臺灣博碩士論文加值系統

在本文中，我們提出一種非線性的轉換模型—具有厚尾誤差分配的雙馬可夫轉換變異數異質性模式(Double Markov switching GARCH model)，來分析平均數及波動的不對稱效果，此模型的特色是門檻變數為一個無法觀察到的變數，其為一階的馬可夫過程。在貝氏方法的架構下，對參數做分析並使用馬可夫鏈蒙地卡羅法進行疊代及估計。在模擬研究中，我們針對轉換機率(transition probabilities) 事前分配做敏感度分析，並比較其參數估計結果。而在實例分析中採用美國S&P 500 之股價報酬率來解釋其他市場之外溢效果，我們應用具有外生變數的雙馬可夫轉換變異數異質性模式，並以法國、德國、義大利、英國、加拿大及日本之股價報酬率為研究對象。而在風險值的部分，我們除了去做風險值的估計外，也採用兩種較客觀的統計檢定方法來檢驗各種風險值模型是否正確估計風險值，與本文中提到的其他模式比較，利用具有外生變數的雙馬可夫轉換變異數異質性模式較能正確地估計出風險值。

In this paper we consider a double Markov switching GARCH model with fat-tailed error distribution for analyzing asymmetric effects on mean and volatility in financial markets. The characteristic of our model is that a regime variable from one state to another is an unobserved variable which is assumed to be a first-order Markov process. We use Markov chain Monte Carlo methods to make statistical inference. In simulation study, we set sensitivity analysis for transition probabilities and then compare these results. As to empirical study, we apply for our DMS-GARCH model with an exogenous variable to capture the asymmetric mean and volatility spillover effects. We consider six daily stock market indices including the CAC 40 of France, ADX 30 of Germany, Milan MIBTel Index of Italy, FTSE 100 of United Kingdom, the Toronto SE 300 of Canada, and Nikkei 225 Index of Japan and employ the daily return on US Standard and Poor''s 500 Index (S&P 500) as an exogenous variable. The data cover the period from 4 January 1999 to 28 April 2006. We also forecast VaR and use two hypothesis-testing methods for evaluating the accuracy of VaR models. These results tell us that our DMS-GARCH model with an exogenous variable performs much better than other considered models.

Contents
1 Introduction . . . . . . . . . . . . . . . . . . . . . 1
2 Bayesian inference . . . . . . . . . . . . . . . . . . 4
3 Testing model adequacy and Value at Risk . . . . . . . 8
3.1 Diagnostic checking of model adequacy . . . . . . . .8
3.2 Forecasting Value at Risk . . . . . . . . . . . . . .9
4 Simulation study . . . . . . . . . . . . . . . . . . 12
5 Empirical study . . . . . . . . . . . . . . . . . . .15
5.1 Data and estimate results . . . . . . . . . . . .. .15
5.2 Value at Risk . . . . . . . . . . . . . . . . . . . 18
6 Conclusion . . . . . . . . . . . . . . . . . . . . . .21
Appendix . . . . . . . . . . . . . . . . . . . . . . . 22
A Markov chain Monte Carlo methods . . . . . . . . . . 22
A.1 Gibbs sampler . . . . . . . . . . . . . . . . . . . 22
A.2 Metropolis-Hastings (MH) algorithm . . . . . . . . .23
B Conditional posterior distributions of probabilities . 24
C Conditional posterior distributions of states . . . . 26
References. . . . . . . . . . . . . . . . . . . . . . . 28

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