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A FREQUENCY DOMAIN APPROACH FOR THE ESTIMATION OF PARAMETERS OF SPATIO-TEMPORAL STATIONARY RANDOM PROCESSES

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  • This article is dedicated to the memory of Professor M. B. Priestley who passed away on 15 June 2013.

Abstract

A frequency domain methodology is proposed for estimating parameters of covariance functions of stationary spatio-temporal processes. Finite Fourier transforms of the processes are defined at each location. Based on the joint distribution of these complex valued random variables, an approximate likelihood function is constructed. The sampling properties of the estimators are investigated. It is observed that the expectation of these transforms can be considered to be a frequency domain analogue of the classical variogram. We call this measure frequency variogram. The method is applied to simulated data and also to Pacific wind speed data considered earlier by Cressie and Huang (1999). The proposed method does not depend on the distributional assumptions about the process.

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