On least squares estimation for long-memory lattice processes

Authors:
Jan Beran;Sucharita Ghosh;Dieter Schell
Affiliations:
Department of Mathematics and Statistics, University of Konstanz, Germany;Swiss Federal Research Institute WSL, Switzerland;Department of Mathematics and Statistics, University of Konstanz, Germany
Venue:
Journal of Multivariate Analysis
Year:
2009

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Abstract

A flexible class of anisotropic stationary lattice processes with long memory can be defined in terms of a two-way fractional ARIMA (FARIMA) representation. We consider parameter estimation based on minimizing an approximate residual sum of squares. The method can be applied to sampling areas that are not necessarily rectangular. A central limit theorem is derived under general conditions. The method is illustrated by an analysis of satellite data consisting of total column ozone amounts in Europe and the Atlantic respectively.