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SUMMARY The marginal and bivariate distributions of the observations generated from a standard autoregressive moving average scheme are derived, assuming the noise to have a double-exponential (Laplace) distribution. The distributions may differ substantially from their Gaussian counterparts. The AR(1) model with double-exponential noise is applied to a series of weekly measurements of sulphate concentration and is shown to give a significantly better fit when compared with the Gaussian model.
Damsleth et al. (Fri,) studied this question.