Literature Cited
T. Anderson, Statistical Analysis of Time Series [Russian translation], Mir, Moscow (1976).
D. R. Brillinger, Time Series Data Analysis and Theory, Holt, Rinehart, and Winston (1975).
É. Khennan, Multidimensional Time Series [Russian translation], Mir, Moscow (1974).
I. A. Ibragimov, “On the estimation of the spectral function of a stationary Gaussian process,” Teor. Veroyatn. Primen.,8, No. 4, 391–430 (1963).
R. Bentkus and V. Rutkauskas, “On the asymptotics of the first two moments of spectral estimates of the second order,” Liet. Mat. Sb.,13, No. 1, 29–45 (1973).
R. Bentkus, R. Rudzkis, and V. Statulyavicius, “Exponential inequalities for estimates of the spectrum of a stationary Gaussian sequence,” Liet. Mat. Sb.,15, No. 3, 25–39 (1975).
R. Bentkus and I. G. Zhurbenko, “Asymptotic normality of spectral estimates,” Dokl. Akad. Nauk SSSR,229, No. 1, 11–14 (1976).
R. Bentkus and R. Rudzkis, “Large errors for estimates of the spectrum of a stationary Gaussian sequence,” Liet. Mat. Sb.,16, No. 4, 63–77 (1976).
E. Parzen, “On consistent estimates of the spectrum of a stationary time series,” Ann. Math. Statist.,28, 329–348 (1957).
U. Grenander, “On empirical spectral analysis of stochastic processes,” Ark. Mat.,1, 503–531 (1951).
M. S. Bartlett and J. Medhi, “On the efficiency of procedures for smoothing periodograms from time series with continuous spectra,” Biometrika,42, 143–150 (1955).
V. G. Alekseev, “On the choice of a spectral window for estimating the spectrum of a Gaussian stationary stochastic process,” Probl. Peredachi Inf.,7, No. 4, 46–54 (1971).
I. G. Zhurbenko, “On an estimate of the spectral function of a stationary process,” Dokl. Akad. Nauk SSSR,214, No. 5, 1005–1008 (1974).
L. W. Cooley and J. W. Tukey, “An algorithm for machine calculation of complex Fourier series,” Math. Computation,19, 297–301 (1965).
M. S. Bartlett, “Periodogram analysis and continuous spectra,” Biometrika.,37, 1–16 (1950).
J. W. Cooley, P. A. W. Lewis, and P. D. Welch, “The application of the fast Fourier transform algorithm to estimation of spectra and cross-spectra,” J. Sound Vib.,12, 339–352 (1970).
I. G. Zhurbenko, “On a statistic of the spectral density of a stationary sequence,” Dokl. Akad. Nauk SSSR,239, No. 1, 34–37 (1978).
N. G. Brein, Asymptotic Methods in Analysis [Russian translation], IL, Moscow (1961).
Additional information
M. V. Lomonosov Moscow State University. Translated from Litovskii Matematicheskii Sbornik (Lietuvos Matematikos Rinkinys), Vol. 20, No. 1, pp. 39–50, January–March, 1980.
Rights and permissions
About this article
Cite this article
Zhurbenko, I.G. Optimal properties of certain spectral density statistics. Lith Math J 20, 13–20 (1980). https://doi.org/10.1007/BF00970850
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00970850