Use of the Fractal Analysis of Non-stationary Time Series in Mobile Foreign Exchange Trading for M-Learning A. Kuchansky 1 , A. Biloshchytskyi 1 , S. Bronin 1(&) , S. Biloshchytska 2 , and Yu. Andrashko 3 1 Taras Shevchenko National University of Kyiv, Kiev, Ukraine kuczanski@gmail.com, sbronin@me.com 2 Kyiv National University of Construction and Architecture, Kiev, Ukraine 3 State University “Uzhhorod National University”, Uzhhorod, Ukraine Abstract. Mobile foreign exchange trading system for m-learning is proposed. It’s used for time series analysis skills learning. Method of pre-forecasting fractal R/S analysis of non-stationary time series is integrated in system. This method includes: persistence, anti-persistence and random level determination based on the calculation of the Hurst exponent. To calculate the average value of the nonperiodic cycle of time series, as well as to establish the potential prof- itable of assets that are represented by financial time series. A criterion for determination of the average length of non-periodic cycles based on the smoothing of V-statistics with simple moving average and Kaufman’s adaptive moving average is proposed. It has been confirmed that most financial time series are more or less persistent and endowed with long-term memory of their initial conditions using computer simulation. Time series of course pairs are close to random. Using fractal analysis in m-learning mobile foreign exchange trading systems for smartphones based on iOS or Android operating systems is suggested. The system is characterized by visualization and description of all stages, which has to be executed for time series analysis. Practical use of this system has shown high ef ficiency for time series analysis skills learning. Keywords: M-learning  Mobile foreign exchange trading system  R/S- analysis  Hurst exponent  Time series 1 Introduction 1.1 Introduction to Time-Series Analysis for M-Learning Tasks The most part of economic, physical, technical and natural processes are non- stationary. Time series representing these processes are the following components’ complex: trend’s function component, cyclic components with different periods, fluc- tuations, etc. While forecasting such time series certain dif ficulties may be faced. Thus, learning system development is up to date and top notch ad it allows to train financial market traders and analysts. Trained specialists will obtain skills in time series analysis, profitability of assets assessment, forecasting tools effectiveness, etc. © Springer Nature Switzerland AG 2021 M. E. Auer and T. Tsiatsos (Eds.): IMCL 2019, AISC 1192, pp. 950–961, 2021. https://doi.org/10.1007/978-3-030-49932-7_88