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ADEQUACY OF ASYMPTOTIC THEORY FOR GOODNESS‐OF‐FIT CRITERIA FOR SPECTRAL DISTRIBUTIONS
Author(s) -
Anderson T. W.,
You Linfeng
Publication year - 1996
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/j.1467-9892.1996.tb00292.x
Subject(s) - mathematics , anderson–darling test , asymptotic analysis , goodness of fit , kolmogorov–smirnov test , statistics , asymptotic distribution , sample size determination , statistical hypothesis testing , statistical physics , physics , estimator
. 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.