In this paper, the labor market is investigated. Unemployment is one of the main problems of the Russian labor market. A crisis during the course of shock therapy in the 90s was followed by the Russian economy growth and unemployment rate decrease. Over the last ten years, the rate of unemployment in Russia tends to go down. This fact is noted both in researches based on the International Labor Organizationmethods and in statistics reports on the number of unemployed persons officially registered in Russia. Also, a particular imbalance between supply and demand of job vacancies depending on job positions is observed. On the one hand, it is the highest number of job openings for experts, doctors and engineers, and, on the other hand, it is the number of people looking for vacancies of accountants, lawyers, technicians, and economists. The rates of employment and unemployment, the supply and demand of job vacancies are very much different in various regions of Russia. The proposed prediction methods for job vacancy numbers in Altai territory labor market are utilized to investigate the trend of an economic indicator viable to the regional labor market. The prediction methods are based on the statistical ARMA model and fuzzy models of time series. The results of different predictions are evaluated, and changes in trend dynamics are investigated.