Innovative approaches to model and forecast of Azerbaijan's economic growth

. One of the indicators of the country's economic growth is the gross domestic product, and one of the factors of economic growth is capital. The main criteria and source of economic development is economic growth. Economic growth is a sustainable increasing tendency of the main indicators of national theory production. Furthermore, absolute value and growth per capita are also considered. The objective and subjective aspects and components of the processes of formation and development of economic growth are investigated. The essence and characteristics of objective and subjective factors of the country's economic growth are given. In economics and statistics, various indicators are used to measure the volume of national production. The most important of these is the gross domestic product. Gross domestic product is expressed by the monetary unit of the final products and services produced in the economy. The fact that gross domestic product comprises final products and services produced within a particular country should be considered. Moreover, the most important is the diversification of sources of gross domestic product growth and ensuring the multiplier influence of the interconnected sectors of the country's economy to increase gross domestic product growth. In this work, the dynamic model that demonstrates the dependence of gross domestic product on investments in the case of the Azerbaijan economy is created. Based on this model, it is possible to more optimally plan and predict promising sources and strategic directions for developing the national economy and ensuring its intensive growth. This approach provides an opportunity for the country's strategic planning of the gross domestic product. In this work, to achieve the desired level of gross domestic product, the volume of investment is used as the independent variable in the dynamic model. However, as indicated above, many other factors affect the amount of investment in gross domestic product. Nevertheless, the dynamic model of the optimal gross domestic product trajectory yielded good results. In modern conditions, optimal and effective modelling is essential to ensure the dynamic development of the country's economies and gross domestic product based on global changes and factors. Similar approaches create opportunities to strengthen the immunity of the national economy to counter global impacts and risks. Further research will consider the other most influential factors on gross domestic product. In this case, a dynamic model of the optimal trajectory of the gross domestic product will give even more adequate results.


