INTERNATIONAL ECONOMICS AND INTERNATIONAL RELATIONS

. In this article, the integration processes between Azerbaijan, Ukraine and Georgia are considered through the indicators of integratedness of Azerbaijan’s GDP and the trade turnover of this country with the other two. All considered time series are non-stationary. So, there are problems of correct modeling of the corresponding time series, the components of which lead to a deviation from stationarity. The publication uses an econometric cointegration methodology for modeling the relationship between the non-stationary time series. A dynamic model of the long-term equilibrium is built, allowing to qualitatively forecast the state of foreign trade integration of the three countries under consideration and analyze the openness of the Azerbaijani economy in the regional aspect.


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from time to time.The research (Kalyuzhna,2020) carried out a retrospective analysis of Ukraine's foreign trade in goods in the deepening of interstate economic contradictions.An econometric analysis in (Orudzhev&Alizade,2020) of the mutual influence of the GDP of Azerbaijan and the trade turnover of this country with Ukraine was carried out.Estimates of the parameters of the econometric model are found, after which, with the execution of the model, the correction of errors of high quality qualitative indicators.From the calculations for the lag (1)(2)(3) of this work, it can be seen that α(-2.147153;-1.755) is a correction vector.At such coordinates, the equilibrium is off the scale.However, in the case of lag (2 2), there are estimates of the cointegrating vector β(1; 13.7559; -0,148975) and cointegrating vector α(-0.017035;-0.146521),where (21.7) (-1.03) (-1.94) (-20.2) t-values are indicated in brackets under the coordinates.
The research (Kovtun&Matviienko,2019) considers current trends in international trade in goods and features of Ukraine's foreign trade.The reorientation in the geographical scope of exports from the CIS countries towards the country application was analyzed, and foreign trade relations of Ukraine with Azerbaijan and Georgia were not considered.The main environmental factors in (Baliuk,2021;Baliuk,2022), that are characteristic for the development of export-import activities of domestic industrial enterprises in modern conditions are summarized, and priority economic strategies for the development of export-import industrial activity in Ukraine are also substantiated.The article (Dyogtev et al.,2016) analyzes the economic connection of Georgia with Russia, Turkey, Iran and Kazakhstan using indicators of the trade turnover of foreign direct investment, cross-border movement of finance, tourism and transport development.The issue of interconnection of Georgia's trade and economic relations with Azerbaijan and Ukraine was not touched upon.The current trends in the world economy, the EU economy, the post-Soviet economy, mainly the economy of Georgia, are considered and the main aspects of the socioeconomic development of Georgia are identified in (Silagadze,2020).
We also note that , the regional organization GUAM (Georgia, Ukraine, Azerbaijan and Moldova) is an organization for democracy and economic development, established in 1997, which is still practically inactive in the implementation of a free trade zone between countries, sectoral cooperation, in the fuel and energy sector , in the field of cross-border transportation, logistics and communication, which could give an incentive to free economic and trade interaction between the GUAM member states in the relevant areas.
The main results of the research.In this study, with a more detailed change from (Orudzhev&Alizade,2020; Orudzhev&Alizade,2021), a new specification of models for the relationship between Azerbaijan's GDP and trade turnover with Ukraine, supplemented with Georgia is defined.Forecasting the qualitative indicators of these countries in terms of export-import operations was carried out by the method of No 155 logarithmic approximation of actual data with reproduction by extrapolation.This study is an addition to the article (Alizade,2022).Descriptive statistics on the logarithms of given indicators from (www.stat.gov.az;www.geostat.ge/ka;www.ukrstat.gov.ua) are shown in Table 1:   Table 1 shows, that the elements of the 2nd, 3rd, and 4th columns have a slight left-sided asymmetry of the empirical curves relative to the theoretical one, and for the element of the 5th column, the vertex is significantly shifted to the left.The excesses for the elements of columns 2, 3, and 4 show that there is a slight peak of the empirical curve, and for the element of the 5th column, this value increases approximately four times, which leads to a significant deviation of the empirical distribution of residuals from the normal one.
Based on a comparative analysis with the results of (Orudzhev&Alizade,2020; Orudzhev&Alizade,2021) and Table 1, it can be assumed that the dependence of the logarithm of Azerbaijan's GDP on the logarithms of Azerbaijan's foreign trade turnover with Ukraine and Georgia is described by a linear regression model As can be seen from the results obtained in Table 2, the general formal model is the most accurate, the coefficient of determination has a higher value of 94%.
The coefficient at LN_UKR_T means that each percent of The stability analysis of the model parameters is explained by the representation of the cumulative sum of squares of the residuals, and the graphical description of the CUSUM test demonstrates that all parameters are dynamically stable, since the curves lie within the critical limits in the 5% region.
Let's pay attention to the correlation coefficients between the factors, presented by the correlation matrix of The correlation coefficients are close to 1, demonstrating an almost complete positive correlation in Table 3.In other words, Azerbaijan's GDP is strongly linked to the growth of trade with regional strategic partners Georgia and Ukraine.
Here, the correlation captures the proximity of shortterm relationships between variables and does not take into account the stationarity or non-stationarity of these indicators.Therefore, building a model based on correlationregression analysis gives biased estimates of the model coefficients.Based on this, it is necessary to consider models based on cointegration analysis, which make it possible to analyze series with non-stationary components, both in the short-term and in the long-term periods.The construction scheme will be described below.
To test the significance of the constructed model (2), the observed and critical values of the Fisher criterion were calculated.These values are respectively equal to 117.2768 and 3.44 at a significance level of 5% and degrees of freedom  1 = 2,  2 = 22.Since 117.2768 > 3.44, the model is considered significant.The significance of the regression coefficients is also confirmed using t-statistics.Autocorrelation had checked using Durbin-Watson d-statistics.According to the table of critical values of d-statistics for the number of observations 25, the number of explanatory variables 2 and the given significance level 0.05, the values   = 1.21 and   = 1.55, which divide the segment [0.4] into five regions, the observed value   = 0.75.Since   = 0.75 <   ,   then there is an autocorrelation of the residuals.Now consider the problem of heteroscedasticity.Heteroskedasticity leads to the fact that the estimates of the regression coefficients are not effective, the dispersions of the distributions of the coefficient estimates increase.Here, the heteroscedasticity of the residuals is verified by the White test,  2 =  *  −  , где  = 25, according to which the value ,  2 −where is the coefficient of determination for the auxiliary regression of the squares of the residuals on all regressors, their squares, pairwise products and a constant, is 5.230084, and this value is less than the value χ 0,16 2 (5)= 5.303272885.The corresponding P-value is greater than 0.05, ithe null hypothesis that the random term is homoscedastic is not rejected.
The results of the extended Dickey-Fuller test showed that the original series and their first differences are not stationary, while the second-order difference operators are stationary.The test results are shown in Table 4: The results of the above tests show that the estimates of the regression coefficients are poor.The reason for this is the nonstationarity of the studied series.One of the No 155 approaches to the correct mathematical description of series is the cointegration approach of Engle-Granger and Johansen.This approach can be applied to build an error correction model if the time series are integrable of the same order.In our case, all series are second-order integrable.For complete information content of the research, in addition to the Granger causality test, it is necessary to analyze the response of impulse functions.These functions No 155 represent the median estimate with a 90% confidence interval of the endogenous variable for a positive shock of one standard deviation of the exogenous variable and indicate the time to return to the equilibrium trajectory.Confidence intervals were obtained by bootstrapping with 100 replications, as described in (Hall,1992).unit of its standard deviation for the entire period.The responses of variables to these shocks in the periods t=1,2,…,10 are estimated.The values of the variables in these time periods represent the corresponding impulse response functions.

