Analysis and forecasting of Ukrainian agrarian exports to the EU countries

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ANALYSIS AND FORECASTING OF UKRAINIAN AGRARIAN EXPORTS TO THE EU COUNTRIES

Sofiia Minenko, Kharkiv Petro Vasylenko National Technical University of Agriculture

Maria Kovylina, National University «Odessa Maritime Academy», Ukraine

Abstract

Purpose. The purpose of the paper is to study the state, perspective directions of Ukrainian exports of agricultural products and the introduction of effective forecasting using the method of mathematical modeling of a continuous system of aperiodic components.

Methodology / approach. In the process of research, the fundamental provisions of modern economic science were used in relation to the groups of factors influencing the resulting indicators of export, foreign trade trends, methods of statistical analysis to assess the weight of factors influencing the resulting function, as well as modern mathematical methods for forecasting of agrarian exports were implemented.

Results. The application of the developed mathematical model and the algorithm based on it, allowed to study the situation with the export of Ukrainian agricultural products to the EU, to identify trends specific to individual countries and the EU market as a whole, to assess the opportunities and prospects of niche markets, expansion nomenclature of export goods. Prognoses were given both on the export prospects of individual goods, product groups, and on the volume of deliveries to the EU. The use of factor analysis for forecasting of export deliveries allowed us to assess the impact of each of the factors and limit their amount.

Originality / scientific novelty. For the first time, the method of mathematical modeling of a continuous system based on changes in its aperiodic components was usedfor efficient and relevant forecasting of agrarian export volumes. Even the stages of application of this method, in particular, the analysis and prognoses for individual items of the nomenclature of export goods, for individual countries - importers make it possible to represent the situation with agrarian exports more accurately and forecast future supplies.

Practical value / importance. The proposed mathematical approach for market analysis and forecasting of markets can be used by both market regulators and producers and exporters of agricultural products. These polynomial equations for analysis and prognostication for individual product groups can be directly used in practice.

Key words: foreign trade, agricultural products, Ukraine, EU, mathematical model, forecasting.

Introduction and review of literature

Ukraine's foreign trade in agricultural products has passed through stages of serious crises in recent years and has undergone significant changes. The closure of the large-capacity Russian market as a result of the war required significant efforts by exporters to diversify exports, enter new markets, including promising and capacious markets in the Middle East and China, open niche markets, and so on. Significant impetus to the export of domestic agricultural products was given by the signing of the «Association Agreement between Ukraine and the EU» (Heyets, 2014; 2016) and the granting of trade preferences for exports to the European Union. This impetus has different dimensions, and not only in the context of increasing trade and expanding the range of goods. Thus, the share of the European Union in the export of Ukrainian agricultural products by volume exceeds a quarter of all export supplies but is characterized by significant fluctuations, typical for goods that predominate in the export of Ukraine. The risks are increased by the predominant specialization of foreign trade in agricultural products, which, unfortunately, has been developed due to the distortion of the conditions of formation of Ukrainian agricultural exports - supplies of grain and oilseeds account for more than U of total exports. Supply volumes are also affected by global crises, in particular the COVID-19 pandemic. The pandemic has made a negative impact, primarily on agricultural exports of fruits and vegetables around the world, which affected the trade of even such a powerful country as the United States. All these circumstances require the formation of an effective policy in all areas - production, storage, transportation, expansion of the range of goods, securing a strong foothold in foreign markets and so on. The criterion for the effectiveness of effective policy-making in this direction is the creation of certain trends and tendencies in foreign trade. This increases the need for a modern mathematical apparatus to obtain reliable and relevant predictions.

Such Ukrainian scientists as Heyets (2014; 2016), Dalevska (2012), Kvasha, Grigoriev (2016), Klyuchnik (2015), Melnyk (2010), Mesel-Veselyak (2010), Sabluk (2008) and others devoted their works to the study of the peculiarities of the export market of agriculture of Ukraine, its potential, opportunities, development trends. Their scientific achievements in the context of the formation of analytical methods for studying trends and tendencies of Ukrainian agro-export were used in the presented work to form a mathematical model. Hadzalo, Lupenko and Pugachev's (2016) methods of analysis of the market capacity of the countries-importers of the Ukrainian agricultural products made an especially valuable contribution. The main trends of the world food market, the role and place of Ukraine in it were studied by Absava (2009), Strashynska (2007), Kernasyuk (2019), Yatsenko, Nitsenko et al. (2019), Heldak et al. (2018), Kucher (2017) etc. Some research results as to the factors of regulatory influence on agro-markets by Yurchyshyn (2005), Lupenko and Gutorov (2018), Ryabokon and Novikova (2016), Shpykulyak (2010), Shpychak (2017), Pronko et al. (2020) were also used in this paper. Unfortunately, Ukrainian scientists paid little attention to modeling of foreign economic activity, prospects for expanding and improving the commodity structure of exports depending on the focus groups of importers, countries and regions, forecasting future periods (Romaneckas et al., 2019). The formation of analytical approaches in these areas received more attention from foreign scientists, some of whom used standard software products for complex economic analysis. In particular, the NARDL package is popular in its direct use (Karamelikli and Korkmaz, 2016; Falco et al., 2020), or with some modifications and improvements (Khan et al., 2020; He et al., 2019). Sometimes this is due to the target setting. For example, big data made it difficult to study (Khan et al., 2020; Kirieieva et al., 2019) by time series. But the nonlinear method applied to the autoregression of the distributed lag made it possible to detect unexpected asymmetric results on model variables (Khan et al., 2020; Yatsenko, Yatsenko et al., 2019; Fenghe, 2020). SBM-DEA model (Dong et al., 2020) helped to identify implicit patterns in the data without prior processing, which allowed establishing the relationship between «positive» and «undesirable» data sets (Dong et al., 2020; Ma, 2020; Gao et al., 2020).

