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A criterion for a continuous spectral density

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  • Bradley, Richard C.

Abstract

For a given weakly stationary random field indexed by the integer lattice of an arbitrary finite dimension, a necessary and sufficient condition is given for the existence of a continuous spectral density. The condition involves the covariances of pairs of sums of the random variables, with the two index sets being "separated" from each other (but possibly "interlaced") by a certain distance along a coordinate direction.

Suggested Citation

  • Bradley, Richard C., 2003. "A criterion for a continuous spectral density," Journal of Multivariate Analysis, Elsevier, vol. 86(1), pages 108-125, July.
    • Handle: RePEc:eee:jmvana:v:86:y:2003:i:1:p:108-125
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    References listed on IDEAS

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    1. Miller, Curtis, 2000. "Spectral Density for Third Order Cumulants under Strong Mixing Conditions," Journal of Multivariate Analysis, Elsevier, vol. 74(2), pages 222-244, August.
    2. Cheng, R., 1992. "Rational spectral densities and strong mixing," Journal of Multivariate Analysis, Elsevier, vol. 42(2), pages 267-283, August.
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    Cited by:

    1. Shaw, Jason T., 2004. "Random fields and the limit of their spectral densities: existence and bounds," Statistics & Probability Letters, Elsevier, vol. 67(3), pages 213-220, April.
    2. Shaw, Jason, 2009. "A continuous spectral density for a random field of continuous-index," Journal of Multivariate Analysis, Elsevier, vol. 100(3), pages 363-376, March.

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