Abstract
This article develops a sequential Bayesian learning method to estimate the parameters and recover the state variables for generalized autoregressive conditional heteroscedasticity (GARCH) models, which are commonly used in the financial time-series analysis. This simulation-based method combines particle-filtering technology with a Markov chain Monte Carlo algorithm when the model is non-linear and the number of observed variables is relatively sparse. We compare the performance of the sequential Bayesian learning approach with the numerical maximum likelihood estimation (NMLE) in estimating models based on S&P 500 return rates. Our research concludes that the sequential parameter learning approach performs more robustly and accurately than the NMLE, by taking into account the uncertainty of the model. We also carry out simulation studies to confirm that the sequential Bayesian learning method is extremely reliable for GARCH models.
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