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Investment potential forecast and strategies for its expansion: case of Ukraine

In the current conditions of capital market liberalization, developing countries achieve a faster economic growth rate by actively attracting various types of foreign investment. The steady rise in the volume of foreign investment into the country could be achieved only due to its high investment potential. Therefore, this study aims to develop the methodology for determining the dynamic changes in the country’s investment potential, and its relevant medium-term indicators identify the degree of informational technology influence on Ukraine’s investment potential. It is essential to define the position of Ukraine in the global context in terms of the level of information technologies as the catalyst for investment attractiveness. The relevant indicators defining Ukraine’s investment potential were forecasted using the Brown-Meyer exponential smoothing model. To calculate the integral indicator of the investment potential, the Hurst exponent was applied. Kohonen self-organizing maps were used to group the countries according to their informational technology parameters. Ukraine’s investment potential was found to decrease since 2019 and is equal to 0.6493 units in 2020 and 0.6407 units in 2021 due to the decline of the indicators describing the human capital, infrastructure, technological development, and socio-economic conditions. Technology has a significant influence on Ukraine’s investment potential. Its impact is rising each year from 1.70% to 5.17% and 13.04% between 2019 and 2021, respectively. According to the level of technology, Ukraine is in the group with Spain, Romania, and Poland since 2017. The decreasing investment potential forecast and the positive influence of technology level on it bring the opportunity to form the priority areas for expansion of investment potential based on the adaptation of world instruments to implement the investment policy within national economic conditions. the highly innovative and technological national projects. It significantly reduces the time necessary to achieve high indicators of social and economic development and brings them opportunities to get all the advantages of modern society. However, every year, investors impose strict requirements for investment facilities and investment attractiveness of the countries they plan to invest in. Such a condition has led to the need for recipient countries’ governments to develop effective investment strategies for certain sectors of the economy and the country in general.


INTRODUCTION
Due to globalization processes, the development of international financial markets provides an opportunity for developing countries to attract investment for embarking on the highly innovative and technological national projects. It significantly reduces the time necessary to achieve high indicators of social and economic development and brings them opportunities to get all the advantages of modern society. However, every year, investors impose strict requirements for investment facilities and investment attractiveness of the countries they plan to invest in. Such a condition has led to the need for recipient countries' governments to develop effective investment strategies for certain sectors of the economy and the country in general.

LITERATURE REVIEW
Over the last decades, investment was the object of scientific research and a vector of social development for prominent political figures. In 2014, a report "Catalyzing a global market in impact investment", initiated by the Prime Minister of the United Kingdom David Cameron, was published. He has formed a group of more than 200 professionals from around the world to conduct surveys throughout the year to identify the potential impact of investment on improving society and the environment. As a result, conclusions were drawn about the leading role of investment in the process of becoming a modern society and development of all countries, and recommendations were made for managing the activities of governments, business, the social sector, and international funds. However, the role of investment in contemporary society has been explored differently in the works of Lagendijk and Hendrikx (2009). Thus, in parallel with determining the leading role of foreign direct investment in the structure of the global economy, the authors critically determine the strengthening role of neoliberal regulation in lob-bying the investment interests of global corporations and their home countries. Therefore, it is fair to say that the topic under study is relevant.
The place of investment in the progressive development of the world economy and international economic relations was explored by Meltzer (2015). He analyzed the investment commitments in bilateral and regional free trade agreements. Moreover, this author pays special attention to the protection of investors' rights and emphasizes the impossibility of state expropriation of private investments, even directed at infrastructure objects. The development of international investment law theory was addressed by Desierto (2016) and Schill (2009) who attempt to summarize the existing practices of state-investor relations and to establish international rules for dispute resolution. Sauvant and Sachs (2009) narrowed the legal issue of investing in bilateral investment treaties (BITs) and double taxation treaties (DTTs). Researchers cite positive and negative aspects of the effect of BITs and DTTs on foreign investments. The researchers pay attention to the legal peculiarities of interaction between international investors and the state, as there is a need to establish equal "rules of the game" in the international market. The solution to any national task of attracting investment into the economy is impossible without a clearly defined legal framework. The negative experience of legal settlement of investment disputes between investors and the state will lead to loss of the flow of international financial resources, even despite the effective national investment strategy. However, in this study, no attention is paid to the legal framework for the formation of the state's investment potential. It is considered a necessary condition for modeling.
In scientific research, it is also necessary to take into account that the investment occurs in the conditions of uncertainty. Chevalier-Roignant, Flath, Huchzermeier, and Trigeorgis (2011), as well as Abel and Eberly (2016), establish multidimensional factors that at different time intervals, can inequitably affect both the cost and the volume of investment. In the proprietary methodology for calculating the investment potential, it is taken into account using the Brown-Meyer model.
Exploring the priority areas of investment that the state should support, Perrotta (2018), Hu (2011), and Schultz (1961) define human capital as the most productive area of investment since its multiplication ensures the continuous growth of the national product. Richard, Holton, and Katsioloudes (2014) investigated the investment in human capital, such as in leadership development interventions. Scientists have analyzed the monetary return on investment in leadership development based on utility analysis (computer simulation modeling to generate random distributions of each utility analysis variable). Continuing to explore priority areas for investing, one should focus on the works of Bojanc, Jerman-Blažič, and Tekavčič (2012). These researchers have demonstrated the importance of investing in information technology. Thus, a mathematical model for optimal evaluation of an investment in security technology has been developed, based on which decisions are made on the feasibility of introducing innovative developments on bank risk identification. Giel, Issa and Olbina (2019) confirm the relevance of investing in the latest technologies. Thus, the authors compared two identical projects, but one of them was implemented with investment in in-novative development, and the other was not. The analysis was based on the measurable cost benefits associated with reduced schedule overruns and reduced change order costs. Based on other numerous scientific works on relevant indicators of investment activity, in the framework of the original research, the following five groups of relevant indicators characterizing the investment potential were selected: socio-economic conditions, science and education, technologies, infrastructure, environment and human health.
Continuing the study of the mathematical formalization of various processes associated with the behavior of investment, and the implementation of investment activities, the works of the following scientists are used. Gomes (2001) formalizes the relationship between investment and cash flow when organizations face the cost of accessing external funds. Myers and Majluf (1984), representatives of behavioral theory, mathematically formalized the peculiarities of the firm's investment activities. They have proposed an equilibrium model of the issue-investment decision, which assesses the risk of non-issue of shares. In turn, Gourio (2015) quantifies the investment distortions created by managerial compensation and determines the correct behavior of the company's managers under the influence of various destructive factors. Dixit and Pindyck (2012) have developed a new approach to investing that recognizes the option value of waiting for better (but never complete) information. The proposed formalization of the investment process allowed forming a theory of improving the investment policy of firms and the government of the country. It is fair to point out that McDonald and Siegel (1986) developed a formula for the investment option value, and it allowed them to establish the optimal timing of an investment in an irreversible project. Mathematical interpretation of other features of the investment activity of firms and organizations was carried out by Lang, Ofek, and Stulz (1996). They quantified the relationship between leverage, investment, and firm growth.

