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Biometrika 1975 62(3):563-570; doi:10.1093/biomet/62.3.563
© 1975 by Biometrika Trust
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Goodness-of-fit tests for correlated data

THEO GASSER

Fachgruppe für Statistik, Eidgenössische Technische Hochschule Zürich

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 and kurtosis 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.

Key Words: Autoregressive-moving average process • Chi-squared test • Goodness-of-fit test • Kurtosis • Skewness • Stationary process • Time series


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