Long-memory wavelet models

This article presents a novel long-memory wavelet model for approximating a stationary long-memory process. The proposed model is constructed in the wavelet domain in which the dependence structure is characterized by the variances of wavelet coefficients at different scales. This model can be easily incorporated into more complex model structures such as a generalized linear model. For inference, maximum likelihood estimation is derived. In a simulation study, we show that the modeling via wavelets has a good performance both in estimating the long-memory parameter and in predicting future observations under various long-memory processes. For illustration, the methodology is applied to modeling the Nile River data.