Abstract

Long-term dependence is an essential feature for the predictability of time series. Estimating the parameter that describes long memory is essential to describing the behavior of time series models. However, most long memory estimation methods assume that this parameter has a constant value throughout the time series, and do not consider that the parameter may change over time. In this work, we propose an automated methodology that combines the estimation methodologies of the fractional differentiation parameter (and/or Hurst parameter) with its application to Recurrent Neural Networks (RNNs) in order for said networks to learn and predict long memory dependencies from information obtained in nonlinear time series. The proposal combines three methods that allow for better approximation in the prediction of the values of the parameters for each one of the windows obtained, using Recurrent Neural Networks as an adaptive method to learn and predict the dependencies of long memory in Time Series. For the RNNs, we have evaluated four different architectures: the Simple RNN, LSTM, the BiLSTM, and the GRU. These models are built from blocks with gates controlling the cell state and memory. We have evaluated the proposed approach using both synthetic and real-world data sets. We have simulated ARFIMA models for the synthetic data to generate several time series by varying the fractional differentiation parameter. We have evaluated the proposed approach using synthetic and real datasets using Whittle's estimates of the Hurst parameter classically obtained in each window. We have simulated ARFIMA models in such a way that the synthetic data generate several time series by varying the fractional differentiation parameter. The real-world IPSA stock option index and Tree Ringtime series datasets were evaluated. All of the results show that the proposed approach can predict the Hurst exponent with good performance by selecting the optimal window size and overlap change.