Кwilinski Alex 7 www.virtual-economics.eu ISSN 2657-4047 (online) Oleksandr Melnychenko, Valerii Matskul, and Tetiana Osadcha Virtual Economics, Vol. 5, No.2, 2022 2022 Volume 5 Number 2 THE DYNAMICS OF TRADE RELATIONS BETWEEN UKRAINE AND ROMANIA: MODELING AND FORECASTING Oleksandr Melnychenko, Valerii Matskul, and Tetiana Osadcha Abstract. The article examines the monthly dynamics of exports, imports and balance of trade between Ukraine and Romania in the period from 2005 to 2021. Time series from 2015 to 2021 were used for modelling and forecasting (since the date the European Union–Ukraine Association Agreement took effect). Adequate models of the dynamics series of the Box- Jenkins methodology were built: additive models with seasonal component ARIMA (Autoregressive Integrated Moving Average)*ARIMAS (or SARIMA) and Holt-Winters exponential smoothing with a dampened trend. Forecasting of exports, imports and trade balance for the fourth quarter of 2021 and first quarter of 2022 were completed. The forecast results showed a small relative error compared to the actual data. Thus, when forecasting the trade balance between countries using the Holt-Winters model, the relative prediction errors were: for October 2021 – 1.3%; for November 2021 – 2.6%; for December 2021 – 0.4%. Keywords: export, import, trade balance, ARIMA*ARIMAS, Holt-Winters models, forecasting JEL Classification: B27; C22; C45 Authors: Oleksandr Melnychenko Gdansk University of Technology, Gdansk, Poland E-mail: oleksandr.melnychenko@pg.edu.pl https://orcid.org/0000-0002-7707-7888 Valerii Matskul Odesa National Economic University, Odesa, Ukraine E-mail: valerii.matskul@gmail.com https://orcid.org/0000-0003-3897-5500 Tetiana Osadcha Odesa Mechnikov National University, Odesa, Ukraine E-mail: tatiana@osadcha.com https://orcid.org/0000-0003-4258-0907 Citation: Melnychenko, O., Matskul, V., & Osadcha, T. (2022). The Dynamics of Trade Relations between Ukraine and Romania: Modelling and Forecasting. Virtual Economics, 5(2), 7-23. https://doi.org/10.34021/ve.2022.05.02(1) Received: January 16, 2022. Revised: February 20, 2022. Accepted: March 9, 2022. © Author(s) 2022. Licensed under the Creative Commons License - Attribution 4.0 International (CC BY 4.0) http://www.virtual-economics.eu/ https://www.google.com.ua/url?sa=t&rct=j&q=&esrc=s&source=web&cd=5&cad=rja&uact=8&ved=0ahUKEwiXt47tstbRAhWmJJoKHYnJAowQFgg_MAQ&url=https%3A%2F%2Fen.wikipedia.org%2Fwiki%2FAutoregressive_integrated_moving_average&usg=AFQjCNEyRYjPb-kc2BB3qnVcxDErIC3NnQ&sig2=elfw1WelGONLRfJ2s8d2zA&bvm=bv.144224172,d.bGs http://oleksandr.melnychenko@pg.edu.pl https://orcid.org/0000-0002-7707-7888 http://valerii.matskul@gmail.com https://orcid.org/0000-0003-3897-5500 http://tatiana@osadcha.com https://orcid.org/0000-0003-4258-0907 https://creativecommons.org/licenses/by/4.0/ 8 www.virtual-economics.eu ISSN 2657-4047 (online) Oleksandr Melnychenko, Valerii Matskul, and Tetiana Osadcha Virtual Economics, Vol. 5, No.2, 2022 1. Introduction In recent years, trade relations between Ukraine and Romania began to develop intensively. After signing the EU–Ukraine Association Agreement, the trade turnover between Ukraine and Romania increased constantly and reached almost 2.3 billion US dollars in 2021 (see Figure 1). Figure 1. Dynamics of trade turnover (in million US dollars) between Ukraine and Romania for the period from 2015 to 2021 Source: SSSU, 2022 The main export items from Ukraine to Romania comprise: products of agriculture, food and metallurgical industries, fertilizers, wood and various finished products from it, while imports from Romania to Ukraine are dominated by the means of land transport (except for railways), aircraft, various products of the chemical (especially pharmaceutical) industry. The relevance of this study is justified by the fact that Romania has become one of the largest trading partners of Ukraine: according to the results of 2021, Romania ranked among the top ten of more than 100 trading partners of Ukraine. 