Abstract
The paper addresses the forecasting of realised volatility for financial time series using the heterogeneous autoregressive model (HAR) and machine learning techniques. We consider an extended version of the existing HAR model with included purified implied volatility. For this extended model, we apply the random forests algorithm for the forecasting of the direction and the magnitude of the realised volatility. In experiments with historical high frequency data, we demonstrate improvements of forecast accuracy for the proposed model.
Highlights
In this paper, the estimation of historical volatility is considered for financial time series generated by stock prices and indexes
We investigated a number of indicators and through the feature selection process, we found that the following indicators were best for forecasting the realised volatility’s direction
The purified implied volatility was shown to be strongly correlated with the realised volatility measures, which indicates that PV can be a useful predictor of realised volatility
Summary
The estimation of historical volatility is considered for financial time series generated by stock prices and indexes. This estimation is a necessary step for the volatility forecast which is crucial for the pricing of financial derivatives and for optimal portfolio selection. Engle (1982) and Bollerslev (1986) first proposed the ARCH model and the GARCH model for forecasting volatility These models have been extended in a number of directions based on the empirical evidences that the volatility process is non-linear, asymmetry, and has a long memory. Such extensions can be referred to EGARCH—Nelson (1991), GJR-GARCH—Glosten et al (1993), AGARCH—Engle (1990), and TGARCH—Zakoian (1994). Studies have found that those models cannot describe the whole-day volatility information well enough because they were developed within low-frequency time sequences
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