ANALYSIS OF ALMOST PROPORTIONAL CHARACTERISTICS OF TIME SERIES BASED ON A CLASS OF SHIFT FUNCTIONS

Staroverov Igor Nikolaevich, Kuzmin Victor Ivanovich

In the world, the amount of information is constantly growing every day and gives rise to the problem of effective methods for analyzing nonlinear fluctuations with a trend that do not change the data structure. In the article, studies were carried out, the purpose of which was to determine the mathematical roughness of the results for the class of shift functions for different metrics. Based on the above goal, the task was to estimate almost proportional characteristics for various types of data. As a hypothesis under study, a statement is made about the coincidence, obtaining close values of almost-proportions for different metrics. The work was carried out on two different time series in terms of behavior - weather and economic data. According to the results of the work, an analysis of almost-proportional characteristics of time series based on distances in functional metric spaces was carried out. To evaluate the parameters of a geometric progression, it is required to determine the origin, the denominator of the progression, and the position of the unit. The analysis was carried out on the basis of a class of functions represented by distances in functional spaces, where two parameters appear - the origin and the denominator of a geometric progression. Based on the results of the analysis carried out, the work revealed a single result of mathematical roughness for the class of shift functions for determining almost-proportions in different functional metric spaces.

Keywords:empirical data, near-proportions, geometric progression, shift functions, functional spaces