Leverage, skewness and amplitude asymmetric cycles

The leverage parameter is shown to turn up as part of the third-order moment when a stochastic volatility process is linearly filtered. If the filter is of the autoregressive class and possesses complex-valued roots or is a Gegenbauer long-memory filter, the leverage effect plays a determinant role in producing Amplitude Asymmetric Cycles, in which the degree of asymmetry depends on the persistence of the process at both levels (conditional mean and variance), the variance of the shocks to the volatility and the value of their inter-temporal correlation with the shocks to the levels.