Ordinal patterns-based methodologies for distinguishing chaos from noise in discrete time series

One of the most important aspects of time series is their degree of stochasticity vs. chaoticity. Since the discovery of chaotic maps, many algorithms have been proposed to discriminate between these two alternatives and assess their prevalence in real-world time series. Approaches based on the combination of “permutation patterns” with different metrics provide a more complete picture of a time series’ nature, and are especially useful to tackle pathological chaotic maps. Here, we provide a review of such approaches, their theoretical foundations, and their application to discrete time series and real-world problems. We compare their performance using a set of representative noisy chaotic maps, evaluate their applicability through their respective computational cost, and discuss their limitations.

ASSESSMENT OF THE COMPETITIVENESS OF INDUSTRIAL ENTERPRISE ACTIVITIE

The purpose of the article is to study and analyze the competitive status of industrial enterprises (on the example of enterprises in the Kryvyi Rih region). Determining the long-term forecast of competitiveness on the basis of extrapolation of performance indicators of an industrial enterprise with the required accuracy. A methodological approach to long-term forecasting of competitiveness on the basis of extrapolation and the use of identification of discrete time series, which allowed to determine the predictive values of factors influencing the competitive status of the enterprise to make effective strategic management decisions. Modern methods of making effective strategic decisions are largely based on the use of forecasting methods, using appropriate statistical material. At the same time, such an approach requires the fulfillment of conditions, the neglect of which leads to the distortion of the obtained conclusions. In particular, this applies to the requirements relating to the identification of discrete time series. For the first time, the application of discrete time series identification is proposed, which is the basis for determining the forecast indicators of enterprise competitiveness on the basis of extrapolation. Analytical dependences on the competitive position of the industrial enterprise of the Kryvyi Rih region and the corresponding factors of influence are constructed. The main components of the impact on competitiveness are analyzed: sales volume; net profit; market share in the product market; intensity of competition in the industry; the ratio of market share of the enterprise being analyzed to the market leader. The results of the study are used in the practice of managers of relevant enterprises in making effective decisions in the system of strategic management. The use of identification of discrete time series allowed to conduct an appropriate assessment of the competitive status of the enterprise and the relevant factors of influence. It is offered to consider the competitive status, to an information and analytical component of competitiveness of the industrial enterprise. Keywords: enterprise, competitive status, forecast, identification, time series, extrapolation. JEL Classification C19, D29 Formulas: 6; fig.: 4; tabl.: 2; bibl.: 31.