Generalized spectral tests for serial dependence
Author: Hong Y.1, *
Source: Journal of the Royal Statistical Society: Series B (Statistical Methodology), Volume 62, Number 3, 2000 , pp. 557-574(18)
Publisher: Blackwell Publishing
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Abstract:
Two tests for serial dependence are proposed using a generalized spectral theory in combination with the empirical distribution function. The tests are generalizations of the Cramér-von Mises and Kolmogorov-Smirnov tests based on the standardized spectral distribution function. They do not involve the choice of a lag order, and they are consistent against all types of pairwise serial dependence, including those with zero autocorrelation. They also require no moment condition and are distribution free under serial independence. A simulation study compares the finite sample performances of the new tests and some closely related tests. The asymptotic distribution theory works well in finite samples. The generalized Cramér-von Mises test has good power against a variety of dependent alternatives and dominates the generalized Kolmogorov-Smirnov test. A local power analysis explains some important stylized facts on the power of the tests based on the empirical distribution function.
Keywords: Craméer-von Mises criterion; Distribution-free tests; Empirical distribution function; Generalized spectrum; Kolmogorov–Smirnov criterion; Multiparameter empirical process; Non-linear time series; Weak convergence
Language: English
Document Type: Research article
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