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

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. Prior studies of RNNs for time series forecasting yield inconsistent results with limited insights as to why the performance varies for different datasets. In this paper, we provide an approach to link the characteristics of time series with the components of RNNs 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 a 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.