ADEQUACY OF ASYMPTOTIC THEORY FOR GOODNESS‐OF‐FIT CRITERIA FOR SPECTRAL DISTRIBUTIONS

T. W. Anderson and Linfeng You

Journal of Time Series Analysis, 1996, vol. 17, issue 6, 533-552

Abstract: Abstract. Any of the Cramér‐von Mises, Anderson‐Darling, and Kolmogorov‐Smirnov statistics can be used to test the null hypothesis that the standardized spectral distribution of a stationary stochastic process is a specified one. The asymptotic distributions of the criteria have been characterized (Anderson, 1993). They are the same as for probability distributions if the observations are independent (all autocorrelations zero), but are different when there is dependence. In this paper simulation with 10000 replications has been used to determine the distributions of the criteria for samples of size 6, 10, 30 and 100 when the observations are independent. These empirical distributions have been compared with the asymptotic distributions in order to ascertain the sample sizes necessary for using the asymptotic tables. For practical purposes they are 30 for the Cramér‐von Mises and Kolmogorov statistics and over 100 for Anderson‐Darling.

Date: 1996
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