Journal
JOURNAL OF MULTIVARIATE ANALYSIS
Volume 99, Issue 4, Pages 606-636Publisher
ELSEVIER INC
DOI: 10.1016/j.jmva.2007.02.002
Keywords
high frequency asymptotics; wavelets; random fields; Multivariate Central Limit Theorem; tests for Gaussianity and isotropy
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We prove a multivariate CLT for skewness and kurtosis of the wavelets coefficients of a stationary field on the torus. The results are in the framework of the fixed-domain asymptotics, i.e. we refer to observations of a single field which is sampled at higher and higher frequencies. We consider also studentized statistics for the case of an unknown correlation structure. The results are motivated by the analysis of high-frequency financial data or cosmological data sets, with a particular interest towards testing for Gaussianity and isotropy. (c) 2007 Elsevier Inc. All rights reserved.
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