Theory of probability and Mathematical statistics

Construction of estimates of spectral densities with a given accuracy over intersecting intervals of observations

N. V. Semenchuk

Yanka Kupala State University of Grodno, 22 Ažeška Street, Hrodna 230023, Belarus

Abstract: The article proposes a new method for determining the number of splitting intervals and the number of observations in 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 the assumption that the spectral density satisfies the Lipschitz condition. Two cases are considered: with a single and arbitrary data taper. As a result, an algorithm is proposed for constructing estimates for intersecting intervals of observations with a 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 random processes using non-parametric methods of spectral analysis in an automated mode.

Keywords: spectral density; stationary random process; estimate bias; estimates for overlapping observation intervals with a given accuracy.

UDC: 519.24

Received: 22.02.2019

DOI: 10.33581/2520-6508-2019-2-34-39