Goodness-of-fit tests for stationary processes are a problem of practical importance, e.g. in the analysis of electroencephalographic data. The distribution of the chi-squared statistic under the normal hypothesis is studied by simulation; power is investigated by an inverse filtering procedure for processes which can be well represented by an autoregressive-moving average model. For a second model, consisting of a Gaussian or non-Gaussian signal plus Gaussian noise, sample skewness andkurtosis

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... are suggested as test statistics. The asymptotic normality and the asymptotic variance of these statistics are derived, as well as the behaviour for a broad class of alternatives. The second model is of primary interest in E.E.G.analysis.