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High frequency asymptotics for wavelet-based tests for Gaussianity and isotropy on the torus

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

Abstract

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.

Suggested Citation

  • Baldi, Paolo & Kerkyacharian, Gérard & Marinucci, Domenico & Picard, Dominique, 2008. "High frequency asymptotics for wavelet-based tests for Gaussianity and isotropy on the torus," Journal of Multivariate Analysis, Elsevier, vol. 99(4), pages 606-636, April.
    • Handle: RePEc:eee:jmvana:v:99:y:2008:i:4:p:606-636
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    References listed on IDEAS

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    1. Poghosyan, S. & Roelly, S., 1998. "Invariance principle for martingale-difference random fields," Statistics & Probability Letters, Elsevier, vol. 38(3), pages 235-245, June.
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