2. Literature Review Thanks to the classic work by Box (1976), time series models began to be intensively applied in various fields of science and technology. Their discrete version is widely used in the practice of economic research. For example, papers by Dzitsaki (2016) and Dzitsaki (2018) used Box- Jenkins-type models to simulate and forecast unemployment in Greece and the United States. In the studies (Ahmed, 2017; Dvorakova, 2017; Dritsaki, 2021; Eissa, 2020; Ghazo, 2021), the dynamics of the GDP in various countries was studied and predicted. The time series methodology (with diverse variations) was used to simulate and forecast inflation dynamics by the following scholas: Alderite (2020), Ahmed (2021), Dadyan (2020), Shinkarenko (2021). The ARIMA model was used by Kayikci (2020) to forecast ice evolution in the polar seas. These models were further developed (in combination with other types of time series models) in the 0 500 1000 1500 2000 2500 2015 2016 2017 2018 2019 2020 2021 http://www.virtual-economics.eu/ 9 www.virtual-economics.eu ISSN 2657-4047 (online) Oleksandr Melnychenko, Valerii Matskul, and Tetiana Osadcha Virtual Economics, Vol. 5, No.2, 2022 works by Khashei (2012), Mohamed (2011), Streimikiene (2020), and Wang (2014). Numerous examples of the practical application of Box-Jenkins (and other) models for simulating and forecasting various economic processes can be found in the papers by Kozak (2017), Melnychenko (2020, 2021a, 2021b), Osadcha et al. (2021a, 2021b). It bears noting that when forecasting using an insufficiently large number of input data, Box-Jenkins models turn out to be more effective than Neural Networks that have been popular in recent years (Matskul, 2020). The latter work (considering the growing interest in international trade) complements the above sources and fills in the gaps in the study of the dynamics of trade relations between Ukraine and Romania. A number of recent scientific research were devoted to the development of the economic systems of the countries of Eastern Europe (Drożdż and Mróz- Malik, 2017; Drożdż et al. 2020a, 2020b; Dźwigoł 2021a, 2021b; Kharazishvili et al. 2021; Miśkiewicz 2019). In addition, it is extremely necessary to mention scientific works with alternative methods of calculation of interdependence and optimal interaction, where models of economic development are presented, which, in one way or another, can contribute to the bifurcation effect in trade relations between countries. This factor should also be taken into account among others in forecasting the development of trade relations between countries. The above-mentioned publications are related to: artificial intelligence components and fuzzy regulators in entrepreneurship development (Bogachov et al. 2020); improving the development technology (Borodin et al. 2021); determinants and evolution methods in the context of digitalization and sustainability (Drożdż et al. 2021; Dzwigol 2020; Dźwigol et al. 2019, 2020; Hezam et al. 2023; Hussainet al. 2021; Ingber 2017; Kharazishvili et al. 2020, 2021b; Kianpour et al. 2021; Kotowicz et al. 2022; Kuzior et al. 2021a, 2021b; Kwilinski et al. 2019a, 2019b, 2019c; 2020a, 2020b, 2020c, 2020d, 2021, 2022a, 2022b, 2022c; Lyulyov et al. 2021a, 2021b; Miśkiewicz 2018, 2020, 2021; Miskiewicz et al. 2021, 2022; Moskalenko et al. 2022a, 2022b; Polcyn et al. 2022; Prokopenko and Miśkiewicz 2020; Saługa 2020, 2021; Szczepańska-Woszczyna Gatnar 2022; Tih et al. 2016; Tkachenko et al. 2019a, 2019b; Trzeciak et al. 2022; Vaníčková and Szczepańska-Woszczyna 2020; Yang et al. 2021). Thus, the purpose of this article is to form a model for predicting the dynamics of trade relations between Ukraine and Romania on the basis of import-export data. The paper consists of 5 parts: introduction, literature review, materials and methods, results and discussion, and conclusions. 