Annotation:  Methods. A synergetic approach was the basis for building the research methodology. In the process of research, general and specific scientific methods were used, namely: abstraction − to identify the epistemological properties of inflation forecasting from the standpoint of the indeterminist paradigm of scientific thinking; probability analysis − to determine the form of distribution and probability density of the value of inflation indices, when calculating their entropy; R / Sanalysis − to calculate the dimensionality of the dynamics of price indices and determine its fractal similarity. Results. It is revealed that the dynamics of a significant number of monthly price indices in Ukraine for the period 2003–2020 is not persistent. For these price indices it was not possible to form forecast time dependences of any kind with a sufficient level of reliability. The Hirst index for industrial producer price indices (by a whole industry, by mining industry, by metallurgical industry), agricultural producer price index, consumer price index and topological dimension of their dynamics is calculated. It is proved that the dynamics of these price indices has a fractallike pattern and corresponds to the stochastic fractals. Five fractal scales of the dynamics of price indices were formed on the basis of the obtained topological dimension. The form of the probability density function for each price index with a sufficiently high level of reliability is determined and the level of entropy and entropy production in each fractal of dynamics (as a whole by fractal and monthly average) is calculated. It is empirically proven that the average monthly entropy production decreases with increasing fractal scale. It is confirmed that during the crisis the aggravation of crisis phenomena coincides with the negative production of entropy in the fractals of the dynamics of price indices. Based on the results obtained above, a forecast is made for the dissipation / growth of entropy of price formation processes in the future. Novelty. The hypothesis on the dual nature of the dynamics of inflation in Ukraine in the 2003–2020 period (determined and indeterminate at the same time) was first proposed and confirmed, which was confirmed by the tools of R / Sanalysis and probabilistic analysis, prices in certain areas of economic activity with long time horizons. Practical value. The obtained results will contribute to the improvement of inflation forecasting processes in Ukraine and can be used to form longterm forecasts of the dynamics of other price indices and macro levels. 
Literature:   1. Mironchuk, V.M., & Chubar, Yu.K. (2018). Prohnozuvannia infliatsii v Ukraini: bahatofaktorna ekonometrychna model. Infrastruktura rynku, Issue 8, 161166.
 2. Pistunov, I.M., & Udovizhka, K.O. (2018). Prohnozuvannia infliatsii v Ukraini na 2018 rik. Globalni ta natsionalni problemy ekonomiky, Issue 22, 10581065.
 3. Averkina, M.F., & Katok, D.K. (2018). Modeliuvannia rivnia infliatsii v Ukraini. Derzhavne upravlinnya: udoskonalennia ta rozvytok, (5). Retrieved from http://www.dy.nayka.com.ua/pdf/5_2018/3.pdf.
 4. Holiuk, V.Ya., & Podvalna, V.V. (2017). Analiz dynamiky ta prychyn infliatsii v Ukraini v 19912016 rr. Naukovyy visnyk Khersonskoho derzhavnoho universytetu, Ser. «Ekonomichni` nauky», Issue 24, Part 2, 6972.
 5. Lukianenko, I.G. (2009). Metodolohichni pidkhody do modeliuvannia infliatsiynykh protsesiv/ Naukovi zapysky. Ekonomichni nauky, T. 94, 5864.
 6. Tsiny. Statystyka NBU. Retrieved from https://bank.gov.ua/ua/statistic/macroindicators#1
 7. Tsiny. Ekonomichna statystyka. Statystychna informatsiia. Retrieved from http: // www.ukrstat.gov.ua/
 8. Gachkov, A.A. (2009). Randominizirovannyy algoritm R/Sanaliza finansovykh riadov. Proceedings from Stochasticheskaya optimizatsiya v informatike, Issue 5, pp. 4064. SanktPeterburg.
 9. Fomenko, A.T. (2018). Naglyadnaya geometriya i topologiya: Matematicheskiye obrazy v realnom mire. Moskva: Izdatelstvo MGU.
 10. Mavrikidi, F.I. (2008). Fractalnaya matematika i priroda peremen. «Delfis», 54(2). Retrieved from http://www.delphis.ru/journal/article/fraktalnayamatematikaiprirodaperemen
 11. Katok, A., & Hasselblatt, B. (1998). Introduction to the Modern Theory of Dynamical Systems. Cambridge University Press. 824 p.
 12. Khaytun, S.D. (2007). Ot Ergodicheskoy gipotezy k fraktalnoy kartine mira. Rozhdenie i osmyslenie novoy paradigmy. Moskva: Komkniga.
