馬可夫鍊蒙地卡羅法估計馬可夫轉換下CARR模型

Abstract

波動性在財務上扮演著關鍵的腳色，Chou(2005) 將GARCH模型結合變幅在波動預測上的優勢，進一步提出了CARR(Conditional Autoregressive Range)模型。馬可夫轉換模型是另一個在非常適合描述非線性效果的時間序列模型，我們依照採用Cai(1994), Hamilton and Susmel(1994), and Lamoureux and Lastraps(1993) 等人提出 Markov Switching GARCH模型的方法，提出Markov Switching CARR模型。 本文先將用馬可夫鍊蒙地卡羅法估計MS-CARR模型的參數公式化，再以用標準普爾500，首先對傳統CARR模型和MS-CARR模型進行樣本內波動性預測能力比較，實證結果可推論MS-CARR對於捕捉樣本內波動性方面優於CARR。再者對MS-CARR模型與AR-GARCH對於GARCH模型進行樣本內波動性預測能力比較，實證結果可得MS-CARR模型捕捉樣本內波動性預測能力同樣優於AR-GARCH跟GARCH。此研究顯現出MS-CARR模型在樣本內預測能力表現非常優異，未來往這方面的研究應可得不錯之研究成果。

It is well know that volatility plays an important role in finance. Chou (2005) has proposed the CARR (Conditional Autoregressive Range) model as an alternative volatility model. Markov Switching models are a promising way to capture nonlinearities in time series. Combining the elements of Markov Switching models with CARR model poses severe difficulties for the computation of parameter estimators. Thus, we develop a Bayesian analysis for Markov Switching Conditional Autoregressive Range model (MS-CARR), bases on a Markov Chain Monte Carlo algorithm. The main motivation in this paper is to compare MS-CARR model and CARR model for the in-sample forecasting power by using the S&P500 index data. We show that MS-CARR model provide more accurate forecasts that the CARR model.