Reactions of impulse response functions
It is clear from Figure 1 that the response of the variables to the deviation from the general stochastic trend is not the same.In the case of response to shocks, the endogenous variable goes its part of the way to equilibrium.
To study the influence of exogenous variables on an endogenous variable over the next 10 years, an econometric  Table 6.1 shows that in the annual forecast ΔLN_GDP_AZ, the largest errors fall on the shocks ΔLN_GDP_AZ, ΔLN_UKR_T and ΔLN_GEO_T, respectively, in the amounts of 88.4% on a two-year horizon, 90% on a ten-year horizon, and 9.3% on a ten-year horizon; for ΔLN_UKR_T these values will be 38.87% on the horizon of two years, 75.7% on the horizon of one year, 10.56% on the horizon of six years, and for ΔLN_GEO_T 32.14% on the horizon of ten years, 6.31% on the horizon four years, 90.46% over the horizon of one year.These figures indicate that the greatest uncertainty in the forecast for ΔLN_GDP_AZ, ΔLN_UKR_T and ΔLN_GEO_T during the first five years is given by their own changes.
Based on the Angle-Granger and Johansen test, to obtain the specification of the Vector Error Correction Model (VECM) at a significance level of 1%, all 5 options were analyzed: no free member; the data does not have a deterministic trend, the cointegration relation contains an intercept and does not contain a trend; the data contains a deterministic trend, the cointegration equation contains an intercept and does not contain a trend; the data has a deterministic linear trend, the cointegration relation has both a trend and an intercept; the data contains a deterministic quadratic trend, the cointegration equation contains a trend and an intercept.In the case of the information criteria, Akaike and Schwartz, respectively, had low values of 1.899115 and 3.297802.All variables are cointegrated, which certifies their long-term relationship and the authenticity of the correlation.Taking into account the information criteria of Akaike and Schwartz, the lag equal to 2 turned out to be the best.One cointegration relation with the degree of integration 2 and the cointegration rank equal to 1 was obtained.
In tables 7.1 and 7.2, to determine the number of cointegration vectors in the time series, we first tested the null hypothesis that there are no cointegration vectors, against the alternative hypothesis that there is one such vector.We rejected the null hypothesis, since the calculated values were greater than the critical values, from which we concluded that there is one cointegration vector.We then tested the hypothesis that there is one vector against the alternative hypothesis that there are two vectors of cointegration.Here, the calculated criteria are less than the critical values, and we accept the null hypothesis.Thus, we concluded that there is one vector of cointegration.According to (Verbeek,2012), the system of integrated order 2 and cointegrated series can be represented in the form of a vector error correction model (VECM) with a lag equal to 2 and rank 1, which expresses a long-term equilibrium relationship of variables and authenticity their correlations.Performing the procedures of the Eviews 8 program, the following error correction equation was found for the second-order differences of the logarithmic values of Azerbaijan's GDP: where in parentheses under the coefficients are the standard errors of the estimate, ∆(•) = ∆  (•); ∆(−) = ∆ − (•) ,  = 1,3 , "•"corresponding variable is marked.
Above, when implementing the Granger causality test, we showed that there are feedbacks between variables.In the Eviews 8 program procedures, following similar procedures, it is easy to obtain error correction models for the remaining variables: No 155 the importance of mutual trade in goods.
6.The proposed assessments can be used to determine the significant factors of interaction in the dynamics of trilateral trade relations and to assess the growth trend in the openness of the economies of these countries in the regional context.The analysis performed allows us to identify a number of stable and unstable features that indicate the possibility of modeling reasonable predictive scenarios for further mutually beneficial trade and economic ties in the membership of the GUAM project in the conditions of the Ukrainian-Russian and Georgian-Russian military-political and economic crisis.

