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Smoothed periodogram asymptotics and estimation for processes and fields with possible long-range dependence

  • Heyde, C. C.
  • Gay, R.
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    In this paper we establish central limit theorems for the smoothed unbiased periodogram [integral operator][pi]-[pi]...[integral operator][pi]-[pi]g([omega],[theta]){I*T,X([omega])-EI*T,X([omega])}d[omega]1...d[omega]r, where {Xt} is a stationary r-dimensional random process or random field, possibly with long-range dependence, which is not necessarily Gaussian. Here I*T,X([omega]) is the unbiased periodogram and g([omega],[theta]) is a smoothing function satisfying modest regularity conditions. This result implies asymptotic normality of the asymptotic quasi-likelihood estimator of a distributional characteristic [theta] of the process {Xt} under very general conditions. In particular, these results show the asymptotic optimality of the Whittle estimation procedure for both short and long-range dependence in the absence of the Gaussian assumption, and extend those of Giraitis and Surgailis (1990) for the case r = 1.

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    Article provided by Elsevier in its journal Stochastic Processes and their Applications.

    Volume (Year): 45 (1993)
    Issue (Month): 1 (March)
    Pages: 169-182

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    Handle: RePEc:eee:spapps:v:45:y:1993:i:1:p:169-182
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