Hostname: page-component-7dd5485656-2pp2p Total loading time: 0 Render date: 2025-10-30T09:27:50.494Z Has data issue: false hasContentIssue false
  • English
  • Français

On estimation of parameters of Gaussian stationary processes

Published online by Cambridge University Press:  14 July 2016

Masanobu Taniguchi
Masanobu Taniguchi*
Affiliation:
Hiroshima University
*
∗ Postal address: Department of Applied Mathematics, Faculty of Engineering, Hiroshima University, Hiroshima, 730 Japan.
Get access Rights & Permissions [Opens in a new window]

Abstract

In fitting a certain parametric family of spectral densities fθ (x) to a Gaussian stationary process with the true spectral density g (x), we propose two estimators of θ, say by minimizing two criteria D1 (·), D2(·) respectively, which measure the nearness of fθ (x) to g (x). Then we investigate some asymptotic behavior of with respect to efficiency and robustness.

Keywords

GAUSSIAN STATIONARY PROCESSSPECTRAL DENSITYPERIODOGRAMASYMPTOTIC EFFICIENCYROBUSTNESS

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 16 , Issue 3 , September 1979 , pp. 575 - 591
Copyright
Copyright © Applied Probability Trust 1979 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

[1] Beran, R. (1977) Minimum Hellinger distance estimates for parametric models. Ann. Statist. 5, 445–463.Google Scholar
[2] Bloomfield, P. (1973) An exponential model for the spectrum of a scalar time series. Biometrika 60, 217–226.Google Scholar
[3] Brillinger, D. R. (1969) Asymptotic properties of spectral estimates of second order. Biometrika 56, 375–390.Google Scholar
[4] Davis, H. T. and Jones, R. H. (1968) Estimation of the innovation variance of a stationary time series. J. Amer. Statist. Assoc. 63, 141–149.Google Scholar
[5] Dzhaparidze, K. O. (1974) A new method for estimating spectral parameters of a stationary regular time series. Theory Prob. Appl. 19, 122–132.Google Scholar
[6] Hannan, E. J. (1970) Multiple Time Series. Wiley, New York.Google Scholar
[7] Taniguchi, M. (1978) On a generalization of a statistical spectrum analysis. Math. Japon. 23, 33–44.Google Scholar
[8] Walker, A. M. (1964) Asymptotic properties of least squares estimates of parameters of the spectrum of a stationary non-deterministic times series. J. Austral. Math. Soc. 4, 363–384.Google Scholar