Introduction. Education is an indicator of the country's intellectual potential. Higher education is a strategic resource through which the state is competitive in the global labour market.complete higher education attests to the professional and cultural level of a considerable number of the population, especially young people, and is not only an indicator of economic growth but also of social stability. The purpose of investigation was determined by the analysis of current state of higher education institutions and the main influencing factors for them. The coefficient of interest of graduates in receiving higher education in Ukraine is determined on the basis of regression analysis. Arima models were constructed using time series theory for prediction of the number of higher education institutions for future periods. Purpose. The purpose of the study is the construction the predictive models of the dynamics of the number of future students and the number of higher education institutions in Ukraine. Methodology. Regression analysis is used as one of the main methods of scientific research in the process of writing the article; time series theory, in particular Arima modeling of the Statistica application package; methods of mathematical modeling, in particular approximating polynomials in the process of modeling the dynamics of the institutions of higher education and the number of students, to determine the ‘coefficient of interest’. Results. The study found that the number of institutions of higher education depends on the one hand on the time factor, on the other – on the number of students. Given that the number of students and the amount higher education institutions can be characterized as a dynamic process, the theory of time series, in particular Arima modelling, was applied. Using Arima models, the number of students and the number of higher education institutions for the next two years is predicted. The relative errors for these models are 6% and 0. 4%, respectively. Based on statistics on the number of graduates of all secondary education institutions and the number of students admitted to higher education institutions of Ukraine, a ‘coefficient of interest’ in higher education was derived, which allows predicting the number of future entrants. The Arima model predicts the number of Ukrainian students in foreign educational institutions. The obtained forecast values regarding the number of students, the amount of higher education institutions of Ukraine, by various methods, adequately reflect the real situation today.
Introduction. The article examines the trends in the levels of average wages, minimum wages and subsistence minimum, which are extremely important for the analysis of wealth and well-being of the population of Ukraine. The time trends of these indicators are constructed and the regularities of their change during 1996-2020 are established. The Keitz index is calculated and investigated. The dependences of the average wage, the minimum wage and the subsistence level on the gross domestic product are analyzed and established. The values of the values of the mutual correlation function are investigated. Purpose. The purpose of this article is a mathematical and statistical analysis of the dynamics of wages and living wage in Ukraine and the factors influencing them. The task is to study the impact of gross domestic product on the average wage, minimum wage, subsistence level and establish a causal relationship between them using mathematical, statistical and econometric models in order to further predict them and make recommendations on social indicators of living standards. Method. The article uses mathematical and statistical methods and regression-correlation analysis as the main methods of scientific research; time series theory; methods of mathematical modeling. Results. Analyzing the statistical data of indicators of average wages, minimum wages, subsistence level and gross domestic product in Ukraine for 1996-2020, their dynamics is studied. Trend models of wage levels and subsistence level have been built. The general tendency of their growth is noted. Emphasis is placed on the need to use mathematical modeling to study socio-economic indicators of living standards. The Keitz index, which reflects the fight against poverty, is calculated and analyzed. It is noted that during 1996-2009 the subsistence level exceeded the minimum wage. In 2010-2011, the values of the minimum wage slightly exceeded the subsistence level; and in subsequent years, small amounts were observed, until 2017 the minimum wage was not doubled. This positive trend has also been observed in recent years. Econometric models of dependence of average and minimum wage on gross domestic product are presented. The correlation-regression dependence of the subsistence minimum on the gross domestic product is constructed. It is shown that the growth of gross domestic product is accompanied by an increase in social indicators of living standards of the population of Ukraine. The values of the values of the mutual correlation function between the gross domestic product and the levels of wages and subsistence, respectively, are calculated and investigated.
Introduction. The hybrid war waged by the russian federation against Ukraine turned into a full-scale military invasion in February 2022. One of the components of Russian military losses in the war is the loss of equipment and personnel. The purpose of the study is to forecast losses of Russian military equipment and its personnel in Ukraine. Methodology. In the process of writing the article, a systematic approach was used as one of the main methods of scientific research; properties of time series, in particular, the Arima model, for determining forecasts. Arima(p,q)(D,Q) was used to model the forecast dynamics of Russian personnel losses in Ukraine. Forecasting losses of Russian equipment is described by Arima(p,d,q). The results. Based on the data analysis of the time period, from February 24, 2022 to March 7, 2023, a conclusion was made about the possibility of using the properties of time series, in particular, the use of time series forecasting by Arima methods. The following models were built: Arima (1,0,1)(0,1,1) – to forecast Russian personnel losses; Arima (1,0,1) – forecasting Russian equipment losses in Ukraine. The performance of these models was checked for adequacy. Based on the obtained models, the forecast for the next seven days is an increase in russian military losses of personnel with a decrease in losses of equipment units in Ukraine.
Introduction. Foreign trade operations significantly affect the development of each country's economy, in particular the value of gross domestic product, which is one of the main indicators of economic development and welfare of population. Therefore, it is necessary to study and model the impact of exports, imports and net exports on macroeconomic indicators of Ukraine. Purpose. The purpose of the article is to analyze publications that consider export-import operations of Ukraine, study of statistical information in this area, construction and analysis of econometric models of the dynamics of foreign trade operations of Ukraine and their impact on gross domestic product. Method. The article uses regression-correlation analysis as one of the main research methods; time series theory; methods of mathematical modeling. Results. The dynamics of foreign economic operations and gross domestic product of Ukraine are researched and analyzed. It is revealed that the balance of export-import operations has a significant impact on the gross domestic product of Ukraine. An econometric model of the dependence of the nominal gross domestic product on the value of exports of goods and services (coefficient of determination 0.9795) is calculated, using statistical information for 2005-2019 years. It is substantiated that with the increase in exports of goods and services by UAH 1 billion Ukraine's nominal GDP grows by an average of UAH 2.2642 billion. The value of coefficients of import dependence and coverage of import by export in foreign economic operations of Ukraine are analyzed. It is noted that the coefficient of import dependence significantly exceeds the allowable level in the study period, due to certain imbalances in foreign trade relations. The coefficient of coverage of imports by exports only in 2005 was greater than one, and during 2006-2019 it became less than one. In this regard, it is necessary to increase export operations, obtain a positive balance of payments, make effective economic and political decisions to increase exports of Ukrainian goods and services, reduce import dependence, using and implementing innovative methods of production and management.
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