Maximum likelihood parameter estimation of F-ARIMA processes using the genetic algorithm in the frequency domain

Abstract

This work aims to treat the parameter estimation problem for fractional-integrated autoregressive moving average (F-ARIMA) processes under external noise. Unlike the conventional approaches from the perspective of the time domain, a maximum likelihood (ML) method is developed in the frequency domain since the power spectrum of an F-ARIMA process is in a very explicit and more simple form. However, maximization of the likelihood function is a highly nonlinear estimation problem. Conventional searching algorithms are likely to converge to local maxima under this situation. Since the genetic algorithm (GA) tends to find the globally optimal solution without being trapped at local maxima, an estimation scheme based on the GA is therefore developed to solve the ML parameter estimation problem for F-ARIMA processes from the frequency domain perspective. In the parameter estimation procedure, stability of the F-ARIMA model is ensured, and convergence to the global optimum of the likelihood function is also guaranteed. Finally, several simulation examples are presented to illustrate the proposed estimation algorithm and exhibit its performance.