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A Comparison of Parameter Estimation Methods for the First-Order of Random Coefficient Autoregressive Model
(2022-10-01)
Araveeporn, Autcha
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.
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Bayesian Approach for Comparing Parameter Estimation of Regression Model for Outlier Data
(2022-06-17)
Araveeporn, Autcha
;
Kumnungkit, Kanchana
This research compares and contrasts the simple regression model's parameter estimation methods, which consisted of a dependent variable and one independent variable. Parameter estimation uses the ordinary least square method, Bayesian method, Markov Chain Monte Carlo (MCMC) method, and local weight Markov Chain Monte Carlo (LWMCMC) method. The standard method is the ordinary least square method, which uses the concept of minimum sum square error to estimate parameters for fitting the linear regression model. However, for a set of the parameter relating to the Bayesian approach, the use of prior and posterior distributions may affect the approximation of the Bayesian, MCMC, LWMCMC methods. This paper considers the ordinal least square method and Bayesian approach by estimating the parameter for outlier data while some data points are far from other observations. The independent variable is simulated from the contaminated normal distribution, and the error is simulated from the normal distribution that made the outlier data on dependent and independent variables for the several sample sizes as 20, 50, 100, and 200. The criterion of the best efficiency is considered by the minimum of the average mean square errors. Through simulation data, the Bayesian method presents the minimum of average mean square errors at the sample sizes 20 and 50. However, when the sample size value increases, the MCMC and LWMCMC method are the best efficiency method at the sample sizes 100 and 200, respectively.

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