Bayesian Analysis of Time Series Regressions with Multivariate t Autoregressive Errors

10.29973/JCSA.200606.0001

Tsung-I Lin

Approximate Bayesian ； conditional variance ； MCMC ； predictive cistribution ； reparameterization

中國統計學報

44卷2期（2006 / 06 / 01）

108 - 129

英文

We consider a Bayesian approach to the regression model with autoregressive multivariate t errors in which the conditional variance satisfies a type of generalized autoregressive conditionally heteroscedastic model. We present the approximate Bayesian posterior and predictive inferences under a non-informative prior. Markov chain Monte Carlo computational schemes are also developed for computing the posterior uncertainties of parameters. To enhance the computational efficiency, we provide a fast computation method of obtaining the inverse autocorrelation matrix of an AR(p) process. A real data example for the U.S. monthly Treasury constant maturity rates is used to demonstrate our methodologies.

1. Lee, J.C.,Wang, R.S.,Lin, T.I.(2004).On the inverse of the autocorrelation matrix for an AR(p) process.Journal of the Chinese Statistical Association,42,81-89.
   連結：
2. Arellano-Valle, R.B.,Galea-Rojas, M.,Zuazola, P.I.(2000).Bayesian sensitivity analysis in elliptical linear regression models.Journal of Statistical Planning Inference,86,175-199.
3. Barndorff-Nielsen, O. E.,Schou, G.(1973).On the reparameterisation of autoregressive models by partial autocorrelations.Journal of Multivariate Analysis,3,408-419.
4. Bollerslev, T.(1986).Generalized autoregressive conditional heteroscedasticity.Journal of Econometrics,31,307-327.
5. Box, G.E.P.,Jenkins, G.M.,Reinsel, G.C.(1994).Time Series Analysis Forecasting and Control third ed.Englewood Cliffs, NJ:Prentice-Hall.
6. Box, G.E.P.,Tiao, G.C.(1973).Bayesian Inference in Statistical Analysis.New York:Wiely.
7. Brooks, S.P.,Gelman, A.(1998).General methods for monitoring convergence of iterative simulations.Journal of Computational and Graphical Statistics,7,434-544.
8. Chen, C.W.S.,Lee, J.C.,Lee, S.Y.,Niu, W.F.(2004).Bayesian estimation for time series regressions improved with exact likelihoods.Journal of Statistical Computation and Simulation,74,727-740.
9. Chib, S.(1993).Bayes regression with autoregressive errors: A Gibbs sampling approach.Journal of Econometrics,58,275-294.
10. Chib, S.,Tiwari, R.C.,Jammlamadaka, S.R.(1988).Bayes prediction in regression with elliptical errors.Journal of Econometrics,38,349-360.
11. Engle, R.F.(1982).Autoregressive conditional heteroscedasticity with estimates of variance of United Kingdom inflation.Econometrica,50,987-1007.
12. Gelman, A.,Carlin, J.B.,Stern, H.S.,Rubin, D.B.(2004).Bayesian Data Analysis.New York:Chapman & Hall.
13. Kim, H.M.,Mallick, B.K.(2003).A note on Bayesian spatial prediction using the elliptical distribution.Statistics and Probability Letters,64,271-276.
14. Ljung, G.M.,Box, G.E.P.(1980).Analysis of variance with autocorrelated observations.Scandinavian Journal of Statistics,7,172-180.
15. McCulloch, R.E.,Tsay, R.S.(1994).Bayesian analysis of autoregressive time series via the Gibbs sampler.Journal of Time Series Analysis,15,235-250.
16. Monahan, J.F.(1984).A note on enforcing stationarity in autoregressive moving average models.Biometrika,71,403-404.
17. Nadarajah, S.,Kotz, S.(2005).Mathematical properties of the multivariate t distribution.Acta Applicandae Mathematicae,89,53-84.
18. Osiewalski, J.(1991).A note on Bayesian inference in a regression model with elliptical errors.Journal of Econometrics,48,183-193.
19. Osiewalski, J.,Steel M.F.J.(1993).Robust Bayesian inference in elliptical models.Journal of Econometrics,57,345-363.
20. Singh, R.S.(1988).Estimation of error variance in linear regression models with errors having multivariate student-t distribution with unknown degrees of freedom.Econometrics Letters,27,47-53.
21. Tarami, B.,Pourahmadi, M.(2003).Multi-variate t autoregressions: innovations, prediction variances and exact likelihood equation.Journal of Time Series Analysis,24,739-754.
22. Zellner, A.(1976).Bayesian and non-Bayesian analysis of the regression model with multivariate student-t error terms.Journal of the American Statistical Association,71,400-405.