3. Material and Methods The data for analysis are available on the website of the State Statistics Service of Ukraine (SSSU, 2022). The time for which the data will be available is the monthly export, import and trade balance (as the difference between export and import between the Ukraine and the Romania) starting from January 2005 and ending in December 2021, covering about 204 input data. The unit is a million of US dollars. Preliminary data processing was carried out in MS Excel spreadsheets. DELL STATISTICA software, version 12, was used when modelling and computing. http://www.virtual-economics.eu/ 10 www.virtual-economics.eu ISSN 2657-4047 (online) Oleksandr Melnychenko, Valerii Matskul, and Tetiana Osadcha Virtual Economics, Vol. 5, No.2, 2022 3.1 Box-Jenkins models We use the following Box-Jenkins additive models of time series: 𝑦𝑡 = 𝑓(𝑡) + 𝑆𝑡 + 𝑒𝑡 , (1) where 𝑦𝑡 is a level of time series at time 𝑡 = 1, 2, . ..; 𝑓(𝑡) - trend is traced the long-term and evolution is deterministic in time; 𝑆𝑡 stands for seasonal fluctuations; 𝑒𝑡 denotes random fluctuations. This design allows exploring the dynamic series by eliminating its components. ARIMA*ARIMAS model. It bears noting that a necessary condition for this model’s application is the stationarity of the dynamic series, which is achieved by taking differences of a certain order (depending on the trend). In addition, the random component must be the so-called "white noise", i.e., satisfy the condition 𝑒𝑡 𝜖 𝑁 (0; 𝜎). In our case, the trend is linear, so the stationarity of the series was achieved by taking the differences of the first order on lag 1. And the distribution of the residuals was visually compared with the normal distribution. After identification, the ARIMA*ARIMAS model for time series will look like: 𝑦𝑡 = 𝑝𝑡−𝑘 𝑦𝑡−𝑘 + 𝑓(𝑡) − 𝑞𝑡−𝑘 𝑒𝑡−𝑘 + 𝑆𝑡, (2) where 𝑝𝑡−𝑘 is the auto-regression coefficients of the k-th order; 𝑞𝑡−𝑘 is a coefficient of the moving average model; 𝑒𝑡−𝑘 is an irregular component (random deviations or so-called white noise). The Smoothed Moving Average of first order 𝑆𝑡 = 𝑐 + 𝑄𝑡−1𝑆𝑡−1 was applied to find seasonal coefficients. Parameters of the model should be estimated at 95% confidence level (or 5% risk) with the condition of minimizing the MSE (Mean Square Error): 𝑀𝑆𝐸 = ∑ (𝑦𝑖−�̃�𝑖) 2 𝑛 𝑛 𝑖=1 , (3) 3.2 Holt-Winters model The specificity of Holt-Winters model is that exponential smoothing (with its own parameter) is applied to each component of the Box-Jenkins model. So, for the main process, the alpha parameter is used, i.e., exponential smoothing is carried out according to the formula: 𝑦𝑡 = 𝛼𝑦𝑡 + (1 − 𝛼)𝑦𝑡+1, 𝑡 = 1,2 (4) The specific feature of this smoothing is that the last levels of the time series are more significant. So, for example, the value of the smoothing parameter alpha = 0.3 means that 30% of the last levels of a series of dynamics determine 70% of the forecast. The delta parameter is used to smoothen the seasonal component, and the trend is damped by the phi parameter. It bears noting that the successful application of exponential smoothing does not require the stationarity condition of the time series. 