Development of an Econometric Model of Crisis and Assessment of the Crisis Risk

In this paper, the classification of crisis states and their dynamics is carried out. The asset crisis model is approximated and formalized. Invariant stationary components and the boundaries of crisis fluctuations are determined, which allows for predictions of the course of a crisis. The hypothesis of the phase invariance of crises is statistically confirmed, and four main phases and five marker points in the development of an investment asset crisis are distinguished. A statistical study of the changes in the value of 620 investment assets over 7 years (1,584,720 values) was conducted, including 710 crisis asset states (9940 values), which allowed us to formulate a mathematical model of crisis variability that makes it possible to detect the onset of crisis phases or the passage of marker points via the values of the first- and second-order derivatives of the model. This model has not only evaluative properties, but also predictive properties relative to the risk of a crisis asset, which is also confirmed experimentally. An experiment is conducted to assess the quality of the econometric crisis model, which is based on real historical data. The results of the experiment showed the high quality of the model as a crisis detection tool. A method of early detection of the initial crisis phase is developed, in which it is seen that a statistically unpredictable state causes such a change in the indicator that it violates the valid bound constraints.