Statistical Properties Of Estimates Of Mutual Spectral Densities With Polynomial Window Of Data Viewing

Abstract

The estimation of mutual spectral density with polynomial window of data viewing of stationary stochastic process X(t),t(Z with discrete time is constructed. The properties of polynomial window of data viewing are investigated. Moments of this estimation are found; their asymptotic behavior and limit distribution of the estimation are investigated. In this report the rate of mathematical expectancy convergence of modified periodogram with polynomial window of data viewing to the mutual spectral density of stationary stochastic process is investigated, if spectral density satisfies the Holder condition continuous with index a, 0 < a < 1.