Abstract
Echo State Neural Networks (ESN) were applied to forecast the realized variance time series of 19 major stock market indices. Symmetric ESN and asymmetric AESN models were constructed and compared with the benchmark realized variance models HAR and AHAR that approximate the long memory of the realized variance process with a heterogeneous auto-regression. The results show that asymmetric models generally outperform symmetric ones, indicating that a correlation between volatility and returns plays an important role for volatility forecasting. Additionally, models utilizing a logarithmic transformation of the time series achieved generally better results than models applied directly to the realized variance. Echo State Neural Networks outperformed HAR and AHAR models for several important indices (S&P500, DJIA and Nikkei indices), but on average they achieved slightly worse results than the AHAR model. Nevertheless, the results show that Echo State Neural Networks represent an easy-to-use and accurate tool for realized variance forecasting, whose performance may potentially be further improved with meta-parameter optimization.
Highlights
Forecasting the volatility of the stock market plays an important role in many areas of finance including risk management, portfolio construction, derivatives pricing and quantitative trading
All of the models (HAR, AHAR, Echo State Neural Networks (ESN) and asymmetric version (AESN)) were applied to 19 stock market indices realized variance time series downloaded from the Oxford Man Institute realized volatility library
Echo State Neural Network models proved to be a viable alternative for realized variance modelling, achieving a competitive performance with the industry benchmark HAR and AHAR models, despite the fact that they used only the last day realized variance as the predictor, indicating that they were able to partially approximate the long memory dynamics of the volatility process with their recurrent layer
Summary
Forecasting the volatility of the stock market plays an important role in many areas of finance including risk management, portfolio construction, derivatives pricing and quantitative trading. In spite of the simplicity of this approach, Echo State Neural Networks upon their introduction significantly outperformed standard recurrent neural networks in a wide variety of benchmark tasks, especially regarding the prediction of univariate chaotic time series such as the Mackey-Glass oscillator They proved to be very efficient in a wide variety of empirical applications, including wind speed forecasting and financial time series prediction (Lukoševičius and Jaeger, 2009). In spite of these successes, there seems to be no previous study (to the knowledge of the author) that would apply Echo State Networks to the issue of realized variance forecasting, which is why the given topic was chosen for this paper. The third section introduces Echo State Neural networks and in the section four are presented results of the empirical study
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