PRELIMINARY WAVELET PROCESSING OF FINANCIAL DATA SERIES IN THE WOLFRAM MATHEMATICA SYSTEM
L E Khairullina, Z. N. Khakimov, Guzel Z. Khabibullinа · Известия Южного федерального университета. Технические науки · 2024
Any time series is a combination of useful information and noise. Therefore, in the analysis of financialtime series, one of the key points is the preprocessing of data in order to reduce the noise component.One of the promising ways to clean up the time series is threading – decomposing the signal into a waveletspectrum to a given level, zeroing out those wavelet decomposition coefficients whose values are less thana certain threshold value, and subsequent wavelet reconstruction of the signal using approximating andrefined detailing coefficients at each level. Tresholding is carried out using modern software tools, amongwhich researchers most often prefer the Matlab environment. This paper presents a demonstration of thecapabilities of the Wolfram Mathematica computer mathematics system in the preliminary processing offinancial data. Wolfram Mathematica has powerful functionality that allows high-quality processing oftime series. The system contains a large collection of wavelet families, multiple variants of discrete andcontinuous wavelet transformations. The history of Sberbank's daily stock quotes over the past 3 years waschosen as the object of the study. An analysis of the results showed that the quality of signal purification isinfluenced by the choice of a basic wavelet – in our case, the use of a 6th-order Daubechies waveletturned out to be preferable. The maximum signal-to-noise ratio is achieved with rigid threshold processingwith a "SURELevel" threshold. The conducted studies have shown that wavelet tresholding overthe detailing coefficients of the wavelet decomposition is an effective method of suppressing outliers andfluctuations of the time series. The cleared signal repeats the shape of the original signal, all peaks arewell expressed. At the same time, more accurate forecast values are obtained in the short-term forecast