PRELIMINARY WAVELET PROCESSING OF FINANCIAL DATA SERIES IN THE WOLFRAM MATHEMATICA SYSTEM

Abstract

Any time series is a combination of useful information and noise. Therefore, in the analysis of financial
time 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 wavelet
spectrum to a given level, zeroing out those wavelet decomposition coefficients whose values are less than
a certain threshold value, and subsequent wavelet reconstruction of the signal using approximating and
refined detailing coefficients at each level. Tresholding is carried out using modern software tools, among
which researchers most often prefer the Matlab environment. This paper presents a demonstration of the
capabilities of the Wolfram Mathematica computer mathematics system in the preliminary processing of
financial data. Wolfram Mathematica has powerful functionality that allows high-quality processing of
time series. The system contains a large collection of wavelet families, multiple variants of discrete and
continuous wavelet transformations. The history of Sberbank's daily stock quotes over the past 3 years was
chosen as the object of the study. An analysis of the results showed that the quality of signal purification is
influenced by the choice of a basic wavelet – in our case, the use of a 6th-order Daubechies wavelet
turned out to be preferable. The maximum signal-to-noise ratio is achieved with rigid threshold processing
with a "SURELevel" threshold. The conducted studies have shown that wavelet tresholding over
the detailing coefficients of the wavelet decomposition is an effective method of suppressing outliers and
fluctuations of the time series. The cleared signal repeats the shape of the original signal, all peaks are
well expressed. At the same time, more accurate forecast values are obtained in the short-term forecast