, here we propose Interpretable multi-time-Scaled Hierarchical Agent-based Time Series Prediction (ISHA-TSP) with linear AutoRegressive (AR) architecture. These time scales, determined based on the instantaneous dominant frequencies of the time series or domain of knowledge, down-sample time series for each agent. Accordingly, a trend prediction signal is offered from a higher time-scale agent to a lower time-scale agent in a hierarchical manner. This hierarchy can also be interpreted reversely, where the lower time-scale agent offers a direction gradient signal to the higher-scale agent to adjust its estimated trend. The optimal learning rate for ISHA-TSP is determined based on a composite Lyapunov function that guarantees convergence. The proposed ISHA-TSP is evaluated with seven datasets in various prediction horizons for accuracy and stop-learning and stop-forecasting steps for robustness. Results show the ISHA-TSP is superior over an equivalent single agent in prediction error. Also, the proposed method adapts against agent failure and data-missing situations. This strategy also leads to simpler models with fewer parameters than a single complex monolithic model. Furthermore, it shows higher interpretability due to its compositional approach.