A Distance Correlation-Based Approach to Characterize the Effectiveness
  of Recurrent Neural Networks for Time Series Forecasting
Christopher Salazar Ashis G. Banerjee
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.