Bayesian Financial Panel Data Models Based On Markov Chain Monte Carlo Sampling Algorithms

The research of panel data modeling and application is one of the most essential and frontier fields of econometrics. However, the current panel data theoretical hypotheses contradict with the practical background of the changeable data generating behaviours and parameter distributions of the economic variables, which cannot guarantee the good properties of the estimators of parameters and are likely to result in small-sample problems and are difficult to obtain the reliable estimators of the model parameters. In addition, some kind of problem has taken place when the researchers are dealing with the simulation of the social and economic issues, that is, it is difficult to numerically compute the high-dimension integration problems, which hinders the development of panel data research and is required to solve those problems with high efficient and reliable computation methods.According to the Bayesian statistical inference process based on MCMC sampling algorithms, we analyse the structures of the panel data model with fixed effect, the panel data model with random effect, the autoregressive panel data model and the panel data model with exogenous variables and conduct Bayesian inference for the models above as well and obtain the likelihood functions of the models and posterior conditional distributions of the parameters. Then the Monte Carlo simulatin experiments are conducted with the designed MCMC sampling algorithms, the results of which indicates that the proposed MCMC computation methods evidently enhance the accuracy and efficiency of the estimation of the parameters in the models.The empirical study is conducted with the data of four security indices of Shanghai Stock Exchange. A panel stochastic volatility (PSV) model describing the volatility characteristics of security markets is constructed based on Bayesian panel data models, followed by the Bayesian inference for the likelihood function and the posterior distribution of parameters in the models, which extends the current time-series-based stochastic volatility models. The parameters of PSV models converge to posterior distributions after iteration and the MC errors are quite small, which demonstrate the high efficiency and accuracy and the models can be applied to the risk analysis and management of the security markets.