# Mathematical Models for Forecasting Unstable Economic Processes in the Eurozone

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## Abstract

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## 1. Introduction

## 2. Literature Review

## 3. Mathematical Model

- The main factor that increases the inflation rate is the growth in the money supply;
- The key role is played by the equilibrium state of the money market;
- The nominal interest rate is determined through the real interest rate and the expected inflation rate (Fisher identity).

- Model of the dynamics of economic growth (recession):$${q}_{Y}={q}_{\overline{Y}}+\rho \left[\frac{1}{\alpha}{\left(\frac{k\mu}{d}\right)}^{\frac{1}{\alpha}}\left(\frac{\dot{\mu}}{\mu}-\frac{\dot{d}}{d}\right)-\dot{r}\right]$$
- Model of forecasting inflation rates:$$\pi =\mu +\frac{\dot{\mu}}{\mu}-\frac{\dot{d}}{d}-{q}_{Y}$$

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Quarterly dynamics of inflation in the Eurozone between March 2015 and March 2023 (developed by authors based on [40]).

**Figure 2.**Quarterly Eurozone GDP dynamics (in 2010 prices) between March 2015 and March 2023 (developed by authors based on [40]).

**Figure 3.**Quarterly dynamics of the monetary base in the Eurozone between March 2015 and March 2023 (developed by authors based on [40]).

**Figure 4.**Quarterly dynamics of the interest rate in the Eurozone between March 2015 and March 2023 (developed by authors based on [40]).

**Figure 5.**Quarterly dynamics of the Eurozone budget deficit between March 2015 and March 2023 (developed by authors based on [40]).

**Figure 6.**Forecasts for the Eurozone on (

**a**) inflation and (

**b**) GDP growth. Source: [41] (developed by authors).

**Figure 7.**Actual and simulated interest rates (developed by authors based on [41]).

**Figure 8.**Simulated growth (decline) rates in the Eurozone for (

**a**) inflation and (

**b**) GDP. (Developed by authors based on [41].)

**Table 1.**Expected macroeconomics indicators in the Eurozone for 2023–2024 (Source: [41]).

Eurozone Forecasts | 2023 | 2024 |
---|---|---|

Average annual inflation rate (%) | 5.8 | 2.775 |

GDP dynamics (%) | +0.95 | +1.425 |

Main Indicators | 2023 | 2024 | 2025 | 2026 | 2027 |
---|---|---|---|---|---|

Money supply growth (%) | 0.06 | 0.05 | 0.05 | 0.06 | 0.06 |

Interest rate (%) | 4.00 | 2.93 | 0.78 | 0.21 | 0.10 |

Budget deficit (% of GDP) | 3.00 | 3.00 | 3.00 | 3.00 | 3.00 |

Inflation (%) | 6.11 | 5.13 | 5.12 | 4.77 | 3.88 |

GDP growth (%) | 0.34 | 1.32 | 1.34 | 1.69 | 2.58 |

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**MDPI and ACS Style**

Akaev, A.; Zvyagintsev, A.; Devezas, T.; Sarygulov, A.; Tick, A.
Mathematical Models for Forecasting Unstable Economic Processes in the Eurozone. *Mathematics* **2023**, *11*, 4544.
https://doi.org/10.3390/math11214544

**AMA Style**

Akaev A, Zvyagintsev A, Devezas T, Sarygulov A, Tick A.
Mathematical Models for Forecasting Unstable Economic Processes in the Eurozone. *Mathematics*. 2023; 11(21):4544.
https://doi.org/10.3390/math11214544

**Chicago/Turabian Style**

Akaev, Askar, Alexander Zvyagintsev, Tessaleno Devezas, Askar Sarygulov, and Andrea Tick.
2023. "Mathematical Models for Forecasting Unstable Economic Processes in the Eurozone" *Mathematics* 11, no. 21: 4544.
https://doi.org/10.3390/math11214544