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Correlation with the realized volatility for "GARCH(1,1)"

Correlations of the volatilities at different time horizons The axises give the time horizons of the volatilities.
Correlations between the historical and realized volatilities, at different time horizons
Asymmetry of the correlations between the historical and realized volatilities, at different time horizons
Correlations of the realized volatilities with the historical volatility increment
Correlations of the realized volatilities with the centered volatility increment