Scientific Journal of KubSAU

An algorithm of phase analysis as the instrument of nonlinear dynamics' methods used to study cyclic recurrence of time series is viewed in current article. The existing classical econometric methods for estimating cyclic recurrence developed for random systems which dynamics matches to the normal distribution. However, there also exists non-random systems characterized by trends, periodic and non-periodic cycles called quasicycles. An example of computing process of identifying quasicycles is illustrated on time series of all grain yields in Russia for the last 119 years. Phase portrait of this time series is illustrated in twodimension space. As a result, the phase portrait consists of 22 frequently unstable quasicycles which tottality forms a strange attractor. Quasicycles have quantitative (length) and quality (configuration) characteristics. Their combination defines very important characteristic called trend-stability. Phase analysis is a powerful form of analysis of time series to assess cyclic recurrence and is a tool for pre-forecasting analysis. Fuzzy sets' mathematical apparatus is also used in this article. An algorithm of formation of fuzzy sets' quasicycles' length is also presented here. Quasicycles' statistics are presented in tables, geometric patterns and in the form of fuzzy sets