Efficient Nonparametric Estimation of Generalized Autocovariances
Alessandra Luati (),
Francesca Papagni () and
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Alessandra Luati: University of Bologna
Francesca Papagni: Free University of Bozen
No 515, CEIS Research Paper from Tor Vergata University, CEIS
This paper provides a necessary and sufficient condition for asymptotic efficiency of a nonparametric estimator of the generalized autocovariance function of a stationary random process. The generalized autocovariance function is the inverse Fourier transform of a power transformation of the spectral density and encompasses the traditional and inverse autocovariance functions as particular cases. A nonparametric estimator is based on the inverse discrete Fourier transform of the power transformation of the pooled periodogram. The general result on the asymptotic efficiency is then applied to the class of Gaussian stationary ARMA processes and its implications are discussed. Finally, we illustrate that for a class of contrast functionals and spectral densities, the minimum contrast estimator of the spectral density satisfies a Yule-Walker system of equations in the generalized autocovariance estimator.
Keywords: Cramér-Rao lower bound; Frequency Domain; Minimum Contrast Estimation; Periodogram (search for similar items in EconPapers)
Pages: 17 pages
Date: 2021-10-14, Revised 2021-10-14
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