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We compare two approaches for estimation of stochastic volatility and jumps in the EUR/ /USD time series-the non-parametric power-variation approach using high-frequency returns and the parametric Bayesian approach (MCMC estimation of SVJD models) using daily returns. We have found that the estimated jump probabilities based on these two methods are surprisingly uncorrelated (using a rank correlation coefficient). This means that the two methods do not identify jumps on the same days. We further found that the non-parametrically identified jumps are in fact almost indistinguishable from the continuous price volatility at the daily frequency because they are too small. In most cases, the parametric approach using daily data does not in fact identify real jumps (i.e. discontinuous price changes) but rather only large returns caused by continuous price volatility. So if these unusually high daily returns are to be modelled, the parametric approach should be used, but if the goal is to identify the discontinuous price changes in the price evolution, the non-parametric high-frequency-based methods should be preferred. Among other results, we further found that the non-parametrically identified jumps exhibit only weak clustering (analyzed using the Hawkes process), but relatively strong size dependency. In the case of parametrically identified jumps, no clustering was present. We further found that after the beginning of 2012, the amount of jumps in the EUR/ /USD series greatly increased, but the results of our study still hold.

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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.