# Modeling of Crisis Processes in the Financial Market

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## Abstract

**:**

## 1. Introduction

## 2. Literature Review

## 3. Modeling of Crisis Processes Based on Moments of Higher Orders

- If the distribution is symmetric with respect to the mathematical expectation, then the coefficient of skewness is $Skew\left(X\right)=0$.
- If $Skew\left(X\right)>0$, then the distribution has a right-sided skewness.
- If $Skew\left(X\right)<0$, then the distribution has a left-sided skewness.

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## 4. Development of an Indicator for Crisis Detection

- Instantaneous (using only current data);
- Moving averages (using, in addition to the current data, previous data for a certain period);
- Cumulative (using all the data from the beginning of the time series).

- Direct (not using intermediate calculations);
- Indirect (using intermediate calculations).

- An instantaneous indicator that determines the crossing of a certain bound. Figure 4 shows a graph of the instantaneous indicator.
- A moving indicator that determines the 30-day average (moving average) (see Figure 5).
- Cumulative indicator that calculates the achieved mathematical expectation (see Figure 6).

- Scaling by the maximum of the series is used in cases when the series is completed and there will be no new data.
- Scaling by the current maximum reached is used when the next data are expected to arrive.
- Nonlinear reversible compression is used to improve the statistics of data with a large number of outliers.

## 5. Variability

- Mean absolute deviation (MAD) is the average of the modulus of deviations of the series values from its mathematical expectation.
- Variance is the mathematical expectation of the squares of absolute deviations.
- Mean square deviation (standard deviation) is the square root of the variance.
- Scedasticity (relative variability) is the ratio of the modulus of deviations to the mathematical expectation.
- Mean cubic deviation is used to identify the trend of growth/decline hidden by white noise. An example is the cubic root of the mathematical expectation of cubes of absolute deviations.
- Mean progressive deviation is used to identify the trend of hidden growth.
- Mean structural deviation is used in the frequency analysis of econometric data.
- Volatility is a measure of the variability of a time series expressed with reference to a time scale. The ratio of the standard deviation to the root of the time period expressed in years.

## 6. Model of Crisis

- Power function: R = 0.942
- Sixth-order polynomial: R = 0.994
- Trigonometric functions: R = 0.997

## 7. Conclusions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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Stage of Development | ${{\mathit{\sigma}}_{\mathit{\sigma}}}^{\prime}$ | ${{\mathit{\sigma}}_{\mathit{\sigma}}}^{\u2033}$ |
---|---|---|

Crisis at an early stage, Initial stage | >0 | 0 |

Acceleration of growth rates | $>0$ | $>0$ |

Slowdown of growth rates | $>0$ | $<0$ |

Plateau of crisis | $0$ | $0$ |

Acceleration of decline rates | $<0$ | $<0$ |

Slowdown of decline rates | $<0$ | $>0$ |

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Ivanyuk, V.
Modeling of Crisis Processes in the Financial Market. *Economies* **2021**, *9*, 144.
https://doi.org/10.3390/economies9040144

**AMA Style**

Ivanyuk V.
Modeling of Crisis Processes in the Financial Market. *Economies*. 2021; 9(4):144.
https://doi.org/10.3390/economies9040144

**Chicago/Turabian Style**

Ivanyuk, Vera.
2021. "Modeling of Crisis Processes in the Financial Market" *Economies* 9, no. 4: 144.
https://doi.org/10.3390/economies9040144