High Frequency Asymptotics for Wavelet-Based Tests for Gaussianity and Isotropy on the Torus

Baldi, Paolo; Kerkyacharian, Gérard; Marinucci, Domenico; Picard, Dominique

High Frequency Asymptotics for Wavelet-Based Tests for Gaussianity and Isotropy on the Torus

Authors

Baldi, Paolo

Kerkyacharian, Gérard

Marinucci, Domenico

Picard, Dominique

Description

We prove a 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 cosmological data or high-frequency financial data sets, with a particular interest towards testing for Gaussianity and isotropy
33 pages, 3 figures