貝氏自迴歸 GARCH 模型之應用

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

陳雅琦(Ya-Chi Chen)

指導教授 ： 林余昭

中原大學/理學院/應用數學系/碩士(2006年)

https://doi.org/10.6840/cycu200600689

摘要

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) 已經被廣泛的使用, 它通常用來研究波動的資料。選擇 GARCH 模型階次的方法和選擇適當的 ARMA 模型的方法相似, 例如使用 AIC 準則和 BIC 準則, 而且使用圖形判斷法類似於使用 ACF 圖和 PACF 圖, 而貝氏方法則使用可逆跳躍式馬可夫鏈蒙地卡羅法 (RJMCMC 法)。
在本篇論文中, 我們假設 AR-GARCH 模型的階次是未知的, 而且所有符合的參數都可以使用貝氏方法來估計近似, 在這裡我們提供一個程序讓它可以自動在 AR-GARCH 模型中選擇一個最好的模型。 最後，我們把這個方法應用在台灣加權股價指數之報酬指數的分析上, 我們選擇的資料是從 2003/1/1 到 2006/5/30, 總共 842 筆, 得到在這個資料下最好的配適模型是 AR(1)-GARCH(1,1) 模型。

關鍵字

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

並列摘要

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. Selecting the order of a GARCH process is in some ways similar to the fitting of an ARMA model, criteria such as AIC, BIC and graphical diagnostics analogous to the ACF and PACF of ARIMA modeling are used. The Bayesian model selection is usually done by the Reversible Jump Markov Chain Monte Carlo.
In this research, we assume the orders of GARCH models are unknown and all the corresponding parameters are to be estimated using the Bayesian approach. 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, 2003- 2006).

並列關鍵字

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

參考文獻

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