Abstract.ARMA processes with non‐normal residuals have applications in surface metrology and have recently been shown by Nelson and Granger (1979) to occur in modelling economic time series. In this paper we obtain the theoretical relationship between the skewness and kurtosis of an ARMA process and the corresponding parameters of its generating noise series and consider some of the implications of these results. Simulation methods for any ARMA process with given skewness and kurtosis, using Johnson transformations are briefly discusse
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