Periodogram Estimator Properties of the Parameters of the Regression Model with Strongly Dependent Noise

The problem of detection of hidden periodicities is considered in the paper. In the capacity of useful signal model the harmonic oscillation observed on the background of random noise, that is a local functional of Gaussian strongly dependent stationary process is taken. For estimation of unknown angular frequency and amplitude of harmonic oscillation periodogram estimator is chosen, for which sufficient conditions of asymptotic normality are obtained and limit normal distribution is found. To obtain the main result there were used limit theorems of random processes, weak convergence of a family of measures to the spectral measure of a regression function, etc. The novelty, compared with the known results in the theory of periodogram estimator in observation models on weakly dependent noise, is assuming that the random noise is a local functional of Gaussian strongly dependent stationary process.

Publication year: 
2012
Issue: 
4
УДК: 
519.21
С. 59—65. Бібіогр.: 17 назв.
References: 

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