運用HAR模型預測VIX指數之實證研究

根據Corsi（2004）的異質性自我迴歸模型(HAR)及修正後HAR模型(HAR-GARCH)來探討2012年7月至2016四年半間VIX指數的波動性預測，並運用MAE、MSE統計損失函數來評估其預測績效；本研究同時加入已實現波動VIX期貨、已實現偏態、已實現峰態、已實現波動VIX指數、VIX波動率之風險溢酬等，探討是否影響VIX指數的波動性預測。在研究期間中，透過HAR及HAR-GARCH模型能夠有效的預測樣本外VIX指數，迴歸結果發現已實現波動率VIX期貨、已實現偏態及VIX波動率之風險溢酬對於VIX指數具有資訊內涵，且確實能夠提升VIX指數的預測能力。預測績效結果顯示，MAE與MSE的損失函數其值較小，使用SPA Test檢測分析模型卻無達到統計之顯著性，代表外生變數之加入確實能夠增加預測績效但差異不大。此外，加入二階動差之HAR-GARCH模型在MAE檢定下，比基準HAR模型來的更有良好之預測效果，並使用實際商品VIX期貨、VIX ETPs來評估其實際績效。

關鍵字

HAR ； HAR-GARCH ； VIX期貨； SPA Test

並列摘要

This study uses HAR model of Corsi (2004) and HAR-GARCH model to predict out-of-sample VIX during July 2012 to December 2016. To explore the information content of additional variables, we use realized volatility of VIX futures, realized skewness of VIX futures, realized kurtosis of VIX futures, VIX volatility, realized volatility of VIX and risk premium of VIX volatility as the exogenous variables in HAR model and HAR-GARCH model to predict one-day-ahead and five-days-ahead VIX. The predicted performance is evaluated by mean absolute error (MAE) and mean squared error (MSE), and statistical significance is provided by superior predictive ability (SPA) test. The empirical results indicate that the HAR and HAR-GARCH model can predict out-of-sample VIX effectively, and incorporating realized volatility of VIX futures, realized skewness of VIX futures and risk premium of VIX volatility into HAR model and HAR-GARCH model can enhance the out-of-sample predictive performance, which implies that these variables contain information content in predicting VIX. However, the SPA test shows that the superior predictive performances are statistically significant. In addition, the predictive performance of HAR-GARCH model is better than HAR model, indicating that modeling time-varying variance of VIX is important for predict out-of-sample VIX. Furthermore, using actual commodities like VIX Futures, VIX ETPs to evaluate their actual performance.

並列關鍵字

HAR ； HAR-GARCH ； VIX Futures ； SPA Test

參考文獻

Adebiyi, A. A., Adewumi, A. O., & Ayo, C. K. (2014). Comparison of ARIMA and artificial neural networks models for stock price prediction. Journal of Applied Mathematics, 2014.

鄒紹輝 (2006)，「隱含波動率之模型及預測：以台灣市場為例」國立中央大學統計研究所碩士學位論文

Abadir, K., & Talmain, G. (2002). Aggregation, persistence and volatility in a macro model. The Review of Economic Studies, 69(4), 749-779.

Amihud, Y. (2002). Illiquidity and stock returns: cross-section and time-series effects. Journal of financial markets, 5(1), 31-56.

Andersen, T. G., & Bollerslev, T. (1997). Heterogeneous Information Arrivals and Return Volatility Dynamics: Uncovering the Long‐Run in High Frequency Returns. The journal of Finance, 52(3), 975-1005.

國際替代計量

運用HAR模型預測VIX指數之實證研究

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