DATA AND METHODOLOGY
Considering the analysis of the existing research on the priority areas of investment, as well as based on the opinion of experts in the Ukrainian investment industry, it is expedient to make the following conclusion. The state's investment potential must be studied within five vectors that comprehensively describe all aspects of this process. Thus, the socio-economic vector characterizes predominantly the general opportunities that are currently formed in the state for developing the investment activity. This group of indicators reveals the level of the state's economic development and the potential of its labor resources. The vector "infrastructure" describes the potential speed of human capital movement and the convenience of delivering goods in a global business environment. The indicators characterizing this vector describe the level of development of all types of transport in the country and energy security. The vector "science and education" is the basis for the creation and further development of high value-added hightech business in the country. This group of indicators characterizes both the level of education of the population and their research activities, and the level of state support for these processes. The vector "environment and human health" has become relevant in the context of the sustainable development concept. The basis of this concept is that the development of any economic process in the long term is impossible without observing environmental requirements and maintaining public health. If the "science and education" vector acts as the basis for the potential creation of new high-tech industries and business processes, then the "technology" vector determines the initial conditions for using the existing human achievements in the country. Thus, the indicators characterizing this vector should give investors an answer to the question: "is it possible to develop advanced technology-based investment in the country, is it necessary to pass through a long development stage?" Empirically, each of these groups can be described using the following indicators: 1) socio-economic conditions: • Soc1 -foreign direct investment, net inflows (% of GDP); • Soc2 -adjusted net national income (annual % growth); • Soc3 -labor for participation rate, total (% of total population ages 15-64) (modeled ILO estimate); • Soc4 -self-employed, total (% of total employ-ment) (modeled ILO estimate); • Soc5 -wages and salaried workers, total (% of total employment) (modeled ILO estimate).
Thus, socio-economic conditions and infrastructure ensure the formation of initial standards for developing the investment potential of the state. Thus, these indicators describe the conditions that are currently formed in the country for implementing the state's active investment policy for attracting foreign and domestic investment. Indicators related to science and education, as well as environment and human health, form the prerequisites for developing the human capital, which most scholars consider to be an indispensable prerequisite for developing the investment potential. Technology indicators are already describing the prospects of the country for developing the most current investment projects. Thus, technology in the conditions of the fourth industrial revolution is the most intensive catalyst for the growth of investment potential. The information for generating an array of input information is taken from the World Bank website for 1999-2018, and is grouped in Tables  A1 and A2.
Taking into account the purpose of the article, which consists both in developing the methodology for the integral assessment of the investment market potential and forecasting this indicator, the prediction of 25 relevant indicators becomes relevant. Thus, the forecasting of non-linear (in the form of a second order polynomial) economic-mathematical models is constructed using Brown-Meyer modeling in the context of each of the 25 indicators characterizing the state's investment potential. The use of this model for forecasting the investment potential indicators is because Brown-Meyer modeling belongs to adaptive forecasting methods. This allows taking into account the main feature of relevant indicators -a constant change under the influence of external and internal factors, as well as the accumulation of the so-called "experience" in the development of each indicator (the model takes into account the variations in the external functioning conditions of the system under study, when the greatest weight is given to the last levels of the time series). The implementation of adaptive forecasting methods involves the following preparatory steps: 1) estimating the parameters of the regression model based on several first levels of the studied time series; 2) calculating the forecasted level of the time series one step further based on the model built at the previous step. The calculated forecasted level of the time series is used for the subsequent calculation of forecasting errors as deviations between the forecast and actual levels of the time series; 3) estimating the next level of the time series, calculated based on the application of the model with the corrected parameters, calculated considering the forecasting error.
Thus, one proceeds to the mathematical formalization of the stages of a nonlinear adaptive Brown-Meyer model construction, which will allow obtaining the value of relevant indicators characterizing the state's investment potential in 2019-2021.
The first stage describes the first levels of the input time series using the square parabola, which is as follows: where n -number of observations.
Thus, provided 0 t = ∑ , the formulae for calculating the parameters of the regression equation (1) will be as follows: Adaptive forecasting based on the second degree polynomial implies the need to describe the time series by the following equation: where l is the forecasting period.
The parameters 0 1 2 , , f f f of the predictive regression equation are determined by the following procedure: 1) evaluation of initial conditions: 2) calculation of exponential averages based on the formula (5): 3) calculation of estimates of the parameters of the forecasted trend regression equation: Having received the data characterizing the state's investment potential, it is possible to build a model of its integral evaluation, which will be grouped on the Hurst exponent. The Hurst exponent (characteristics of time series persistence) is calculated based on the magnitude of the cumulative deviation of the indicators and reflects the economic essence of the concept of potential: where H -Hurst exponent, R -scope of cumulative deviation of the indicator, S -mean square deviation of the time series, N -number of observation periods, α -positive number given by a constant. Whence: where the magnitude of the accumulated deviation: where y -the arithmetic mean of the time series, t y -the level of the time series.
Considering the fact that the Hurst exponent provides for the construction of the regression equation, which consists of an effective indicator and factor attributes, and the potential one is looking for is the degree of the number, it is necessary to introduce an effective indicator in the model. It was proposed to choose the global index of attractiveness of foreign direct investment, as such an indicator (calculated by the World Bank as part of the Doing Business ranking), and the factor attributes of the regression model will be 25 relevant indicators related to the socio-economic conditions, infrastructure, science and education, environment and human health, and technology. It is suggested to choose not the absolute value of the global index of attractiveness of foreign direct investment, presented in the form of ranks, but the derived indicator, determined by applying Savage normalization, as an effective attribute: Comparing the results of the ranking with factor attributes will allow obtaining the adequate results of calculations.
Considering the fact that the hypothesis that information technologies play the most important role in shaping the state's investment potential has been put forward in the process of studying the peculiarities of investment activity, one of the stages of mathematical formalization of the process of assessing the state's investment potential is proposed to compare two development scenarios: the projected level of the state's investment potential at the projected level of information technology and the projected level of the state's investment potential, provided that the development of information technology at the current level is established.
However, it is fair to point out that the calculations received form a limited information database for adopting a well-considered and effective investment strategy for the development of the state. Therefore, it is necessary to supplement this information base with the specific tools for the activation of investment potential used by other countries. However, it should be noted that it is not effective to use the experience of any, even successful, country, as all countries differ in terms of initial conditions of investment potential development. Therefore, to accomplish this task, it is proposed to group the countries according to the level of investment potential and to adapt the best practices to national conditions. Thus, first, the investment potential of each country is calculated according to the proposed methodology, and second, the cluster for Ukraine is specified based on the self-organizing map (SOM) construction. Moreover, the most successful country is identified and its best achievements in the field of investing are adapted to national economic conditions.

