Statistical Analysis of the Spectral Density Estimate Obtained via Coifman Scaling Function

Abstract

Spectral density built as Fourier transform of covariance sequence of stationary random process is determining the process characteristics and makes for analysis of it’s structure. Thus, one of the main problems in time series analysis is constructing consistent estimates of spectral density via successive, taken after equal periods of time observations of stationary random process. This article is devoted to investigation of problems dealing with application of wavelet analysis methods for solving task of spectral density nonparametric estimating of stationary random process with discrete time.