**5. Conclusions**

The social and economic development of the Arctic region depends directly on the number of its residents, migration changes, and its migration attractiveness. The analysis of the region's migration attractiveness helps to identify the reasons for population outflow and, therefore, makes it possible to influence and eliminate them.

The study of the migration attractiveness of the Arctic regions was carried out in several stages. The first stage was devoted to a detailed analysis of the foreign and domestic literature on the problems and prospects of the development of the Northern territories, the migration attractiveness of the region, and various ways of assessing it. Analysis of migration processes in the Russian Arctic showed that there was an outflow of population from all regions over the past decade. The authors assume that there is a relationship between the migration processes currently taking place in the Arctic regions and their attractiveness to the working population.

In the second stage of the study, key social and economic indicators that contribute to the region's attractiveness to potential migrants were identified. For this purpose, the authors involved experts on the problems of economic development of the Arctic territories. The result of the expert survey was a list of 12 quantitative socio-economic indicators characterizing the attractiveness of the Arctic region.

To assess the dependence of migration processes on each of the selected socio-economic indicators, the authors conducted a correlation analysis using official data from state statistics bodies. It was revealed that not all indicators have a linear relationship with migration growth; simple relationships are attributed to a greater association between the number of

arrivals and departures in the region and the level of its social development. This confirms that the motives for moving to the Far North are not just economic incentives.

Migration processes were modeled using the tools of a complex-valued economy. In particular, simple linear regression complex-valued models were used that reflect the relationship between a pair of dependent and a pair of independent model variables. The number of arrivals and the number of departures in the Arctic region were selected as a pair of dependent variables. For the independent variable of the linear complexvalued model, four pairs of indicators were proposed that reflect the social and economic attractiveness of the region. Thus, the authors formed four linear complex-valued models in order to test them for their ability to form good predictions of migration indicators. Calculations performed on the Murmansk region as an example showed that these models are suitable for forecasting, since the values of the number of arrivals and departures in the region calculated for 2018 are close to the actual data.

In the final stage of the study, a comparative analysis of the attractiveness of the Arctic regions (Murmansk region and Nenets, Yamalo-Nenets and Chukotka Autonomous districts) was performed. The authors evaluated the integral indicators of the social and economic attractiveness of the region on the basis of 12 indicators by calculating the weighted averages. It was found that the most attractive region over a 10-year period in terms of the economic situation is the Yamalo-Nenets Autonomous district, whereas the Chukotka Autonomous district is the most attractive in terms of social conditions. However, it should be noted that the Yamalo-Nenets Autonomous district is the country's oil and gas center, which implies significant tax revenues at all budget levels, as well as a high level of income of the population. The Chukotka Autonomous district is a region with a minimum population density, which affects the statistical indicators in terms of their increase.

Further research in this area will focus on modeling migration processes in all Arctic regions using linear and non-linear econometric complex-valued models.

**Author Contributions:** Conceptualization A.C. and P.K.; Methodology A.C., P.K. and N.R.; Validation P.K.; Investigation A.C. and A.N.; Formal Analysis A.C., N.R. and A.N.; Writing—Original Draft Preparation A.C., N.R. and A.N. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Publicly available datasets were analyzed in this study. This data can be found here: https://eng.gks.ru.

**Conflicts of Interest:** The authors declare no conflict of interest.