Analyzing the work of foreign scientists, we can find a certain regularity. Application of empirical-analytical approaches, for example, using elastic variables and GEASI model (Lusk et al., 2019), improved by Komer on the Cobb-Douglas approach of the Solow model (Edeme et al., 2016; Zamula et al., 2020), direct analysis of the connections between break-even and yield (Tun and Phyo, 2019), the method of comparative indicators of benefits (Seleka and Dlamini, 2020; Ostapenko et al., 2020) for the formation of export forecasts for countries with unfavorable starting conditions (which is interesting for Ukraine) (Bilan et al., 2017; Lavrysh, 2018), are changing to more complex models using linear splines, robust combination of constraints, etc. give more relevant results. For example, Bayesian modeling by the corrective approach of RMA (Liu and Ker, 2020), or GARCH modeling taking into account the change of parameters over time according to the Karali approach (Karali et al., 2019). That is, scientists move away from standard methods to the formation of analytical models and apply new approaches specialized for specific circumstances of foreign economic activity (Kravchenko et al., 2020; Ursul and Ursul, 2018). More often, the latest approaches to the formation of algorithms use some elements of time- tested approaches to simplify calculations, reduce time and computer resources, reduce sets of variables that affect the target functions, and so on (Awwad, 2018; Schonhart et al., 2009; Werner et al., 2019). The analysis of scientific works allows establishing that scientists look for and find new mathematical models for the forecast of export deliveries of agricultural products (Pyburn et al., 2016). This search allows identifying new mathematical approaches adapted to specific problems, circumstances and goals of modeling, which allows getting more relevant results. export ukrainian agricultural products

The purpose of the article. The purpose of the paper is to study the state, perspective directions of Ukrainian exports of agricultural products and the introduction of effective forecasting using the method of mathematical modeling of a continuous system of aperiodic components.

Methodology. A mathematical model was developed to forecast the export of agricultural products. Forming the model was based on the fact that agro-export is a continuous system, a component of which is represented by individual product groups and markets of individual importing countries. As known, in a broad sense, the nature of the functional dependencies of exports in goods or in cash, other functional representations of exports by individual product groups and for individual importing countries is aperiodic. During the analytical study it was found that the use of classical gravity model, in particular, in its logarithmic representation (Braha et al., 2017; Raisiene et al., 2019) had certain limitations on the accuracy and relevance of the results, especially for the dynamic aperiodic change of factors. But this approach was used by us as one of the elements of the model, in particular, to assess the importance of influencing factors and, accordingly, to reduce their number. The approach of Campa, Goldberg, Berman for modifications of Karamelikli was also partially used (Karamelikli and Korkmaz, 2016). The method of studying the export of niche goods by Zhang (2020) with elastic supply, cointegration relations by Ongan and Gocer (2020) and the method of estimating the dependence of agro-exports on currency exchange rate volatility (Kandilov, 2008) also turned out to be useful. Analysis of Ukrainian exports of agricultural products to the EU using the method (Melnikov et al., 2015; Ostapenko et al., 2020; Bazaluk et al., 2020) allowed establishing the results of regulatory measures, in particular, the agreement between the EU and Ukraine, to reduce the negative effects of this factor on export earnings (by 67 %).

The peculiarities inherent in these commodity groups are superimposed on foreign trade by individual commodity groups. But there should be common trends for this range of goods, which depend on the general trends of the world market of agricultural products, aggressive policy of Ukrainian agricultural management, joint action in foreign markets and so on. Obviously, the use of factor analysis to forecast Ukrainian agro-exports for such a large number of groups of differently directed factors of different weight and dependent on different groups of variables is impossible.

