Volatility increment conditional on the historical volatility for "Constant volatility with Student innovations"

Conditional average of the centered volatility increment, conditional on the historical volatility

The horizontal axis gives the volatility, the vertical axis gives the time horizons for the historical volatility and volatility increment.

Conditional correlation between the centered volatility increment and the historical volatility, conditional on the historical volatility

The horizontal axis gives the volatility, the vertical axis gives the time horizons for the historical volatility and volatility increment.