Bayesian Estimation of the GARCH(1,1) Model with Normal Innovations

David, Ardia (2006): Bayesian Estimation of the GARCH(1,1) Model with Normal Innovations. Published in: Student , Vol. 5, No. 3-4 (September 2006): pp. 283-298.

Abstract

In this article, we propose the Bayesian estimation of the parsimonious but effective GARCH(1,1) model with Normal innovations. We sample the parameters joint posterior distribution using the approach suggested by Nakatsuma (1998). As a first step, we fit the model to foreign exchange log-returns time series and compare the Maximum Likelihood and the Bayesian estimates. Next, we illustrate some appealing aspects of the Bayesian approach through interesting probabilistic statements made on the parameters.

• Item Type: MPRA Paper
• Language: English
• Keywords: GARCH model; Bayesian estimation; Markov Chain Monte Carlo
• Subjects: C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C52 - Model Evaluation, Validation, and Selection; C - Mathematical and Quantitative Methods > C2 - Single Equation Models; Single Variables > C22 - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C15 - Statistical Simulation Methods: General; C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C11 - Bayesian Analysis: General

References

Andrews, D. W. K. (1991). Heteroskedasticity and autocorrelation consistent covariance matrix estimation. Econometrica, vol. 59, number 3, pp. 817-858

Andrews , D. W. K., Monahan, J. C. (1992). An improved heteroskedasticity and autocorrelation consistent covariance matrix estimator. Econometrica, vol. 60, number 4. pp. 953-966

Chib, Siddhartha, Greenberg, Edward (1994). Bayes inference in regression models with ARMA(p,q) errors. Journal of Econometrics, vol. 64, pp. 183-206

Engle, Robert F. (1982). Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica, vol. 50, number 4, pp. 987-1008.

Gelman, Andrew, Rubin, Donald B. (1992). Inference from iterative simulation using multiple sequences. Statistical Science, vol. 7, number 4, pp. 457-472

Geweke, John F. (1999). Simulation methods for model criticism and robustness analysis. In J. O. Berger, J. M. Bernardo, A. P. Dawid, and A. F. M. Smith, editors, Bayesian Statistics, volume 6, pages 275-299. Oxford: Oxford University Press

Geweke, John F. (2004). Getting it right: Joint distribution tests of posterior simulators. Journal of the American Statistical Association, vol. 99, number 467, pp. 799-804

Nakatsuma , Teruo (1998). A Markov-chain sampling algorithm for GARCH models. Studies in Nonlinear Dynamics and Econometrics, vol. 3, number 2, pp. 107-117

Nelson, Daniel B. (1991). Conditional heteroskedasticity in asset returns: A new approach. Econometrica, vol. 59, number 2, pp. 347-370

Phillips, P. C. B., Perron, Pierre (1988). Testing for a unit root in time series regression. Biometrika, vol. 75, pp. 335-346

Silverman, B. W. (1986). Density estimation for statistics and data analysis. London: Chapman and Hall