6533b831fe1ef96bd12983dd

RESEARCH PRODUCT

ON THE ASYMPTOTIC DISTRIBUTION OF BARTLETT'S Up-STATISTIC

Rainer Dahlhaus

subject

Statistics and ProbabilityAnderson–Darling testApplied MathematicsMathematical analysisV-statisticAsymptotic distributionKolmogorov–Smirnov testEmpirical distribution functionsymbols.namesakeSampling distributionsymbolsTest statisticStatistics Probability and UncertaintyCentral limit theoremMathematics

description

Abstract. In this paper the asymptotic behaviour of Bartlett's Up-statistic for a goodness-of-fit test for stationary processes, is considered. The asymptotic distribution of the test process is given under the assumption that a central limit theorem for the empirical spectral distribution function holds. It is shown that the Up-statistic tends to the supremum of a tied down Brownian motion. By a counterexample we refute the conjecture that this distribution is in general of the Kolmogorov-Smirnov type. The validity of the central limit theorem for the spectral distribution function is then discussed. Finally a goodness-of-fit test for ARMA-processes based on the estimated innovation sequence is given, and it is shown that this test statistic is asymptotically Kolmogorov-Smirnov distributed.

yearjournalcountryeditionlanguage
1985-07-01Journal of Time Series Analysis
https://doi.org/10.1111/j.1467-9892.1985.tb00411.x