On Nonparametric Estimates of Higher Order Spectral Densities
V. G. Alekseev · Theory of Probability and Its Applications · 2010
In the paper we present a short description of symmetry properties and nonparametric estimates of third and fourth order spectral densities of a strictly stationary random process $\{X(t), t\in{\bf Z}\}$. We provide estimates of minimal (second) order spectral densities of the periodically nonstationary random process $\{X(t), t\in{\bf R}\}$, too. We criticize the approach by Zhurbenko [Spectral semi-invariant, in Probability and Mathematical Statistics. Encyclopedia, Yu. V. Prokhorov, ed., Bol'shaya Rossiyskaya Entsiklopediya, Moscow, 1999 (in Russian)], [Spectral analysis of random processes and fields, in Probability and Mathematical Statistics. Encyclopedia, Yu. V. Prokhorov, ed., Bol'shaya Rossiyskaya Entsiklopediya, Moscow, 1999 (in Russian)], which ignores the symmetry property of higher spectral densities.