RESULTS AND DISCUSSION
Before practical testing of the methodology described earlier, some additional calculations will be made. Thus, one calculates the first levels of the input time series using a second-order parabola, evaluates the initial conditions for the formation of an integral indicator, determines the exponen-  tial average values, and identifies the parameters of the regression trend equation for adaptive forecasting. Therefore, the adaptive forecasting study results of socio-economic conditions and infrastructure will be presented in Table B1 and Figure  B1 (Appendix B).
The equations obtained in Table 1 allow determining the patterns of development and consequently predicting ten relevant indicators characterizing Ukraine's investment potential in terms of socio-economic conditions and infrastructure ( Figure B1).
Based on the data in Figure B1, it is fair to note that only five of the ten relevant studied indicators show a positive prediction. They are air transportation, fixed broad band subscriptions, quality of port infrastructure, adjusted net national income, and self-employed. These consistencies indicate that there are no prerequisites for developing the investment potential in Ukraine.
The corresponding mathematical calculations within science and education, as well as environment and human health, are given in Table B2 and Figure B2 (Appendix B).
The analysis of the regression equations parameters characterizing the first levels of the input time series using the square parabola and the adjusted parameters of the regression equation of adaptive forecasting shows a slight variation of their values for most of the time series in terms of science and education, as well as environment and human health. Thus, only for indicators of research and development expenditure, government expenditure on education, people using at least basic sanitation services, current health expenditure, limited savings: particulate emission damage, there is a dramatic change of signs (directions of impact) to the opposite during the implementation of the adaptive mechanism.
Analyzing the data presented in Figure B2, it should be noted that the environmental and health indicators of Ukrainians create a positive situation for the development of human capital, which is defined at the theoretical level as the basis for the growth of Ukraine's investment potential. At the same time, three out of five relevant indicators characterizing the science and education group in 2020-2021 show a downward trend. This confirms the situation in Ukraine that has been As for analyzing the dynamic changes and further tendencies in the development of information technology indicators, Table 3 and Figure 3 will be built. The analysis of retrospective data in the context of the indicator of medium and hightech industry indicates the description of this data set with the second degree polynomial with the branches down, i.e., this indicator tends to increase to a certain turning point 56.22% of the average level, after which it decreases over time. In the context of all other information technology characteristics (ICT service exports, ICT goods exports, high-technology exports, secure internet servers), nonlinear trends have been identified to describe retrospective data, which show a general tendency to decline over time to a certain threshold level (2.6512%, 0.9634%, 2.3043%, 1.5532 %, respectively) over which the value of the indicator increases with time.
The transition to constructing regression equations for adaptive forecasting of information technology characteristics (the last three rows of Table 3) (Table 4).
Having forecasted the generalizing indicators of groups characterizing components of the investment potential of Ukraine, it becomes possible to calculate it directly based on the Hurst exponent, as well as to test the hypothesis regarding the level  Therefore, it is fair to conclude that the hypothesis of the significant impact of technology on investment potential is correct, and the gap be-  The final stage of the study is countries grouping according to their level of technology. It is based on SOMs construction and identification of the Ukrainian cluster, which let us gain relevant international experience to implement the national investment policy. The given data depicts the past and current grouping according to the countries' level of technology and its changes during the last years ( Figure 2).
Having transformed the obtained graphical results into a tabular form (Table 5), it is fair to note that the results of using the SOMs tool have iden-

