Comparing random coefficient autoregressive model with and without autocorrelated errors by Bayesian analysis
Abstract
We proposed a Bayesian analysis for estimating an unknown parameter in a Random Coefficient Autoregressive (RCA) model and its AutoRegressive (AR) process errors. We called this model an RCA model with autocorrelated errors (RCA-AR). A Markov Chain Monte Carlo (MCMC) method was used to generate samples from a posterior distribution which, after having been averaged, gave the estimated value of the unknown parameter. We used a Gibbs sampling algorithm in our MCMC calculation. To compare the performances of the RCA and the RCA-AR models, a simulation was performed with a set of test data and then the mean square errors obtained were used to indicate their performance. The result was that the RCA-AR model worked better than the RCA model in every case. Lastly, we tried both models with real data. They were used to estimate a series of monthly averages of the Stock Exchange of Thailand (SET) index. The result was that the RCA-AR still worked better than the RCA model, similar to the simulation of test data.
References
[1] | Engle R.F., Autoregressive conditional heteroscedasticity with estimates of the variance of United. % |
[2] | Kingdom inflation, Econometrica % 50: ((1982) ), 987-1007. |
[3] | Bollerslev T., Generalized autoregressive conditional heteroscedasticity, Journal of Econometrics 31: ((1986) ), 307-327. |
[4] | Tsay R., Conditional heteroscedastic time series models, Journal of the American Statistical Association 82: ((1987) ), 590-604. |
[5] | Nicholls D.F., and Quinn B.G., Random coefficient autoregressive models: An introduction Springer-Verlag Inc, New York, (1982) . |
[6] | Hwang S.Y., and Basawa I.V., Parameter estimation for generalized random coefficient autoregressive process, Journal of Statistical Planning and Inference 68: ((1998) ), 323-337. |
[7] | Chandra S.A., and Taniguchi M., Estimating Functions for Nonlinear Time Series Data, Annals of the Institute of Statistical Mathematics 53: ((2001) ), 125-136. |
[8] | Wang D., and Ghosh S.K., Bayesian analysis of random coefficient autoregressive models, Model Assisted Statistics and Applications 3: ((2002) ), 281-295. |
[9] | Haggan V., and Ozaki T., Modeling nonlinear vibrations using an amplitude-dependent autoregressive time series model, Biometrika 68: ((1981) ), 189-196. |
[10] | Tong H., Threshold models in nonlinear time series analysis, Springer-Verlag Inc, Heidelberg, (1982) . |
[11] | Bossaerts T., , Hardle W., and Hafner C., Foreign exchange-rates have surprising volatility, Athens Conference on Applied Probability and Time Series 2: ((1996) ), 55-72. |
[12] | Gelfand A., and Smith A.F.M., Sampling-based approaches to calculating marginal densities, Journal of American Statistical Association 85: ((1990) ), 398-409. |
[13] | Geman S., and Geman D., Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images, IEEE Transactions on Pattern Analysis and Machine Intelligence 6: ((1984) ), 721-741. |
[14] | Lunn D.J., , Thomas A., , Best N., and Spiegelhalter D., WinBUGS-a Bayesian modeling frameork: Concepts, structure, and extensibility, Statistics and Computing 10: ((2000) ), 325-337. |
