The paper presents a study of temporal dependence in nonlinear transformations of time series. We examine the effects of parametric transformations on autocorrelation values and the persistence range with special emphasis on long memory processes. We derive an invariance property for the order...

A class of autoregressive moving-average (ARMA) models proposed by Jorgensen and Song [Journal of Applied Probability (1998), Vol. 35, pp. 78-92] with exponential dispersion model margins are useful to deal with non-normal stationary time series with high-order autocorrelation. One property...