4. Results and Discussions Figure 2, therefore, shows the dynamics of export, import and trade balance. http://www.virtual-economics.eu/ 11 www.virtual-economics.eu ISSN 2657-4047 (online) Oleksandr Melnychenko, Valerii Matskul, and Tetiana Osadcha Virtual Economics, Vol. 5, No.2, 2022 Figure 2. The dynamics of the export, import and trade balance between January 2005 to December 2021 Sources: developed by the authors. The descriptive statictics of the data are given in Table 1. Table 1. Descriptive characteristics of the data Variable Average Minimum Maximum Standard deviation Export 58.49688 16.7 117.4 20.34272 Import 55.08229 5.1 152.1 29.0717 Trade Balance 3.414583 -93.7 47.8 31.44937 Source: estimated by the authors. A visual analysis, as well as descriptive characteristics of time series, lead to a conclusion that for the period of 2005-2014, the dynamics of trade relations between the countries was noticeably unstable. Therefore, the period from 2015 to the present was selected for modelling and forecasting. A steady increase in the volume of export-import operations between two countries after signing the EU-Ukraine Free Trade Zone Agreement (even despite the COVID-19 pandemic), as well as a stable positive trade balance between Ukraine and Romania were of utmost importance. Modelling and forecasting of export-import dynamics using one of the Box-Jenkins models (1) – the additive model ARIMA*ARIMAS – requires the model identification. First, the trends (the standard Least Squares Method is used to find the trend component) are built. -150 -100 -50 0 50 100 150 200 1 7 1 3 1 9 2 5 3 1 3 7 4 3 4 9 5 5 6 1 6 7 7 3 7 9 8 5 9 1 9 7 1 0 3 1 0 9 1 1 5 1 2 1 1 2 7 1 3 3 1 3 9 1 4 5 1 5 1 1 5 7 1 6 3 1 6 9 1 7 5 1 8 1 1 8 7 1 9 3 1 9 9 export import trade balance http://www.virtual-economics.eu/ 12 www.virtual-economics.eu ISSN 2657-4047 (online) Oleksandr Melnychenko, Valerii Matskul, and Tetiana Osadcha Virtual Economics, Vol. 5, No.2, 2022 (a) (b) Figure 3. The dynamics of export (a) and import (b) from January 2015 (1) to December 2021 Sources: developed by the authors Analysis of correlograms in Figure 4 (graphs of autocorrelation coefficients) reveals the presence of the first-order autocorrelation at lag 1, as well as the presence of annual seasonality at lag 12. Graphs in Figure 5 show that there are no higher-order autocorrelations. So, the model identification process is complete. To find estimates of the parameters of the ARIMA*ARIMAS model and forecasts, the "Time series and forecasting" module of the STATISTICS program is used. Elimination of the trend is carried out by transforming the time series by taking the first- order differences at lag 1. When smoothing both the main process and seasonal components, a simple two-point smoothing at lag 1 is used. y = 0.5228x + 22.34 R² = 0.6057 0 10 20 30 40 50 60 70 80 90 100 1 3 5 7 9 11131517192123252729313335373941434547495153555759616365676971737577798183 http://www.virtual-economics.eu/ 13 www.virtual-economics.eu ISSN 2657-4047 (online) Oleksandr Melnychenko, Valerii Matskul, and Tetiana Osadcha Virtual Economics, Vol. 5, No.2, 2022 (a) (b) Figure 4. Autocorrelation functions dynamics of export (a) and import (b) Sources: developed by the authors (a) (b) Figure 5. Partial autocorrelation functions dynamics of export (a) and import (b) Sources: developed by the authors Finally, the ARIMA*ARIMAS models for the EXP (export) and IMP (import) variables have the following form: 𝑦𝑡 = 𝑝𝑡−𝑘 𝑦𝑡−𝑘 + 𝑓(𝑡) − 𝑞𝑡−1𝑒𝑡−1 + 𝑆𝑡 , (5) where 𝑦𝑡 = 1.81̅̅ ̅̅ ̅̅ is the levels of time series; 𝑓(𝑡) = 0.6965𝑡 + 46.077 for variable EXP and 𝑓(𝑡) = 0.5388𝑡 + 21.963 for variable IMP are a trend components; 𝑝𝑡−1 is the auto- regression coefficients of the first order; 