A comparison of two least-squared random coefficient autoregressive models: with and without autocorrelated errors

Abstract

This paper compares a Least-Squared Random Coefficient Autoregressive (RCA) model with a Least-Squared RCA model based on Autocorrelated Errors (RCA-AR). We looked at only the first order models, denoted RCA(1) and RCA(1)-AR(1). The efficiency of the Least-Squared method was checked by applying the models to Brownian motion and Wiener process, and the efficiency followed closely the asymptotic properties of a normal distribution. In a simulation study, we compared the performance of RCA(1) and RCA(1)-AR(1) by using the Mean Square Errors (MSE) as a criterion. The RCA(1) exhibited good power estimation in both cases where the data is stationary and nonstationary. On the other hand, when data oscillates around its mean, RCA(1)-AR(1) performed better. For real world data, we applied the two models to the daily volume of the Thai gold price and found that RCA(1)-AR(1) performed better than RCA(1).