MODWT-ARMA model for time series prediction

Many time series in the applied sciences display a time-varying second order structure and long-range dependence (LRD). In this paper, we present a hybrid MODWT-ARMA model by combining the maximal overlap discrete wavelet transform (MODWT) and the ARMA model to deal with the non-stationary and LRD time series. We prove theoretically that the details series obtained by MODWT are stationary and short-range dependent (SRD). Then we derive the general form of MODWT-ARMA model. In the experimental study, the daily rainfall and Mackey–Glass time series are used to assess the performance of the hybrid model. Finally, the normalized error comparison with DWT-ARMA, EMD-ARMA and ARIMA model indicates that this combined model is an effective way to improve forecasting accuracy.