Printed in Qreat Britain Goodness-of-fit tests for correlated data BY THEO GASSER

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 statis-tic 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 are suggested as test statistics. The asymptotic normality and the asymptotic variance of these statistics are derived, as well as the be-haviour for a broad class of alternatives. The second model is of primary interest in E.E.G.-analysis. Some key words: Autoregressive-moving average process; Chi-squared test; Goodness-of-fit test; Kurtosis; Skewness; Stationary process; Time series. 1