A note on the properties of power-transformed returns in long-memory stochastic volatility models with leverage effect

The autocorrelation function (acf) of powered absolute returns and their cross-correlations with original returns are derived, for any value of the power parameter, in the context of long-memory stochastic volatility models with leverage effect and Gaussian noises. These autocorrelations and cross-correlations generalize and correct recent results on the acf of squared and absolute returns.