A Distance Correlation-Based Approach to Characterize the Effectiveness of Recurrent Neural Networks for Time Series Forecasting

TL;DR

This paper introduces a distance correlation-based method to analyze how RNNs process time series data, revealing their strengths and limitations in modeling various time series characteristics and aiding practitioners in assessing model effectiveness.

Contribution

The study links time series features with RNN layer behavior using distance correlation, providing interpretability and insights into RNN performance variations.

Findings

RNN layers effectively learn lag structures

Performance degrades over layers for large lag series

Activation layers struggle with moving average and heteroskedastic processes

Abstract

Time series forecasting has received a lot of attention, with recurrent neural networks (RNNs) being one of the widely used models due to their ability to handle sequential data. Previous studies on RNN time series forecasting, however, show inconsistent outcomes and offer few explanations for performance variations among the datasets. In this paper, we provide an approach to link time series characteristics with RNN components via the versatile metric of distance correlation. This metric allows us to examine the information flow through the RNN activation layers to be able to interpret and explain their performance. We empirically show that the RNN activation layers learn the lag structures of time series well. However, they gradually lose this information over the span of a few consecutive layers, thereby worsening the forecast quality for series with large lag structures. We also show that the activation layers cannot adequately model moving average and heteroskedastic time series processes. Last, we generate heatmaps for visual comparisons of the activation layers for different choices of the network hyperparameters to identify which of them affect the forecast performance. Our findings can, therefore, aid practitioners in assessing the effectiveness of RNNs for given time series data without actually training and evaluating the networks.