Therefore, for mathematical modeling of agro-exports, it is proposed to apply an approach that has not yet been used to predict economic trends in foreign markets. Some aspects of this approach are presented in scientific work (Melnikov et al., 2015; Zamula et al., 2020). This is the prediction of the motion vector of a continuous system, the component of which are successive attractors of the same type of aperiodic functional dependences of the first order on the response surface of the target function. Functional dependencies of individual export goods, obviously, can be represented by the same type of aperiodic functional dependencies of the first order.

An algorithm for constructing correlation matrices, motion vectors, and reaction vectors of continuous linearized systems using dispersion matrices and transposed matrices of their reactions is described in the scientific literature for stochastic variables that form stationary (in the general sense) functional dependencies. In this case, it is possible to consider this system as a multidimensional representation «input - output». This, in turn, allows using the approach of finding the scalar components of motion vectors and reaction vectors of continuous linearized systems by selecting on matrices representing these vectors, matrices splitting the output vector into scalar components by dividing the output matrix into separated matrices and finding correlation dependences input-output functions. Then the Lyapunov matrix equation (or system of equations) can be applied to market indicators (so-called «colored noise»), which is known to differ from the so-called «white noise» by the strength and direction of individual indicators. As a subtask within the implementation of the proposed mathematical model there is a problem of studying the effectiveness of individual factors influencing the volume of exports of agricultural products.

The basic parameter for dynamic systems is time t. Let us denote the vector of exogenous influence of a factor or group of factors - ~w(t). As pilot tests of the model have shown, short-term forecasts are more reliable. The error for annual forecasts is growing. The basic equation for finding the derivative of the state vector on the attractor Y(t) is (1) under conditions (2):

where Z(t) - output vector;

? - deviation at the output;

А, В, С - state matrices, input and output parameters.

The appropriate condition is (3):

where R - known mathematical operator.

The scalar components of the output vector are the reactions of commodity markets by focus groups, the reactions of related industries in the markets, and so on. Output variance D_z will be a matrix and can be found in accordance with (1) - (3) by equation (4) (Melnikov et al, 2015):

where М - in this case, a mathematical operator, which means a mathematical expectation.

As known, to find the mathematical expectation of a continuous stochastic variable, it is necessary to determine the density of its distribution, for which the nature of the functions is checked and it is found that they correspond to the normal distribution law.

Equation (4) indicates that it is possible to simplify the calculations greatly - to reduce the problem of finding the variance matrix using the Lyapunov equation if we present the system as an aggregate structure and a certain mathematical filter that will reveal a statistically significant so-called «colored» signal. The proposed approach, however, requires considerable time and computer resources, so at the first stage to model foreign economic relations a stationary gravity model and factor analysis were used, which, in addition to comparing the results, also limited the number of factors influencing agricultural exports for each item of agro-exports, by certain product groups (oilseeds, cereals, etc.), by importing countries and to individual markets as a whole.

As known, according to the gravity model, exports from the supplier country to the importing countries are considered to depend on the distance between them and their so-called «economic weight», which is taken as their GDP. Logarithmic representation of the gravity model (5), more convenient for the formation of the algorithm:

where i - index of the exporting country (Ukraine); j - index of the importing country; p - impact factor index;

- weighing coefficient of the impact factor;

- free member of power dependence - the theoretical value of the annual turnover which does not depend on the identified impact factors;

Тij - annual trade turnover between countries (exports plus imports); y - parameter (GDP, GDP per capita, population, distance between countries, etc.); d - systematic deviation related, for example, to the shadow economy. The fact of the possibility of detecting such a systematic deviation and conducting its numerical evaluation in terms of forming an effective set of regulatory effects is a significant result of this mathematical representation.

Results and discussion

In order to assess the task facing the authors, we present some data sets that have been analyzed (see Table 1, Table 2, Table 3). This sample of data, which served as a basis for analytical research, is specially presented so as to be as representative as possible. Table 1 shows the total export volumes for all types of products.

Table 1. Volumes of exports of Ukrainian products by importing countries

Source: based on European Commission, 2020.

Table 2 shows the volume of exports of products that, along with cereals, form the basis of Ukrainian agro-export - sunflower oil. Table 3 presents data on exports of the type of Ukrainian agricultural products recognized among consumers, which can be attributed to niche export goods - honey.

As seen in the above tables, despite some fluctuations related to crop and non-crop years, the integrated export volume indicator for the European Union and the United Kingdom (abbreviated EU 28 in the tables) has a steady upward trend. Honey, like other goods subject to quotas, after reaching certain limits shows a certain stability in supply. However, some countries, especially those with small populations, such as Croatia and Cyprus, show some fluctuations in supply volumes. Larger fluctuations in the volume of supplies to certain countries show data on exports of one type of product (see Table 2). Despite the growth of the integrated index, the amplitude of its oscillations is more significant than in table 3.

Table 2. Exports of sunflower oil by importing countries