IJPAM: Volume 14, No. 1 (2004)

MULTITAPER MULTIVARIATE SPECTRAL
ESTIMATORS OF TIME SERIES WITH
DISTORTED OBSERVATIONS

A.A.M. Teamah$^1$, H.S. Bakouch$^2$
$^{1,2}$Department of Mathematics
Faculty of Science
Tanta University
Tanta, EGYPT
$^1$e-mail: abdelmoneim2002uk@yahoo.co.uk
$^2$e-mail: hbakouch@yahoo.com


Abstract.The nonparametric estimation of some multitaper spectral measures for a strictly stationary multidimensional time series $\mathbf{X(t)},\mathbf{t}=0,\pm 1,...,$is considered in the case, where only an amplitude modulated process $\mathbf{Y(t)=d(t)X(t)}$ is observed. The stochastic process $\mathbf{d(t)}$ takes the value $1$ when $\mathbf{X(t)}$ is observed and $\mathbf{\in }$ , non-zero constant, when $\mathbf{X(t)}$ is distorted. Statistical properties of the process $\mathbf{Y(t)}$ are obtained. Asymptotic statistical properties of these estimators are investigated.

Received: March 31, 2004

AMS Subject Classification: 62M10, 62M15

Key Words and Phrases: amplitude modulated process, distorted observations, multitapering, spectral estimators, stationarity

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2004
Volume: 14
Issue: 1