Autocorrelation Structure of a Novel Generalized Harmonically Weighted Process

Abstract

The main objective of our work is to introduce a new generalization of Harmonically Weighted process to enhance the model’s flexibility by incorporating the parameter a, we establish several properties of the proposed model, including the harmonic inverse transformation, spectral density and autocorrelation function. The model demonstrates a capacity to capture short, long, and moderately long memory. Its persistence and memory characteristics are analyzed theoretically using the spectral density, autocorrelation function, and impulse response function. Furthermore, we compare the Moderate Harmonically Weighted (M-HW) process with related models such as Harmonically Weighted process, ARFIMA, and GAR models. We conduct a simulation study to check the validity of the theoretical findings, providing graphically the spectrum, ACF and IRF for our model, followed by comparisons with its competitors.