應用樹狀演算法預測高頻數據下的波動度-以台灣股票市場為例

Forecasting Volatility under High Frequency Data with Tree-based Algorithm：Evidence from the Taiwan Stock Market

范姜峻浩(Fan Jiang Jun-Hao)

指導教授 ： 岳夢蘭

國立政治大學/商學院/財務管理學系/碩士(2022年)

https://doi.org/10.6814/NCCU202200887

摘要

本篇論文使用5分鐘高頻資料所計算的真實波動度來當作市場波動度的衡量，以HAR-RV (Corsi, 2009)模型及其衍生模型為架構，應用機器學習技術中的樹狀演算法，預測台灣股市中三個指數的波動度，探討是否能透過捕捉變數間的非線性關係來改善線性模型的樣本外預測表現。除了真實波動度值的預測外，我們也關心波動度方向的準確度，提出使用樹狀演算法來預測未來波動度變大或變小兩種情況的分類模型。我們的結果顯示，隨機森林演算法在大多數的情況都能取得良好於其他模型的預測表現，在所有時間水平的預測下皆取得了較低的RMSE (Root Mean Square Error)及MAE (Mean Absolute Error)，大部分的情況下也有較低的MAPE (Mean Absolute Percentage Error)，Diebold-Mariano檢定結果也顯示隨機森林演算法有顯著優於線性模型的預測誤差，表示透過非線性的樹狀演算法進行模型擬合確實能夠提高預測表現。此外，研究結果也發現我們的模型在預測電子類指數之波動度時表現較佳，獲得相較於其他兩個指數更低的MAPE，並且在方向的預測上也有較高的準確度 (Accuracy)及精確度 (Precision)。

關鍵字

真實波動度 ； HAR-RV模型 ； 波動度預測 ； 機器學習 ； 決策樹 ； 隨機森林

並列摘要

This paper provides an evaluation of forecasting performance of the realized volatility calculated with 5-minute frequency data. Based on HAR-RV (Corsi, 2009) series model, Tree-based algorithms, the machine learning approach, were used to predict the realized volatility of three indices in the Taiwan stock market. In the comparison with linear regression model, we investigated whether the predictive performance in out-of-samples can be improved by tree-based algorithms which could easily capture non-linear relationships between variables. In addition to forecasting the value of realized volatility, we also considered the accuracy of the realized volatility direction, and propose a classification model that applied tree-based algorithms to predict the volatility directions, up and down. Our result showed that the random forest algorithm could achieve better predictive performance than other models in most cases. Lower RMSE and MAE at all time horizons of prediction were gained, and in most cases, there were also lower MAPE. The results of the Diebold-Mariano test also showed that the random forest had a significantly better predictive error than the linear model indicating that models fitted with non-linear tree-based algorithms could indeed improve the predictive performance. Furthermore, we also found that our model performed better in forecasting the volatility of the Taiwan Electronics Index, which obtained lower MAPE than the other two indices, and also had a higher accuracy and precision in the direction prediction.

並列關鍵字

Realized Volatility ； HAR-RV Model ； Volatility Forecasting ； Machine Learning ； Decision Tree ； Random Forest

參考文獻

[1] Andersen, T. G., & Bollerslev, T. (1998). Answering the Skeptics: Yes, Standard Volatility Models do Provide Accurate Forecasts. International Economic Review, 39(4), 885–905.

[2] Andersen, T.G., Bollerslev, T., Diebold, F.X. & Labys, P. (2003). Modeling and Forecasting Realized Volatility. Econometrica, 71, 579-625.

[3] Andersen , T.G. & Teräsvirta, T. (2009). Realized Volatility. In: Mikosch, T., Kreiß, JP., Davis, R., Andersen, T. (eds) Handbook of Financial Time Series. Springer, Berlin, Heidelberg.

[4] Andersen, T.G., Bollerslev, T. & Diebold, F.X. (2007). Roughing It Up: Including Jump Components in the Measurement, Modeling, and Forecasting of Return Volatility. The Review of Economics and Statistics, 89 (4), 701–720.

[5] Barndorff-Nielsen, O.E., Shephard, N. (2004). Power and Bipower Variation with Stochastic Volatility and Jumps, Journal of Financial Econometrics, Volume 2, Issue 1 , 1–37.