A.V. Gulyaev1, S.V. Pivneva2

1,2 Russian State Social University (Russia, Moscow)
Gulyaev81@gmail.com

When studying a time series, it is traditionally customary to use a generalized mathematical model where a trend component, a cyclic component that describes the repeatability of a cyclic process over time intervals and a random component or noise – this component is responsible for factors hidden from the observer.

It is assumed that the main trend and the cyclical component can be accurately described because they are formed by known factors that can be taken into account within the framework of models.

The discrete wavelet transform is traditionally used to decompose BP into additive components. The first discrete wavelet transform was invented by the Hungarian mathematician Alfred Haar (1910-1920).

In parallel with this method, in the 70s and 80s, the idea of a time series analysis method called SSA (Singular Spectrum Analysis) arose in Russia, the method was called "Caterpillar". During the existence of the method, it has received an extension of its application – automation of the allocation of trend and cyclic components of BP has been developed.

Using the example of a study of the real time series of TRAFFAT, two methods of decomposition time series into additive components are considered. The complexity of determining the initial parameters is compared, the applicability to the decomposition of real time series is tested, and the quality of decomposition by both methods of one reference time series is compared. An assessment of the quality of the decomposition of the time series into components was made, as well as a comparison of the two methods in terms of the complexity of the analyst's application and the possibility of automating the selection of parameters.

Gulyaev A.V., Pivneva S.V. Application of wavelet transformation and singular spectral analysis in time series decomposition. Highly Available Systems. 2024. V. 20. № 2. P. 76−84. DOI: https://doi.org/10.18127/j20729472-202402-06 (in Russian)

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