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(phi
₁
,thetas
₁
)) 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 size
ⁿ
. The study contains comparison among these algorithms depending on MSE value. One can conclude that (hGA) can give good estimators (phi
₁
,thetas
₁
) of ARMA(1,1) parameters and more reliable than estimators obtained by cGA and sDA algorithm.