Bayesian Estimation of the GARCH(1,1) Model with Normal Innovations
AbstractIn 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.
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Bibliographic InfoPaper provided by University Library of Munich, Germany in its series MPRA Paper with number 12985.
Date of creation: Sep 2006
Date of revision:
Publication status: Published in Student 3-4.5(2006): pp. 283-298
GARCH model; Bayesian estimation; Markov Chain Monte Carlo;
Find related papers by JEL classification:
- C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models &bull Diffusion Processes
- C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
- C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
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- Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
- Chib, Siddhartha & Greenberg, Edward, 1994. "Bayes inference in regression models with ARMA (p, q) errors," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 183-206.
- Nakatsuma Teruo, 1998. "A Markov-Chain Sampling Algorithm for GARCH Models," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 3(2), pages 1-13, July.
- Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-70, March.
- John Geweke, 2004. "Getting It Right: Joint Distribution Tests of Posterior Simulators," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 799-804, January.
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