Implementation of particle swarm optimization (PSO) algorithm for estimating parameter of arma model via maximum likelihood method
Pushpa Publishing House
Place of Publication
School of Business and Law
Autoregressive moving average (ARMA) model is popular for stationary univariate time series analysis. Parameter estimation plays an important role for model fitting in statistical analysis tools. Maximum likelihood estimation (MLE) method is a quite common procedure to estimate ARMA model parameter. Furthermore, the process of maximization of the likelihood function in some cases becomes an optimization problem. Standard procedures tend to be sensitive to the initial values. Therefore, it is necessary to apply the optimization method with heuristic approach to reach the optimal solution. Particle swarm optimization (PSO) is a heuristic-based optimization method that is flexible and powerful to handle various optimization problems. The weight of inertia and the size of the population are parts of the parameter control affecting the performance of PSO. This paper investigates the implementation of PSO in solving MLE optimization problem for parameter estimation of ARMA model. The performance would be evaluated from a variety of inertia weights and population sizes. PSO algorithms are implemented to solve the MLE results in estimators that are similar to the actual parameters. All of PSO settings (inertia weight: none, linearly decreasing, simulated annealing; particle size: 20, 30) converge after approximately 25 iterations. Statistically, the experimental results show that different PSO settings were capable for producing accurate estimators.