Table 2 Estimated multiple regression model with logarithms of variables
(2)wth in foreign trade turnover between Azerbaijan and Ukraine is followed by an increase in Azerbaijan's GDP by 0.23% per year, and a 1% increase in Azerbaijan's trade with Georgia leads to an increase in Azerbaijan's GDP by 1.04 % in(2).At the same time, the indicator of foreign trade turnover does not reflect multidirectional shifts in exports and This work is distributed under the terms of the Creative Commons Attribution-ShareAlike 4.0 International License (https://creativecommons.org/licenses/by-sa/4.0/).Proceedings of the 1st International Scientific and Practical Conference «Modern Knowledge: Research and Discoveries» (May 19-20, 2023).Vancouver, Canada No 155 the imports.It should be noted that this model does not take into account changes in other important indicators that directly affect the size of Azerbaijan's GDP.Nevertheless, the results achieved during the construction of the model can be correlated, for example, with the GDP forecast according to the IMF (http://www.imf.org/external/Publs/ft/weo/2017/weodata/weoselagr.aspx).

Table 6 .3 Decomposition of the variance of forecast errors ΔLN_GEO_T by shocks
This work is distributed under the terms of the Creative Commons Attribution-ShareAlike 4.0 International License (https://creativecommons.org/licenses/by-sa/4.0/).