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Asymptotic normality and efficiency of a weighted correlogram

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Abstract

For a process X(t)=Σ M j=1 g j (t j (), where gj(t) are nonrandom given functions, \((\xi _j (t),j = \overline {1,M} )\) is a stationary vector-valued Gaussian process, Eξk(t) = 0, and Eξk(0) Eξl(τ) = r kl(τ), we construct an estimate \(\hat r_{kl} (\tau ,T)\) for the functions r kl(τ) on the basis of observations X(t), t ∈ [0, T]. We establish conditions for the asymptotic normality of \(\sqrt T (\hat r_{kl} (\tau ,T) - r_{kl} (\tau ))\) as T → ∞. We consider the problem of the optimal choice of parameters of the estimate \(\hat r_{kl} \) depending on observations.

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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 7, pp. 937–947, July, 1998.

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Maiboroda, R.E. Asymptotic normality and efficiency of a weighted correlogram. Ukr Math J 50, 1067–1079 (1998). https://doi.org/10.1007/BF02528835

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  • DOI: https://doi.org/10.1007/BF02528835

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