Efficient Nonparametric Estimation of Generalized Autocovariances

Luati AlessandraPapagni FrancescaProietti Tommaso
CEIS Research Paper
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.

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Number: 515
Keywords: Cramér-Rao lower bound; Frequency Domain; Minimum Contrast Estimation; Periodogram
Volume: 19
Issue: 5
Date: Thursday 14 October 2021
Revision Date: Thursday 14 October 2021