Wavelet-Based Estimation of Anisotropic Spatiotemporal Long-Range Dependence

Abstract

In this article, the estimation of spatiotemporal long-range dependence is formulated in the spectral wavelet domain. Sample information is provided by functional spectral data. Their high local singularity at the origin is captured by the wavelet transform. Weak consistency of the spectral wavelet estimators proposed is derived. Two functional estimation algorithms are implemented. A simulation study is developed to illustrate the efficiency of the computational methods derived. An approximation to the empirical convergence rate of the spectral wavelet periodogram is computed in some simulated examples.

Keywords:

• Separable Riesz kernel
• Spatiotemporal long-range dependence
• Wavelet periodogram
• Weak consistency

Mathematics Subject Classification:

• Primary 60G10, 60G15, 60G20
• Secondary 60G60

Acknowledgments

This contribution is dedicated to the memory of Professor Lakshmikantham. It was organized and communicated by Vo Anh, Member of JSAA.

This work has been supported in part by projects MTM2009-13393 of the DGI, MEC, and P09-FQM-5052 of the Andalousian CICE, Spain.