Асимптотична нормальнiсть оцiнки найменших квадратiв у тригонометричнiй регресiї з сильно залежним шумом

Abstract

The least squares estimator asymptotic properties of the parameters of trigonometric regression model with strongly dependent noise are studied. The goal of the work lies in obtaining the requirements to regression function and time series that simulates the random noise under which the least squares estimator of regression model parameters are asymptotically normal. Trigonometric regression model with discrete observation time and open convex parametric set is research object. Asymptotic normality of trigonometric regression model parameters the least squares estimator is research subject. For obtaining the thesis results complicated concepts of time series theory and time series statistics have been used, namely: local transformation of Gaussian stationary time series, stationary time series with singular spectral density, spectral measure of regression function, admissibility of singular spectral density of stationary time series in relation to this measure, expansions by Chebyshev-Hermite polynomials of the transformed Gaussian time series values and it’s covariances, central limit theorem for weighted vector sums of the values of such a local transformation and Brouwer fixed point theorem.