On Short-Term Forecasting of Time Series Based on Subband Representations

Abstract

An important task of short-term forecasting of time series values based on prehistory (extrapolation) is considered without a priori setting the ratios that determine the dependence of future values on previous observations. It is shown that such an extrapolation can be based on the concept of the energy part of a time series segment corresponding to a certain subband of the domain of definition of the Fourier transform (subband representation). The relations for calculating the forecast are obtained and the conditions under which it will be error-free are determined. Estimates are given for the standard deviations of the future value estimation in the presence of random measurement errors in the form of white noise.