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5 ConclusionsThis paper presents a new model for volatility forecasting which extends the HAR modelof Corsi (2009) by isolating three main determinants of volatility dynamics, namely heterogeneouslagged continuous volatility, heterogeneous legged negative returns and heterogeneouslagged jumps. We find that each component plays a different role at differentforecasting horizons, but all the three are highly significant and neglecting each one ofthem is detrimental to the forecasting performance of the model. Moreover, when othervolatility measures proposed in the literature are inserted in the LHAR-CJ model theyeither drop out or only marginally contribute to the performance of the model confirmingthe ability of the LHAR-CJ model to capture the main determinants of volatilitydynamics.Explicitly modelling the jump component is important for two distinct reasons. First,it has a trimming effect on the dynamics of the persistent component of volatility whichallows a better prediction of future volatility, confirming Andersen et al. (2007). Secondly,as suggested in Corsi et al. (2009), they have a direct positive and significant impact onfuture volatility. Moreover, there are evidences that this direct impact of jumps is ofa short lived nature. Our simulated experiments indicated that this mechanism can bestatistically reproduced by a model having contemporaneous jumps in price and volatility.On the other hand, we find that not only daily but also weekly and monthly negative pastreturns are highly significant and have a significant forecasting power on future volatility,suggesting a slowly decaying impact of negative returns similar to that of continuousvolatility. This novel effect seems to confirm the heterogeneous structure of the marketand cannot be explained by continuous-time models, though flexible, as the ones specifiedso far in the literature.We conclude by noting that our model is very simple to implement, as it does not requiressophisticated computational technique. The estimation of the model parameters can be22
performed through a simple OLS regression, and the computation of the explanatoryvariables is trivial. We think that, for all the aforementioned reasons, this model weproposed may be effectively used for risk management.23
Page 1 and 2: HAR volatility modellingwith hetero
Page 3 and 4: measures introduced by Corsi et al.
Page 5 and 6: neglected so far.This paper explore
Page 7 and 8: largest time scale, assume that ˜
Page 9: (2008), and Boudt et al. (2008). An
Page 12 and 13: of standard realized volatility mea
Page 14 and 15: t−statt-statistics of daily jump
Page 16 and 17: In-sample Mincer-Zarnowitz R 20.820
Page 18 and 19: variation (RAV) which shows a more
Page 20 and 21: Mincer-Zarnowitz R 2 is reported in
Page 24 and 25: Out-of-sample Mincer-Zarnowitz R 20
Page 26 and 27: SVIJSVCJ0.90.85HARHAR−CJLHAR−CJ
Page 28 and 29: SVIJ regressionSVCJ regression1 day
Page 30 and 31: Frequency Data. Journal of Financia

HAR volatility modelling with heterogeneous ... - ResearchGate

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