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Generalized spectral tests for serial dependence
Author(s) -
Hong Yongmiao
Publication year - 2000
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/1467-9868.00250
Subject(s) - autocorrelation , mathematics , asymptotic distribution , asymptotic analysis , von mises distribution , empirical distribution function , moment (physics) , stylized fact , kolmogorov–smirnov test , independence (probability theory) , pairwise comparison , power (physics) , statistics , statistical physics , von mises yield criterion , statistical hypothesis testing , finite element method , physics , macroeconomics , classical mechanics , quantum mechanics , estimator , economics , thermodynamics
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.

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