UDC 519.332
ANALYSIS AND FORECASTING OF NONSTATIONARY TIME SERIES WITH A SEASONAL COMPONENT
A. I. Novikov, Dr. Sc. (Tech.), associate Professor department of higher mathematics RSREU, Ryazan, Russia,
orcid.org/0000-0002-8166-8234, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.
A. G. Agafonov, student of RSREU, Ryazan, Russia,
orcid.org/0009-0005-1939-1106, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.
The aim of the work is to develop methods for analyzing and predicting time series that are an ad-ditive mixture of low-frequency (trend), cyclic and random components. A feature of cyclic, in particular, seasonal component in the examples under consideration is the change in its amplitude during the transition from one time interval corresponding to the oscillation period to the next period. Several approaches to the study of such series are considered. A traditional approach is when a trend, a cyclical component and the remainder of the series are sequentially highlighted. The modification consists in the fact that in order to account for changes in the amplitude of cyclic component, a description of the coefficients in the model of harmonic component for sine and cosine functions in the form of linear functions of time is proposed. In the second case, all the parameters of the model describing such a series are found together using the least squares method (LSM). This makes it possible to increase the accuracy of both the approximation of the series and its forecast. To improve the accuracy of time series forecast, in the dynamics of which local features appear that are not taken into account by a mathematical model of the series, the authors propose the difference between the values of the original series and the estimates to be included in a forecast model according to the model used for the time period preceding a forecast period and coinciding with it in length.
Key words: : time series, trend, cyclic component, seasonality, forecasting, discrete Fourier transform, amplitude spectrum.