Introduction.
The main criteria and source of economic development is economic growth.Economic growth is a solid stimulant for the growth of the leading indicators of national production (GDP, GNI).Furthermore, Absolute value and growth per capita are also kept in mind.In economic theory and statistics, various indicators are used to measure the volume of national production.The most important of these is gross domestic product (GDP).GDP is an expression in the monetary unit of the final products and services produced in the economy.This refers to the final products and services produced Marketing and Management of Innovations, 2022, Issue 2 199 http://mmi.fem.sumdu.edu.ua/enwithin the borders of a particular country.
Three main methods are used to calculate GDP: 1) Added value method (production method).With this method, GDP is determined by the sum of added values on the cost, wages and income generated in the production process and characterised by the actual share in the final product in this enterprise for all sectors and types of production; 2) By expenses.Using this method, the GDP is calculated as the sum of all expenses in society (daily expenses of the population, investments of producers, expenses of the government on goods and services), net exports (balance of imports and exports of the country); 3) Calculation of GDP by income -the total amount of all income in the company (excluding the wages of workers being paid from the state budget, as long as their wages are paid from the state budget), property income, income, interest on capital, depreciation, rent payments.
The timeliness of the topic is brought about by the global threats and new challenges in the field of effectiveness, increase of the economic mechanisms taking into account the innovatization of the national economy and the intensification of the use of high technologies, including 'smart technologies'.Under these conditions, it is especially necessary to deepen innovative functions and approaches to the maximum optimisation of the existing mechanisms of the economic development model in the country and forecasting of the economic growth, including expansion of GDP formation sources.Over the last 10-15 years, the economy in Azerbaijan increased almost three times.However, economic contraction is observed due to the negative impact of global problems, especially the covid-19 pandemic, in recent years.Therefore, new and improved mechanisms are required to increase economic growth and GDP intensifying.
There are objective and subjective factors of economic growth.Objective factors are factors that directly and finally affect the rate of economic growth.Subjective factors are indirect factors affecting the scale and pace of economic growth.
The objective factors of economic growth are the following: 1) increase in the volume and quality of fixed capital; 2) changes in production technologies; 3) increase in the volume of economic resources; • increase in entrepreneurial activity of the population; • increase in the quantity and quality of labour resources; • Activation of the population's needs, leading to an increase in production volumes.Subjective factors of economic growth are the following: • expansion of the credit system.The activation of this system allows the population to consume as much as possible.This, in turn, stimulates production.
• Reduction of monopoly in the markets for products and services.This, in turn, activates entrepreneurial activity; • Reducing the cost of production resources.This process increases production and prices.This, in turn, allows for growing demand.
• Tax cuts.Tax cuts lead to an increase in overall economic activity.
• At the present stage of economic development, economic growth affects the following factors: • natural resources directly affect economic growth.The value of these resources is growing every day since resource resources are limited; • Population growth, increase in labour resources; • increase in the capital within the borders of the country.The increase in capital creates opportunities for increasing production and scale, conducting new scientific and technical research and investing in human resources; • scientific and technological progress, which is the basis of economic growth, as scientific and technological progress, contributes to the transition of the quality of economic development to a new level.
The relationship between economic growth factors within the national economy is becoming more http://mmi.fem.sumdu.edu.ua/encomplicated.In such a situation, the state's primary goal is to effectively use existing economic factors to promote economic growth to benefit the general populace, as said by Zang (1999).
As mentioned above, one of the indicators of a country's economic growth is gross domestic product (GDP), and one of the factors of economic growth is capital.A dynamic model that demonstrates the dependence of GDP on investment in the country's economy is given in the article.
Literature Review.The central hypothesis is optimising the dynamic system of fundamental problems in revealing reserves and turning them into productive sources of GDP growth and the added value to the country's economy.Similar approaches solve the accumulated problems based on optimal and integrated solutions with the development of more effective measures and mechanisms in the economic system.In the works of Barro andLee (1994), Bryson (1972) and Gurman (1995), attention is paid to the analysis of sources and determinants of growth.Further, the most important aspect is the macroeconomic analysis, which identifies the predominant factors used by the economic -organisational and management mechanisms to ensure GDP growth (Goliuk, 2017).
In their research and approaches, Wang and Li (2021) review several important issues concerning resource potential, the issues of effective use of the human capital and labour force, the use of production forces, and its role in strength improvement of the national economy.In Aslanli (2015) research, the formation of foreign exchange reserves due to the incomes of the oil export and the implementation of more effective mechanisms for insurance of sustainable economic growth are reviewed.
In the work of Hasanov and Huseynov ( 2013), a special emphasis is placed on the economic and financial aspects of the processes of ensuring the growth of the output in the non-oil sectors in the economy of Azerbaijan, which can help to reduce the dependence of the economy on the oil and gas factor and help to form more productive sources of economic growth.The most critical issues and factors provoking an increase in inflation, which has a negative impact on social and economic, macroeconomic and macro-financial stability, are considered then.The author reviews a number of priorities for the enhancement of the economic activity and improvement of the active economic mechanisms for restraining the inflation rate and insurance the sustainable economic growth in Azerbaijan.
Besides, the works of Ciarreta and Nasirov (2012) consider the most important trends of oil and gas sector development in Azerbaijan, which has a decisive influence on the development of the economy of the country, GDP growth, insurance of competitiveness of Azerbaijan in the international system of differentiation of labour and on the formation of the country as one of the strategic energy partners of the EU.
The scientific work of Sabiroglu and Bashirli (2012) considered the economic policy and sources of economic development in Azerbaijan in the context of oil export and the income of the oil revenues.The main argumentation of the authors lies in the innovatization of the economy in the country and the creation of abundant sources of GDP growth alongside the oil and gas sector (Hassan et al., 2011).
In the approaches of Golichenko (1999), Jurasek and Potocky (2020), and Mikhnevych et al. ( 2020), bias is made on conditions of imperfect competition.The need to preferentially use a more innovative focus on the development of economic processes and certain sectors of the national economy is justified, thereby accelerating the formation of more reliable sources of economic growth; mainly, the country's GDP is considered.In scientific arguments and assumptions of a group of scientists - Hasanli and Ismayilova (2017), Huseynov (2021), Huseynov et al. (2021) modelling of national economy due to econometric calculations and correlation with identification of interrelation and the primary elements promoting the acceleration of GDP growth is considered.In addition, the emphasis is on innovative development, considering balancing the country's socio-economic development in the context of global shocks and threats.Group of researchers -Hvolkova and Klement (2019), Roubini and Sala-I-Martin Marketing and Management of Innovations, 2022, Issue 2 201 http://mmi.fem.sumdu.edu.ua/en(1992), Levchenko et al. (2018), Zang (1999), and Kasaeva (2019) most all drew attention to the possibilities of expanding the structure of the economy to ensure GDP growth, taking into account the increase in the efficiency of the applied economic mechanisms, natural, financial, labour and, in general, economic resources to increase the growth of the country's economy (Acemoglu et al. 2005).
In the works of a number of Azerbaijani scientists -Ibraghimov (2022), Ibrahimovet al. ( 2021) focus given to the innovative development of the Azerbaijani economy, increasing the competitiveness of certain sectors of the national economy in the context of sustainable development with the involvement of the required financial and credit resources with the active participation of banking and credit organisations and the use of financial inclusion mechanisms, which could have a positive effect on economic growth.
The main aim of the article is to develop and realise the more effective mechanisms and models considering the active use of innovative approaches and functions for optimisation of the economic calculations and forecasts of the dynamic development of the economy in Azerbaijan, including in particular the sustainable growth of the GDP.It is necessary to form a more optimal and productive environment for the activity and development of the national economy and, thus, ensure the innovativeness of the data in the article of calculations and forecasts on the dynamics of the economy's growth in the country as a whole.
Methodology and research methods.The structure built by the author is taken as methodological approaches and analyses, where the main goal is optimal research and forecasting of GDP in Azerbaijan in the context of global transformation and a period of difficulty in ensuring the dynamic growth of the country's economy.The main factors and problems associated with the slowdown or vice versa, intensification of GDP growth, have been consistently analysed.The main methods and forms of GDP calculation with emphasis on expenses and income, as well as a grouping of objective and subjective factors of economic growth in Azerbaijan, are systematised.Several important approaches are substantiated that could positively affect GDP growth, for example, minimising monopolism in different sectors of the economy and further optimising the stimulating effects of tax mechanisms and instruments.The views and arguments of Zang (1999), who considered the relationship between a number of factors of economic growth in the structure of the country's economy, are used as methodological approaches.
Further, the author considered it advisable to build a model of the optimal trajectory for achieving the desired level of GDP, taking into account the determination of the amount of investment to solve this problem.In this case, the coefficients are determined by authors Shafizade and Hasanova (2018) and Golichenko (1999).Based on analysis and synthesis, as well as carrying out mathematical calculations and solving problems, the effectiveness of factors that allow strategic planning and forecasting of GDP growth is further determined.At the same time, the volume of investments is considered one of the key factors contributing to GDP growth.
The model of the optimal trajectory to achieve the desired level of GDP was developed and estimated.The reliance is placed on attracting the required volume of investment resources and capital to various sectors of the national economy, thereby ensuring the dynamism of GDP growth.Further, the statistical data on the volume of GDP and investments in the industry of Azerbaijan in 2006-2020 and indicators of GDP were used, as well as the results of the calculated model Model Values of GDP in 2006-2020.
The model of the optimal trajectory to achieve the desired level of GDP.Consider the following task: how much investment should be allocated in a certain year to achieve the desired level of GDP after a certain time?

