The Maximum Likelihood Method of Random Coefficient Dynamic Regression Model

The Random Coefficient Dynamic Regression (RCDR) model is to developed from Random Coefficient Autoregressive (RCA) model and Autoregressive (AR) model. The RCDR model is considered by adding exogenous variables to RCA model. In this paper, the concept of the Maximum Likelihood (ML) method is used to estimate the parameter of RCDR(1,1) model. Simulation results have shown the AIC and BIC criterion to compare the performance of the the RCDR(1,1) model. The variables as the stationary and weakly stationary data are good estimates where the exogenous variables are weakly stationary. However, the model selection indicated that variables are nonstationarity data based on the stationary data of the exogenous variables.

Authors:

• Autcha Araveeporn

Keywords:

• Autoregressive
• Maximum Likelihood Method
• Nonstationarity
• Random Coefficient Dynamic Regression
• Stationary.

References:

[1] T.G. Anderson and J. Lund, Estimating continuous time stochastic
volatility models of the short term interest rate, Journal of Econometrics,
77, p. 343-377, 1977.
[2] A.R. Gallant and G. Tauchen, Estimation of continuous time models
for stock returns and interests rates, Macroeconomic Dynamics, 1, p.
135-168, 1997.
[3] Q. Yao and H. Tong, Quantifying the influence of initial values on
nonlinear prediction, Journal of the Royal Statistical Society, Series B,
56, p. 701-725, 1994.
[4] R.F. Engle, Autoregressive conditional heteroscedasticity with estimates
of the variance of United Kingdom inflation, Econometrica, 50, p. 987-
1007, 1982.
[5] T. Bollerslev, Generalized autoregressive conditional heteroscedasticity,
Journal of Econometrics, 31, p. 307-327, 1986.
[6] D.B. Nelson, Conditional heteroskedasticity in asset returns : a new
approach, Econometrica, 59, p. 347-370, 1991.
[7] R. Tsay, Conditional heteroscedastic time series models, Journal of the
American Statistical Association, 82, p. 590-604, 1987.
[8] D.F. Nicholls and B.G. Quinn, Random coefficient autoregressive models:
An introduction., Springer- Verlag Inc, New York, 1982.
[9] B.W. Silverman, Penalized maximum likelihood estimation, Encyclopaedia
of Statistical Sciences, 6, p. 664-667, 1985.
[10] R. Dahlhous and P. Polonik, Nonparametric quasi-maximum likelihood
estimation for Gaussian locally stationary process, The Annals of
Statistics, 34, p. 2790-2824, 2006.
[11] C. Hwang and B.P. Carlin, Parameter estimation for generalized random
coefficient autoregressive process, Journal of Statistical Planning and
Inference, 68, p. 323-337, 1998.
[12] G. Casella and R.L. Berger, Statistical Inference, CA : Duxbury, 2002.
[13] H. Akaike, A new look at the statistical model transactions, IEEE
Transactions on Automatic Control, 19, p. 716-723, 1984.
[14] G. Schwarz, Estimating the dimension of a model, Annals of Statistics,
6, p. 461-464, 1978.