𝑞𝑡−1 is a coefficient the moving average model; 𝑒𝑡−1 is an irregular component (random deviations or so-called white noise). The Smoothed Moving Average of first order 𝑆𝑡 = 𝑐 + 𝑄𝑡−1𝑆𝑡−1 is applied to find seasonal coefficients. http://www.virtual-economics.eu/ 14 www.virtual-economics.eu ISSN 2657-4047 (online) Oleksandr Melnychenko, Valerii Matskul, and Tetiana Osadcha Virtual Economics, Vol. 5, No.2, 2022 Parameters of the model should be estimated at 95% confidence level (or 5% risk) with the condition of minimizing the MSE (formula (3)). As a result, the following parameter estimates are obtained (Table 2). Table 2. Parameter estimates of the model ARIMA*ARIMAS Variable EXP IMP Parameter Estimate Standard deviation Estimate Standard deviation 𝑝𝑡−1 0.214581 0.165761 0.567133 0.133668 𝑞𝑡−1 0.780591 0.103687 0.912063 0.056426 𝑄𝑡−1 -0.381932 0.144834 -0.641404 0.125851 Source: estimated by the authors. The adequacy of the ARIMA*ARIMAS models is confirmed by the closeness to the normal law of the distributions of residuals (differences between the actual and modelled levels of the time series), which are presented in Figure 6. (a) (b) Figure 6. Normality graphs of the models’ residuals distribution: (a) export, (b) import Sources: developed by the authors The constructed models are applied to predict the volumes of exports and imports for the first quarter of 2021 (t = 82, 83, 84). Forecasting results, as well as relative forecasting errors, which are determined by the formulas (6) are shown in Table 3. 𝛿𝑡 = |𝑦𝑡 𝑝𝑟𝑒𝑑𝑖𝑐𝑡 −𝑦𝑡 𝑎𝑐𝑡𝑢𝑎𝑙| |𝑦𝑡 𝑎𝑐𝑡𝑢𝑎𝑙| ; 𝑡 = 82, 83, 84, (6) Table 3. Forecasts for ARIMA*ARIMAS model and actual data Export (EXP) Import (IMP) Forecasts Actual Residuals Forecasts Actual Residuals 80.49 79.9 0.007 53.64 51.5 0.039 116.62 112.4 0.036 90.31 83.6 0.074 123.28 119.5 0.031 53.27 49.5 0.070 Source: estimated by the authors. http://www.virtual-economics.eu/ 15 www.virtual-economics.eu ISSN 2657-4047 (online) Oleksandr Melnychenko, Valerii Matskul, and Tetiana Osadcha Virtual Economics, Vol. 5, No.2, 2022 From Table 3, it can be concluded that the relative prediction errors for the EXP variable do not exceed 3.6%, and for the IMP variable they account for 7.4%. Doing research, modelling and forecasting the trade balance (variable TB = EXP-IMP), similarly to the above, the ARIMA*ARIMAS model is applied first. Figure 7 shows the dynamics of the trade balance for 2015-2021: Figure 7. Graphs of the trade balance between Ukraine and Romania from January 2015 to December 2021 (with a trend) Sources: developed by the authors After identifying the model and applying the "Time series and forecasting" module of the STATISTICS program, the ARIMA*ARIMAS model is obtained (formula (5)) for the TB (trade balance) variable. The trend looks like 𝑓(𝑡) = 0.1177𝑡 + 24.113; autocorrelation and smoothing parameters are shown in Table 4. Table 4. Parameter estimates of the model ARIMA*ARIMAS Variable TB Parameter Estimate Standard deviation 𝑝𝑡−1 0.179219 0.226005 𝑞𝑡−1 0.754857 0.169613 𝑄𝑡−1 -0.305027 0.117950 Source: estimated by the authors. To simulate again, the "Time Series and Prediction" module of the STATISTICS program is used again. Before building the Holt-Winters model, in order to find the optimal values of the smoothing parameters, the so-called "Search on the grid" is conducted. As a result, the following values were found: the smoothing parameter of the main process alpha = 0.3; smoothing seasonal component parameter delta = 0.1; trend damping parameter phi = 0.1. Table 5 shows the results of modelling and forecasting. y = 0.4265x + 16.963 R² = 0.3341 0 20 40 60 80 100 120 1 3 5 7 9 11131517192123252729313335373941434547495153555759616365676971737577798183 