On Calculation of Spectra of Stationary Random Processes on the Basis of Large Samples

The article presents the results of large-scale numerical experiments aimed at computing the spectral density of a stationary random process (and its derivatives) on the basis of large samples. Both nonnegative and sign-changing weighting functions were employed to set up the spectral density estimates. In all cases, sign-changing weighting function (higher-order weighting functions) resulted in a substantial decrease in estimation error. Similar results were obtained in estimating the derivatives of the spectral density. In this case the use of higher-order weighting functions resulted in estimation errors that were many times lower.