ARMA Model identification using Particle Swarm Optimization Algorithm

Abstract

In this paper, a new approach to ARMA model identification using evolutionary particle swarm optimization (PSO) algorithm has been proposed. ARMA is a popular method to analyze stationary univariate time series data. Stationarity checking, model identification, model estimation and model checking are usually four main stages to build an ARMA model and model identification is the most important stage in building ARMA models. However there is no method suitable for ARMA model that can overcome the problem of local optima, which is suitable for any ARMA model. The effectiveness of PSO Algorithm which is used to choose the parameters of ARMA Model automatically is tested for ARMA (2,2) model example. The identification of model ARMA(2,2): x <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</sub> +0.1x <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t-1</sub> -0.2x <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t-2</sub> = a <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</sub> +0.2a <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t-1</sub> -0.5a <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t-2</sub> . The simulation shows that the PSO-based model identification method can present better solutions than the MINIC model identification method.