On A Spectral Estimate Obtained by an Autoregressive Model Fitting

A stationary Gaussian process X(t) is considered which is expressed as an autoregressive process of infinite order. An autoregressive model of finite order K is fitted for this process and an estimate for the spectral density is obtained. The consistency and the asymptotic normality of this estimate...

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Bibliographic Details
Main Author: Huzii, Mituaki
Format: Report
Language:English
Subjects:
Autoregressive model fitting
ESTIMATES
Likelihood equations
LINEAR REGRESSION ANALYSIS
MATRICES(MATHEMATICS)
PROBABILITY DENSITY FUNCTIONS
RANDOM VARIABLES
SPECTRUM ANALYSIS
STATIONARY
STATISTICAL PROCESSES
Statistics and Probability
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Summary:A stationary Gaussian process X(t) is considered which is expressed as an autoregressive process of infinite order. An autoregressive model of finite order K is fitted for this process and an estimate for the spectral density is obtained. The consistency and the asymptotic normality of this estimate under some conditions are shown. This estimate has an asymptotically efficient property in a sense under some conditions which are stronger than Berk's conditions.