Results. The Model Of
The Optimal Trajectory To Achieve The Desired Level Of GDP was applied to Azerbaijan based on statistical data (Table 1).From 2006-2020 the GDP in Azerbaijan had dynamic growth.However, unstable growth has been observed over the past seven years: for example, in 2015, the GDP growth in Azerbaijan decreased by % 8,46 in comparison with 2014.In 2019 the economic development slowed down, and in 2020 the national economy decreased its development rates by %13.12 because of covid-19.From this data,  0 was found to be 18746.2.Problems ( 26)-( 28) were reworked in MATLAB with coefficients k1=-5, k2=0.6,q=100000.The following results were found (Table 2): Table 2 shows the dynamics of GDP, considering the expected effect from the invested investment resources according to the Model Values of GDP.A visual comparison of the statistic GDP values and GDP values to achieve the desired level is given in Figure 1, from which we can see that the actual results are not adequate to the calculations obtained due to the development and calculation of models.Therefore, maximum optimisation and deepening of the innovativeness of the existing mechanisms for forecasting and organising the activities of various sectors of the national economy are required following new challenges and requirements.So, suppose we summarise the research materials on the most critical factors of the modelling process in the context of forecasting GDP in Azerbaijan.In that case, they can be grouped in the following blocks (Table 3).

Table 3. Rational scheme of GDP forecasting in Azerbaijan
Components of GDP forecasting model construction Questions to be answered

Theoretical approaches
It is necessary to analyse theoretical approaches and foundations, problems of ensuring GDP growth, and it is necessary to answer the question: how do we more effectively build a model for predicting GDP in Azerbaijan?

Methodological features
The methods and approaches of various authors and scientists are used, who studied the essence of the problem of ensuring economic growth and the development of methods of accelerating GDP growth with the solution of the problem: how better use objective and subjective factors for economic growth in the context of global transformations?

Formation of the prediction model
Based on the task and perspectives of the development of the country's economy, determining the sources of economic growth required answering the following questions: how to construct an optimal model for ensuring the projected level of the country's GDP?

Objectives and conclusions
Research, analysis, synthesis and generalisation are needed to answer the following questions: what factor most affects the country's adequate GDP growth in the current global transformations?
Sources: developed by the authors.
As a result of research, based on calculations and estimates, it is concluded that among the factors affecting GDP growth and the success of the country's GDP forecasting model, the key factors are adequate definitions of the volume of investments and the effective use of available resources in the processes of forming the main sources of growth of the country's economy in current conditions.
Conclusions.This approach provides an opportunity for strategic planning of GDP for the country.In this work, to achieve the desired level of GDP, the volume of investment is used as the independent variable in the dynamic model.Nevertheless, as indicated above, many other factors affect GDP, Marketing and Management of Innovations, 2022, Issue 2203 http://mmi.fem.sumdu.edu.ua/en

Figure 1 .
Figure 1.Comparison of statistical GDP values (red line) and GDP values to achieve the desired level (blue line) Sources: developed by the authors based on (The State Statistical Committee of the Republic of Azerbaijan).