Wavelet estimation of the memory parameter for long range dependent random fields

In this paper we study the estimation of the spatial long memory parameter for stationary long range dependent random fields using wavelet methods. We first show the relation between the wavelet coefficients of the random fields and its long memory parameter. Based on this relation, we construct a log-regression wavelet estimator of the long memory parameter. Under some mild regularity assumptions, the asymptotic properties of the estimators are investigated. Finally, a small simulation study illustrates the method. Copyright Springer-Verlag Berlin Heidelberg 2014