Application Of Time Series Methods On Stock Volatility

With the development of information technology and globalization of financial markets, the decision process of financial investment and banking operations are becoming more and more complex compared with previous ages. Meanwhile, regional financial crisis and bankruptcy of banks indicate that it is essential to strengthen the research on stability of financial product. The volatility of financial products is the core provoking risk factor of financial crisis for financial system, and almost all the crisis of finance are closely related with financial volatility. As a result, researches and studies on financial volatility have become one of important parts of financial econometrics. Nowadays, many statistical techniques have been used in these fields, and many researches show there are clustering effect and heavy-tail effect in financial data, which means that normal ARMA related models are not compatible with the financial data. GARCH model is a powerful tool for analyzing financial data, and the parametric GARCH models are the most commonly used models. However, the ways of estimation of parametric GARCH model's coefficients are always hard problems. Traditional method is to use the ML-based method to estimate the parameters, then, do some appropriate statistical references and ML method is essentially an optimization method. But GARCH models typically have many constraints among parameters, which will result in the failure of trust of MLE results, and ML related statistical inferential methods, like: LM, Wald, LR, etc. This paper we use Markov Monte Carlo (MCMC) method to estimate the parameters of normal-based GARCH(1,1) model. The MCMC technique try to simulate several Markov chains to converge to the posterior distribution of parameters that we wish to estimate. Since MCMC method avoids the difficulties of constraints in optimization problems and statistical inferences about parameters avoid complicated asymptotic results , so the results based on MCMC are more reliable and we also show results based on MCMC are better than ones of ML based by using real financial data. Finally, we use our results to compute Value-at-risk (VaR) as an application of our research.