Construction of estimates of spectral densities with a given accuracy over intersecting intervals of observations
The article proposes a new method for determining the number of splitting intervals and the number of observationsin them when building estimates of the spectral densities of stationary random processes with a given accuracy over intersecting observation intervals based on asymptotic results, obtained for the first moment of convergence rate under theassumption that the spectral density satisfies the Lipschitz condition. Two cases are considered: with a single and arbitrarydata taper. As a result, an algorithm is proposed for constructing estimates for intersecting intervals of observations witha given accuracy. This algorithm was tested on model examples for random AR(4) processes, using data taper of Riesz,Bochner, Parzen. The proposed method will be useful to the researcher in analyzing data in the form of stationary randomprocesses using non-parametric methods of spectral analysis in an automated mode.