Abstract
Abstract Background: Since high-frequency data have become available, an unbiased volatility estimator, i.e. realized variance (RV) can be computed. Commonly used models for RV forecasting suffer from strong persistence with a high sensitivity to the returns distribution assumption and they use only daily returns. Objectives: The main objective is measurement and forecasting of RV. Two approaches are compared: Heterogeneous AutoRegressive model (HAR-RV) and Feedforward Neural Networks (FNNs). Even though HAR-RV-type models describe RV stylized facts very well, they ignore its nonlinear behaviour. Therefore, FNN-HAR-type models are developed. Methods/Approach: Firstly, an optimal sampling frequency with application to the DAX index is chosen. Secondly, in and out of sample predictions within HAR models and FNNs are compared using RMSE, AIC, the Wald test and the DM test. Weights of FNN-HAR-type models are estimated using the BP algorithm. Results: The optimal sampling frequency of RV is 10 minutes. Within HAR-type models, HAR-RV-J has better, but not significant, forecasting performances, while FNN-HAR-J and FNNLHAR- J have significantly better predictive accuracy in comparison to the FNN-HAR model. Conclusions: Compared to the traditional ones, FNN-HAR-type models are better in capturing nonlinear behaviour of RV. FNN-HAR-type models have better accuracy compared to traditional HAR-type models, but only on the sample data, whereas their out-of-sample predictive accuracy is approximately equal.
Highlights
Volatility is most important variable in asset pricing, portfolio management and risk estimation since it is an indicator of financial disturbances
First set of inputs describes long-memory (RVs aggregated on the daily, weekly and monthly basis), the second set of inputs is extended for the jumps (J), and the third set of inputs includes leverage (L) effects
The results showed that 2 neurons for Feedforward Neural Networks (FNNs)-HAR, 4 for FNN-HAR-J and 4 for FNN-LHAR-J is the optimal number of hidden neurons
Summary
Volatility is most important variable in asset pricing, portfolio management and risk estimation since it is an indicator of financial disturbances. Volatility is usually measured by variance of price returns, i.e. as a constant parameter Nowadays it is accepted as a time-varying unobservable variable. According to the theory of quadratic variation of semi-martingales, the integrated volatility (true but unknown parameter) can be consistently estimated by the realized variance (Barndorff-Nielsen et al, 2002a, b). This is unrealistic, as prices are not continuously observed in practice and leads to the biased estimates of true volatility and to the market microstructure noise, which makes RV less accurate (Degiannakis et al, 2015). FNN-HAR-type models have better accuracy compared to traditional HAR-type models, but only on the sample data, whereas their out-of-sample predictive accuracy is approximately equal
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