HAR變異數與共變異數預測模型-隔夜報酬、(共)跳躍與不對稱效果資訊的重要性

HAR Volatility and Co-Volatility Forecasting-The Importance of Overnight Returns, (Co)Jumps, and Asymmetric Effect Information

蔡宗儒(Tsung-Ju Tsai)

指導教授 ： 賴雨聖

國立暨南國際大學/管理學院/財務金融學系/碩士(2015年)

https://doi.org/10.6837/NCNU.2015.00278

摘要

為了取得全天的金融資產日報酬變異數與共變異數估計值，本研究依照Blair et al.(2001)、Hansen and Lunde(2005)、De Pooter et al.(2008)以及Andersen et al.(2011)的調整方法將非全天交易的金融資產已實現變異數(Realized Variance, RV)與已實現共變異數(Realized Covariance, RCOV)各自加上它們標的資產的隔夜報酬平方值或交乘值。並且該調整隔夜報酬(共)變異過後的 RV^(+ON) 與RCOV^(+ON) 估計值皆可以再各自拆解成三個序列特徵相似但實際上卻不相同的部分:非交易時段的隔夜報酬(共)變異、交易時段的連續波動部分與離散(共)跳躍部分。

運用台灣證券交易所發行的產業股價指數高頻資料以及近似緩長記憶的HAR模型，本文實證研究發現對於非24小時全天交易的金融資產而言，最佳的 RV^(+ON) 與 RCOV^(+ON) 樣本內估計式分別為 HAR-RV^(+ON)-CJ-SON-ASYM 及 HAR-RV^(+ON)-TCJ-CON-CASYM 模型；並且所有產業指數樣本的 HAR-RV^(+ON)-X 與 HAR-RCOV^(+ON)-X 模型部分項檢定(Redundant Variable Test)幾乎都顯著地拒絕隔夜報酬平方(交乘)項、離散(共)跳躍項以及(共同)不對稱項之迴歸係數皆為0的虛無假說。這證實了良好的報酬(共)變異數估計模型應該將它的自身落後期波動度(或共變異數)解釋因子拆解成非交易時段的隔夜報酬(共)變異因子、交易時段的連續與(共)跳躍因子、以及不對稱項因子；並且這四個因子個別對於未來的金融資產報酬(共)變異數(或 RV^(+ON) 與RCOV^(+ON))之預測皆具有額外、並顯著的解釋能力。

最佳的 RV^(+ON) 與 RCOV^(+ON) 樣本外預測則以精簡的模型勝出。其中最佳的樣本外 RV^(+ON) 估計式為純粹考慮交易時段連續波動部分的 HAR-RV^(+ON)-C 模型；而最佳的樣本外 RCOV^(+ON) 估計式則是由純粹考慮交易時段連續共變異部分加上不對稱效果的 HAR-RV^(+ON)-TC-CASYM 模型勝出。

關鍵字

波動度預測 ； 已實現變異數 ； 已實現共變異數 ； 隔夜報酬 ； 不對稱效果 ； 資產價格跳躍 ； 資產價格共跳躍 ； 異質性自我迴歸模型

並列摘要

To obtain the whole day financial asset return variance or covariance estimators, the current research follows Blair et al.(2011), Hansen and Lunde(2005), De Pooter et al.(2008) as well as Andersen et al.(2011) by incorporating squared overnight returns or crossed overnight returns between different paired financial assets into the realized variance (RV) or realized covariance (RCOV) estimators, which can be obtained only among trading hours. Besides, both the adjusted RV^(+ON) and RCOV^(+ON) estimators can also be separated into three different components which possess similar but actually different series characters: non-trading hour overnight return (co)variance, trading hour continuous (co)volatility components, and discrete (co)jump components.

Using sector indices’ high frequency data released by Taiwan Stock Exchange as well as the approximated long-memory HAR model, the empirical study found that for financial assets not traded entire 24 hours a day, the best in sample RV^(+ON) and RCOV^(+ON) estimating models are HAR-RV^(+ON)-CJ-SON-ASYM and HAR-RCOV^(+ON)-TCJ-CON-CASYM models. Besides, almost all of the redundant variable tests of HAR-RV^(+ON)-X and HAR-RCOV^(+ON)-X models rejected the null hypothesis that all regressors of suqared (crossed) overnight returns terms, (co)jumps terms or asymmetric effect terms are zero. These empirical results suggested that a well-defined whole day asset return (co)variance estimating model should have its own lag autoregressive explanatory terms divided into four elements: that is, the non-trading hour overnight return (co)variance element, the trading hour continuous (co)variance and discrete (co)jump elements as well as asymmetric effect element. Furthermore, all of these four elements have their own extraordinary and significant explaining power for future financial asset returns’ (co)variance forecasting.

Parsimonious models win almost all of the out of sample RV^(+ON) and RCOV^(+ON) forecasting comparisons. Among all, the best out of sample RV^(+ON) forecasting model is HAR-RV^(+ON)-C model, which purely takes the continuous volatility component of trading hours into account; while the best out of sample RCOV^(+ON) forecasting model is HAR-RCOV^(+ON)-TC-CASYM mode, which merely takes the continuous co-volatility component and asymmetric effect into consideration.

並列關鍵字

Volatility Forecasting ； Realized Variance ； Realized Covariance ； Overnight Returns ； Asymmetric Effect ； Jumps ； Cojumps ； HAR models

參考文獻

Andersen, T.G., Bollerslev, T., Diebold, F., Ebens, H., 2001a. The distribution of realized stock volatility. Journal of Financial Economics 61, 43–76.

Andersen, T.G., Bollerslev, T., Diebold, F.X., Labys, P., 2001b. The distribution of realized exchange rate volatility. Journal of the American Statistical Association 96, 42–55.

Andersen, T.G., Bollerslev, T., Diebold, F.X., Labys, P., 2003.Modeling and forecasting realized volatility. Econometrica 71, 529–626.

Andersen, T.G., Bollerslev, T., Diebold, F.X., Wu, J., 2006. Realized beta: persistence and predictability. In: Fomby, T., Terrell, D. (Eds.), Advances in Econometrics: Econometric Analysis of Economic and Financial Time Series in Honor of R.F. Engle and C.W.J. Granger, vol. B., 1–40.

Andersen, T.G., Bollerslev, T., Diebold, F.X., 2007. Roughing it up: including jump components in the measurement, modeling and forecasting of return volatility. Review of Economics and Statistics 89, 701–720.