Clusters
Year Clusters Thus, it is fair to point out that state executive and legislative authorities should draw on the expe-rience of countries such as Poland and Spain in the process of shaping Ukraine's newest investment strategy, which will be based on increasing investment potential. The opportunity to replicate the breakthrough of Estonia, which is now one of the leaders in living standards in Europe, was lost in 2008, when Ukraine was in the same cluster with the country, and thus had similar starting conditions.

CONCLUSION
This paper presents the framework of determining and forecasting Ukraine's investment potential with regard to 25 relevant indicators from the following areas: socio-economic conditions, infrastructure, science and education, environment and human health, technology. Furthermore, it provides the influence of information technology on the general parameter that describes the investment potential.  Poland Slovak Republic uncover their potential in Ukraine fully. This requires the urgent intervention of the state authorities in intensifying the reforms related to the investment climate improvement and ensuring the progressive development of the innovative growth of all spheres of society.
Based on the clustering of the countries according to their level of information technologies for 2003-2018, Ukraine was found to lose the opportunity to recreate the development trajectory of Estonia since 2008 because that year, they were in the same group with the characteristics of investment activity components. At present, Ukraine is in the same cluster with Poland, Spain, and Romania, so one believes that adapting the instruments of these countries for increasing the level of information technologies and investment potential in general is a priority for the executive and legislative branches of Ukraine.
Further scientific research should be aimed at the analysis of instruments for intensifying the technological component of investment activity in the country and creating favorable conditions for attracting the external investment in the innovation activities of Poland and certain territories of Spain. Besides, it is important to develop an optimal mechanism for adapting the technologies of Poland and Spain to the current situation in Ukraine to improve its investment attractiveness.