A Comparison of Parameter Estimation Methods for the First-Order of Random Coefficient Autoregressive Model

Abstract

This paper compares the least-squares, maximum likelihood, and Bayesian methods for estimating an unknown parameter in the random coefficient autoregressive (RCA) model. The RCA model depends on the random coefficients and the time series data in terms of the autoregressive model. We mention estimating unknown parameters by using least-squares, maximum likelihood, and Bayesian methods. We concentrate on only the first-order models of the RCA model depending on the unknown parameter under time series data. The least-squares method is a widely used method by minimizing the sum of squared residuals and differential concerning unknown parameters. Next, the maximum likelihood method is another method that is well-known and often used for estimating parameters based on the likelihood function and observed data. Finally, the Bayesian method carries out Markov chain Monte Carlo (MCMC) method to generate samples from a posterior distribution, which, after being averaged, give the estimated value of the unknown parameter. We use a Gibbs sampling algorithm in our MCMC calculation. The efficiency of the three methods is to compare according to the average mean square error for simulation data. The least-squares method performs better than the maximum likelihood and Bayesian method except for the trend data for simulation data. The average mean square error of the least-squares method shows the minimum values that indicated their performance in most cases.  Lastly, we try these methods with the series of days of the gold price per one-baht weight on one year as actual data. The result shows that the least-squares method still worked better than the maximum likelihood and Bayesian method, similar to the simulation of test data.