Abstract

This paper compares the frequentist method that consisted of the least-squares method and the maximum likelihood method for estimating an unknown parameter on the Random Coefficient Autoregressive (RCA) model. The frequentist methods depend on the likelihood function that draws a conclusion from observed data by emphasizing the frequency or proportion of the data namely least squares and maximum likelihood methods. The method of least squares is often used to estimate the parameter of the frequentist method. The minimum of the sum of squared residuals is found by setting the gradient to zero. The maximum likelihood method carries out the observed data to estimate the parameter of a probability distribution by maximizing a likelihood function under the statistical model, while this estimator is obtained by a differential parameter of the likelihood function. The efficiency of two methods is considered by average mean square error for simulation data, and mean square error for actual data. For simulation data, the data are generated at only the first-order models of the RCA model. The results have shown that the least-squares method performs better than the maximum likelihood. The average mean square error of the least-squares method shows the minimum values in all cases that indicated their performance. Finally, these methods are applied to the actual data. The series of monthly averages of the Stock Exchange of Thailand (SET) index and daily volume of the exchange rate of Baht/Dollar are considered to estimate and forecast based on the RCA model. The result shows that the least-squares method outperforms the maximum likelihood method.

Highlights

  • The modeling of time series data has been applied in a field of finance, business, and economics.Normally the time series data exhibit changing data as trend, volatility, stationary, nonstationary, and random walk, especially when the time series data are a sequence taken at successive space points in time

  • The Conditional Heteroscadastic Autoregressive Moving average (CHARMA) model [1] is an alternative way to model by using when volatility arises

  • Another model that is approached to CHARMA models is called the Random Coefficient Autoregressive (RCA) model studied by Nicholls

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Summary

Introduction

The modeling of time series data has been applied in a field of finance, business, and economics. The RCA model is being concentrated on the past of time series data to determine the order and obtain estimates of the unknown parameter as a volatility model. The frequentist method is approached by the random coefficient model [7], which has proposed two estimation methods for the coefficients of the explanatory variables, namely, the generalized least squares and the maximum likelihood estimator for the covariance matrix. This study considers the frequentist methods for estimating the parameter of the RCA model based on the least-squares and maximum likelihood methods. The performance of these methods uses the criterion as the Average Mean Square Error (AMSE) on simulated and Mean.

Least-Squares Method
Maximum Likelihood Method
Simulation Study
The time series plot of Case
Histogram estimated parameter thethe least-squares method in Case β βwith
Histogram of estimated parameter with least-squares method
Application
12 December
Conclusions
Full Text
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