自迴歸 GARCH 模型之貝氏模型選擇

A Bayesian Model Selection of AR-GARCH Models Using the Reversible Jump MCMC Approach

林均豪(Chun-Hao Lin)

指導教授 ： 林余昭

中原大學/理學院/應用數學研究所/碩士(2009年)

https://doi.org/10.6840/cycu200900922

摘要

時間序列模型在財務金融分析上有著相當重要的應用，但其概似函數通常無法求得，因此在分析時就會比線性模型困難許多。在金融的時間序列上，一般化自我迴歸條件異質變異數分析模型 (GARCH 模型) 已經被廣泛應用，通常用來研究具有波動性的資料。
　　馬可夫鏈蒙地卡羅法 (MCMC 法) 成功地應用在估計 GARCH 模型的參數，而且可逆跳躍式馬可夫鏈蒙地卡羅法 (RJMCMC 法) 可以更進一步解決模型選擇的問題，使得吉氏抽樣法 (Gibbs sampling) 能夠突破以往的限制，在不同空間的模型作參數估計。
　　在本篇論文中，我們假設 AR-GARCH 模型的階次皆是未知的，所有的參數都可以利用貝氏方法來估計，我們運用統計軟體讓資料在 AR-GARCH 模型中選擇一個最好的模型。
　　最後，我們將此方法應用在台灣加權股價指數的收盤指數，選擇的資料從 2005/01/01 到 2009/05/31，共計 1,088 筆，在這組資料下，我們得到最好的配適模型是 AR(1)-GARCH(1,1) 模型。

關鍵字

GARCH model ； AR model ； Metroplis–Hastings algorithm ； Reversible Jump Markov Chain Monte Carlo

並列摘要

The time series models have important applications in financial analysis. However, their likelihood functions are usually not available in the explicit form. Generalized AutoRegressive Conditional Heteroskedasticity (GARCH) models capture certain characteristics commonly associated with financial time series, they give a statistical way of representing the changing volatility of data. And the estimation of such models has intensively and successfully been studied.
Markov Chain Monte Carlo (MCMC) method has been successful in estimating the parameters of GARCH models. Moreover, the Reversible Jump Markov Chain Monte Carlo (RJMCMC) method is employed to solve the model selection problem. It enables the Gibbs sampling schemes to work in different spaces.
In this research, we assume the orders of both AR and GARCH parts in the models are unknown and the corresponding parameters are to be estimated using the Bayesian approach. That is, we provide a procedure that automatically chooses the best one among AR-GARCH models.
Finally, this technique is applied to real data (Taiwan stock index, 2005/01/01-2009/05/31) and the best model is AR(1)-GARCH(1,1).

並列關鍵字

Reversible Jump Markov Chain Monte Carlo ； Metroplis–Hastings algorithm ； AR model ； GARCH model

參考文獻

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