Comparing the First and the Second Orders of Random Coefficient Autoregressive Model on Time Series Data

Abstract

The random coefficient autoregressive (RCA) model develops from the autoregressive model and the hierarchical model. The RCA model has considered a constant parameter and coefficient parameter depended on past data. The least squares method is a widely used method by minimizing the sum of squared residuals and differential with respect to the unknown parameter. In this paper, the concept of the least squares method is used to estimate an unknown parameter of the first and the second orders of Random Coefficient Autoregressive (RCA) model or called RCA(1) and RCA(2) models. The efficiency of the two models is to compare by considering the minimum value of mean square error. The RCA(1) and RCA(2) are then applied to a time series data in the form of nonstationary data. The monthly averages of the Stock Exchange of Thailand (SET) index and the daily volume of exchange rate Baht/Dollar are fitted on these models. The prediction of RCA(1) and RCA(2) models is shown that the RCA(l) model outperforms the RCA(2) model, similar to two data sets.