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.

Entropy is one of the most frequently and effectively used measure of the complexity of systems of various nature. And if the Shannon's canonical entropy is more a measure of the randomness of the system, then the approximate, sample, permutation and other new type entropy that have appeared recently, exploiting the Shannon entropy form have allowed us to quantify the complexity of the systems in question using fast and efficient algorithms. For the first time, a new type of recurrence entropy is used to analyze the dynamics of financial time series under crashes conditions. It is shown that recurrent entropy can be used as the indicatorpredictor of financial crashes.

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.

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