HAR volatility modelling with heterogeneous ... - ResearchGate

Realized volatility memory0.8volatilityleverage (−)leverage (+)jumps0.6correlation0.40.20−0.20 10 20 30 40 50Lag (days)Figure 1: Lagged correlation function between X t and daily integrated varianceRV t+h as a function of h, with X t being RV t itself, negative returns,positive returns and jumps for the S&P 500 serie from 28 April 1982 to 5February 2009 (more details on the data are provided in Section 3).are estimating the usual autocorrelation function of realized volatility, which displays thewell known feature to be very slowly decaying and possibly long memory. When X t arethe negative returns, we observe that they have a large impact on future volatility, andthis is the well known leverage effect. However, Figure 1 also shows that the impact ofnegative returns on future volatility is slowly decaying as well. Also jumps have a positiveand large impact (as large as the negative returns when h = 1), but with a faster decayingpace. Finally, positive returns have a very small and almost insignificant impact on futurevolatility.The slowly decaying impact of negative returns might well be a by-product of the slowlydecaying auto-correlation function of volatility. However, since the same phenomenon isnot observed with the jump component, it can be also suggestive of the fact that leverageeffect might be very persistent (potentially long memory), a possibility which has been4