Abstract

In the paper, we continue to investigate measures of dependence for random variables with infinite variance. For random variables with regularly varying tails, we introduce a general class of such measures, which includes the codifference and the spectral covariance. In particular, we investigate the α -spectral covariance, a new measure from this general class, for linear random fields with infinite second moment. Under some conditions on the filter of a linear random field, we investigate asymptotic properties of the α -spectral covariance for linear random fields with infinite variance. We also provide an application of spectral covariances for limit theorems for stationary and associated random fields with infinite variance.

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