This is an introductory text to a collection of selected papers from the M3E2 2019: The 8th International Conference on Monitoring, Modeling & Management of Emergent Economy, which was held in Odessa, Ukraine, on the May 22-24, 2019. It consists of short introducation and some observations about the event and its future.

The paper focuses on monitoring and modelling of the cryptocurrency market. The application of the chosen research methods is based on the analysis of existing methods and tools of economic and mathematical modelling of time series research on the example of the cryptocurrency market. It is proved that the use of individual methods is not relevant, as they do not give an adequate assessment of the specified market, so a comprehensive approach is the most acceptable. Therefore, monitoring and modelling of some cryptocurrency pairs with different capitalization degree were implemented by fractal and recurrent methods of the financial markets. The daily values of currency pairs for the period from September 2015 to November 2019 were chosen as information basis for monitoring and modelling. The use of R/S modelling method make it possible to conclude the persistence of time series of the selected cryptocurrencies indicating that the market trends are clearly defined, the currency pair of XRP/USD has the highest level of trend resistance. To compare the obtained results, the comprehensive approach is offered using recurrent diagrams that help to determine the cryptocurrency stability. The results of modelling by the recurrent method show that the most stable cryptocurrencies are the ones with the highest capitalization, namely Bitcoin and Ripple.

The article describes the construction of a model for the analysis and forecasting of critical phenomena in economic systems based on the equation of the damped oscillations. The model of the damped oscillations based on the analysis of wavelet coefficient energy allows identifying critical phenomena, in the first place, crashes. Two parameters of the model, the initial phase and the damping coefficient, are the most appropriate for the analysis and prediction of the critical events in the economic systems. The sequence of steps for conducting research is presented and the possibility to automate the process of predicting critical phenomena is described. Critical phenomenon can be predicted based on the initial phase and the damping coefficient, the prediction horizon depends on the scale at which the model of the damped oscillations was constructed. The study of the results of the model is based on the known crashes and shocks given in the work.

In this article, we present the results of simulation for cryptocurrency market based on fractal and entropy analysis using six cryptocurrencies in the first 20 of the capitalization rating. The application of the selected research methods is based on an analysis of existing methodologies and tools of economic and mathematical modeling of financial markets. It has been shown that individual methods are not relevant because they do not provide an adequate assessment of the given market, so an integrated approach is the most appropriate. Daily values of cryptocurrency pairs from August 2016 to August 2020 selected by the monitoring and modelling database. The application of fractal analysis led to the conclusion that the time series of selected cryptocurrencies were persistent. And the use of the window procedure for calculating the local Hurst coefficient allowed to detail and isolate the persistant and antipersistant gaps. Interdisciplinary methods, namely Tsallis entropy and wavelet entropy, are proposed to complement the results. The results of the research show that Tsallis entropy reveals special (crisis) conditions in the cryptocurrency market, despite the nature of the crises’ origin. Wavelet entropy is a warning indicator of crisis phenomena. It provides additional information on a small scale.