Bayesian Estimation of the GARCH(1,1) Model with Normal Innovations
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.
|Date of creation:||Sep 2006|
|Date of revision:|
|Publication status:||Published in Student 3-4.5(2006): pp. 283-298|
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Web page: http://mpra.ub.uni-muenchen.de
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- 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.
- 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.
- 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.
- 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.
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