Hybrid canonical genetic algorithm and steepest descent algorithm for optimizing likelihood estimators of ARMA (1, 1) model

This paper presents a hybrid genetic algorithm (hGA) for optimizing the maximum likelihood function ln( L(phi₁,thetas₁)) of the mixed model ARMA(1,1). The presented hybrid genetic algorithm (hGA) couples two processes: the canonical genetic algorithm (cGA) composed of three main steps: selection, local recombination and mutation, with the local search algorithm represent by steepest descent algorithm (sDA) which is defined by three basic parameters: frequency, probability, and number of local search iterations. The experimental design is based on simulating the cGA ,hGA, and sDA algorithms with different values of model parameters, and sample sizeⁿ. The study contains comparison among these algorithms depending on MSE value. One can conclude that (hGA) can give good estimators (phi₁,thetas₁) of ARMA(1,1) parameters and more reliable than estimators obtained by cGA and sDA algorithm.