Fractional bivariate exponential estimator for long-range dependent random field

Abstract

Estimating long-range dependence parameter of a random field, which provides a measure for the extent of long-range dependence, is a challenging problem. Fractional Bivariate EXponential (FBEXP) estimator is proposed for long-range dependence parameter estimation in random fields observed on a regular lattice. FBEXP is a generalized version of the commonly used FEXP estimator in time series. FBEXP estimator belongs to the class of broadband semiparametric estimators, which makes it free from the optimal bandwidth selection problem, present in other semiparametric estimators. The behavior of FBEXP estimator depends on the model order of bivariate exponential model. Three data-driven model order selection criteria are introduced to serve as a guide in appropriate choice of model order for efficient estimation of long-range dependence using FBEXP. The finite sample performance of the FBEXP estimator and model order selection criteria are illustrated via simulation study. FBEXP estimator provides an efficient estimate for the long-range dependence parameter, especially when the spectral density is sufficiently smooth everywhere except at the points of singularities. Total column ozone amounts in Europe and Mediterranean region illustrate the applicability of FBEXP estimator in providing efficient estimates for direction specific long-range dependence parameters and the spectral density of the process.