Дискретное вейвлет-преобразование в анализе деловых циклов и идентификации поворотных точек

Вопросы статистики. 2026. Т. 33. № 2. С. 23–39.

Lola I. S., Asoskov D.

The paper proposes a discrete wavelet transform (DWT) method and its modifications that expand existing approaches in analyzing business cycles and identification of turning points as well as practice of their application. The purpose of the work is to test DWT method and assess the effectiveness of its implementation in applied analysis, aimed at developing the indicator approach; as well as at identification of he business cycle turning points. The empirical basis of the study was the results of surveys of business activity by the Federal State Statistics Service (Rosstat), which included estimates of about 25,000 respondents in the main basic sectors of the Russian economy in 2013–2024.
As a result of applying a maximal overlap discrete wavelet transform (MODWT) with the LA8 Daubechies filter, we are developing a new composite indicator – the Business Confidence Index (BCI) for the first time in Russian statistical practice. The constructed index is used to identify turning points of the business cycle.
The results of the study show a predominantly synchronous relationship between short-term growth cycles in the BCI time series and the reference index of physical volume of GDP. It shows a high degree of relevance of the method for constructing nonparametric composite indicators. The proposed approach made it possible to identify 8 turning points in the BCI dynamics from 2017 to 2024. However, the deviations of these points from the peaks and troughs identified in the dynamics of the GDP index of physical volume are no more than one quarter.
After testing over 30 wavelet filters, we selected the bior2.2 filter as the best for turning point identification.

Keywords: деловой цикл, поворотные точки, непараметрические данные, метод обнаружения, индекс деловой уверенности (ИДУ)

Publication based on the results of: Assessment of the business climate based on the results of conjuncture surveys in the conditions of formation of a new model of economic growth (2025)