http://www.virtual-economics.eu/ 16 www.virtual-economics.eu ISSN 2657-4047 (online) Oleksandr Melnychenko, Valerii Matskul, and Tetiana Osadcha Virtual Economics, Vol. 5, No.2, 2022 Table 5. Results of the modelling and forecasting (fragment) using the Holt-Winters model of exponential smoothing Observation TB Smoothing TB Residual Season component 1 7.9 16.29 -8.39 -3.67 2 1.2 12.32 -11.12 -5.07 3 8.2 16.90 -8.70 3.22 4 21.0 16.85 4.14 0.61 5 26.6 15.17 11.43 4.58 6 29.0 21.04 7.96 7.26 7 29.1 22.57 6.53 5.01 8 26.3 16.64 9.66 -2.12 9 28.7 24.53 4.16 2.34 10 22.7 24.84 -2.13 0.73 11 22.7 12.84 9.85 -11.21 12 28.3 18.58 9.72 -9.32 81 70.58 82 70.58 83 71.45 84 76.49 85 84.66 86 86.40 87 97.77 Source: estimated by the authors. The adequacy of the obtained the Holt-Winters model of exponential smoothing by analysing the histogram of residuals and Normal curve is convincing (Figure 8). Figure 8. Graphs histogram of the residuals and Normal curve Sources: developed by the authors The following Figure 9, which shows the original and simulated time series, clearly demonstrates the quality of the constructed model. http://www.virtual-economics.eu/ 17 www.virtual-economics.eu ISSN 2657-4047 (online) Oleksandr Melnychenko, Valerii Matskul, and Tetiana Osadcha Virtual Economics, Vol. 5, No.2, 2022 Figure 9. Visualization of source data and results obtained using the Holt-Winters model of exponential smoothing Sources: developed by the authors The constructed ARIMA*ARIMAS and Holt-Winters models are applied to predict the trade balance between Ukraine and Romania for the fourth quarter of 2021 (t = 82, 83, 84). The forecasting results, as well as the relative forecasting errors (which are determined by formulas (6)) are shown in Table 6. Table 6. Forecasts for ARIMA*ARIMAS and Holt-Winters models and actual data Forecasts (ARIMA* ARIMAS) Actual Residuals Forecasts (Holt- Winters) Actual Residuals 29.35162 28.4 0.032421 28.79413 28.4 0.013688 31.93121 28.8 0.098061 28.05349 28.8 0.02661 69.91722 70 0.001184 70.28544 70 0.004061 Source: estimated by the authors. Analysing the results presented in Table 6, it bears concluding that the relative forecast errors for the TB variable according to the ARIMA*ARIMAS model do not exceed 9.8%, and according to the Holt-Winters exponential smoothing model – 2.6%. 5. Conclusions The conducted studies allowed for modelling and forecasting the dynamics of trade relations between Ukraine and Romania to build adequate models of Box-Jenkins time series: ARIMA*ARIMAS and Holt-Winters exponential smoothing. The results showed small relative forecast errors compared to actual data. In the paper, modelling and forecasting used the http://www.virtual-economics.eu/ 18 www.virtual-economics.eu ISSN 2657-4047 (online) Oleksandr Melnychenko, Valerii Matskul, and Tetiana Osadcha Virtual Economics, Vol. 5, No.2, 2022 latest available data. So, according to preliminary data for January 2022, the models showed good forecasting results. After the Russian invasion of Ukraine, statistical data are not available. However, Romania remains Ukraine's largest trading partner. The results of this study can be used in further research on models for predicting the dynamics of the trade relations development, in particular in the context of digitalization and sustainability. References Ahmed, R. R., Vveinhardt, J., Ahmad, N., & Štreimikienė, D. (2017). Karachi Inter-Bank Offered Rate (KIBOR) Forecasting: Box-Jenkins (ARIMA) Testing Approach. E & M: Ekonomie a Management, XX(2), 188–198. http://dx.doi.org/10.15240/tul/001/2017-2-014 Ahmed, R. R., Štreimikienė, D., Ghauri, S. 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