Non-Gaussian VARMA model with stochastic volatility and applications in stock market bubbles

In order to analyze the stock market bubble phenomenon, the vector autoregressive moving average (VARMA) model with non-Gaussian innovations and stochastic volatility components (VARMA-t-SV) is constructed for financial modeling. Considering the estimation complexity of VARMA-t-SV model, the Kronecker structure of likelihood function is employed to speed up computation. Then we develop the corresponding Markov chain Monte Carlo (MCMC) sampling method to test the covariance structure specifications. Model comparisons illustrate that the VARMA model with flexible covariance structures perform better performances. The model parameter estimation results show that the fat tail and the heteroscedasticity features are useful in raising the performances compared to the standard form. Finally, using Chinese financial markets data, the effects of monetary policy on stock market bubbles are analyzed based on the VARMA-t-SV model. The empirical studies provide evidence to support the rational asset price bubble theory, namely, the tightening monetary policy may not succeed in shrinking the asset price bubble, which provides suggestions for regulators and investors.