On memory-augmented gated recurrent unit network

This paper addresses the challenge of forecasting multivariate long-memory time series. While statistical models such as the autoregressive fractionally integrated moving average (ARFIMA) and hyperbolic generalized autoregressive conditional heteroscedasticity (HYGARCH) can capture long-memory effects in time series data, they are often limited by dimensionality and parametric specification. Alternatively, recurrent neural networks (RNNs) are popular tools for approximating complex structures in sequential data. However, the lack of long-memory effect of these networks has been justified from a statistical perspective. In this paper, we propose a new network process called the memory-augmented gated recurrent unit (MGRU), which incorporates a fractionally integrated filter into the original GRU structure. We investigate the long-memory effect of the MGRU process, and demonstrate its effectiveness at capturing long-range dependence in real applications. Our findings illustrate that the proposed MGRU network outperforms existing models, indicating its potential as a promising tool for long-memory time series forecasting.