MODELING OF EXPORTS IN ALBANIA

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1 MODELING OF EXPORTS IN ALBANIA Prof. Assoc. Dr. Alma Braimllari (Spaho) Applied Mathematics Department, Faculty of Natural Sciences, University of Tirana, (Albania) ABSTRACT Exports of goods represent one of the most important sources of foreign exchange income that alleviate the pressure on the balance payment and create employment opportunities. Exports opportunities for products in Albania have been increasing significantly, but still they are far from their real capacity. This study is an attempt to model the Albania s monthly export and to forecast the exports value for coming months. The data used in this study are covering the period January 2005-January 2016, and are taken from the database of Albanian Institute of Statistics. Seasonal autoregressive integrated moving average (SARIMA) methodology is used to model the data. In this study is found that the SARIMA (0,1,1)x(3,0,0) 12 model best fits to the natural logarithm of exports data. The results indicated that for the period February-December 2016, exports of goods are forecasted to decrease compared to the respective months of the year Therefore, the policies of government of Albania should support and encourage the exports. These findings are useful for customers, producers and policymakers. Keywords: forecast, SARIMA methodology, stationarity, trend. I. INTRODUCTION International trade is an important element of the global economy and is a key component of economic growth. Foreign trade is of particular importance for the small economies, such as that of Albania. The performance of exports plays an important role in the perspective and sustainable development of the Albanian s economy, and in the trade balance. The export growth rate in several years is an important indicator and its increase directly impacts the economic growth. Exports of goods represent one of the most important sources of foreign exchange income that ease the pressure on the balance payment and create employment opportunities. Albania s geographical location offers a trade potential, especially with the European Union market and the free trade agreements with all Balkan countries have created opportunity for trade development all over the region. Exports' opportunities in Albania have been increasing significantly, but still they are far from their real capacity. Mainly due to lack of marketing facilities (storage, processing, packing of products), low standards related to products safety, low level of competiveness in the market of Albanian products due to low quality and relatively high cost of the Albanian products, and deficiency and low levels of production and industry [1]. The Seasonal autoregressive integrated moving average (SARIMA) methodology has been applied for modeling and forecasting exports of products from several countries. Using monthly data from July 2000 to June 2006, [2] proposed the SARIMA (1,1,0)x(0,1,1) 12 to model Bangladesh export values. Using the data of Meat Exports from India for the period November 1992 to December 2011, [3] found a SARIMA(2,1,0)x(1,1,0) 12 to best fits 15 P a g e

2 to the original data. In the study of [4], with yearly data of Pakistan exports for the period , is found the ARIMA(1,2,2) model to forecast the exports. [5] found the ARIMA (1,1,4) as the most appropriate model among other ARIMA models to forecast Pakistan s exports, using the yearly data for the period of 1975 to [6] used the yearly data from 1969 to 2008 and selected the ARIMA (0,1,2) as appropriate model to generate forecasts export of fish product from Tamilnadu. [7] used a time series data from and ARIMA model to forecast the Pakistan s imports and exports; they found the ARIMA (1,1,0) model with constant as the best fitted model for imports and exports. This study aims to study the exports of Albania. The main objectives are: to propose an appropriate SARIMA model for forecasting the monthly exports of Albania, and to generate forecasts of exports values for coming months using the best fitted SARIMA model, based on the value of Akaike s Information Criteria. The forecast values for the period February-December can help policy makers to improve the exports, and to lead the country ecomomy toward economic growth, development and the improvement of the balance of payment of Albania. II. MATERIALS AND METHODS The time series models are used in this paper to model exports. Stationarity is required for fitting a time-series into SARIMA framework. A time series is called stationary if the mean, variance, and covariance of the underlying series do not depend on time (time invariant). To determine the stationarity, the time plot, autocorrelation function (ACF) and partial autocorrelation function (PACF) can be used as a first attempt. The Augmented Dickey Fuller (ADF) unit roots test can be used to detect the stacionarity of a time series. The ADF unit roots test performs a regression model of the form t 0 1 t 1 i t i t i 1 m X t X X u (1) where m indicate the lag order, and Xt Xt Xt 1. The null hypothesis is: the time series {X t } has a unit root or the series is not stationary (H 0 : ρ = 0; Ha: ρ < 0). If the p value is less or equal to 5%, the null hypothesis is rejected and is concluded that the series is stationary. When a time series is not stationary usually non seasonal and seasonal differencing at the appropriate lag can be applied to achieve stationarity. The multiplicative seasonal autoregressive integrated moving average model is given by s d s D s t ( B) (B )(1 B) (1 B ) X ( B) (B ) Z (2) t where {Z t } is a sequence of uncorrelated random variables with zero mean and constant variance σ 2 (white noise), s is the seasonal lag, B is the backward shift operator (B k X t = X t-k and B k Z k = Z t-k ), p s s Ps q ( B) 1 1B pb and ( B) 1 1B qb, ( B ) 1 1B PB s s Qs 1 Q ( B ) 1 B B ([8],[9]). The Akaike s Information Criterion (AIC) is useful for determining the order of an SARIMA model, and it can be written as AIC 2log( L) 2k where L is the likelihood for an SARIMA model, k is the number of estimated parameters in the model (including σ 2, the variance of the residuals). For small sample sizes, that is, if and 16 P a g e

3 n/k is less or equal to 40, the corrected AIC should be used instead: AIC C 2kn 2log( L) n k 1 where n is the sample size after differencing. The good models are obtained by minimizing either the AIC or AICc value. The residuals of the best fitted model are used for the diagnostic checking. The Ljung-Box test is used to the residuals to determine if the residuals are random and that the model provides an adequate fit to the data in the study. In order to evaluate the performance of the best model are used the Mean Absolute Error (MAE), Root Mean Square Error (RMSE) and the Mean Absolute Percentage Error (MAPE). The value of exports of goods, imports of goods and Gross Domestic Product data used in this study, measured in ALL million, for the period January 2005 January 2016 were taken from the database of Institute of Statistics of Albania [10]. To model and to forecast the monthly exports, the natural logarithm of exports value was used. R statistical package is used to analyze and model the monthly exports data. III. RESULTS AND DISCUSSION The level of exports of Albanian goods was low compared to Gross Domestic Production (GDP). Fig.1 shows the yearly exports values as percentage of Gross Domestic Product of Albania, and during the last years it varied from 8% in 2005 to 16% in Figure 1. Exports as percentage of GDP The fig. 2 shows the value of exports of goods, imports of goods and trade deficit for the period January January The value of monthly exports is increased during the period under study. The value of imports is higher than the value of exports, on average the value of exports is 34.5% of the value of imports. The lowest value of total exports was in August 2005, ALL million; whereas the highest value in May 2014 with ALL million Exports of goods Import of goods Trade Deficit Figure 2. Exports and imports of goods 17 P a g e

4 The fig. 3 shows the value of monthly exports by group of commodities. Three groups have dominated the others: textile and leather manufactures; minerals, fuels, and electricity; and construction materials and metals Food, beverages, tobbaco Minerals, fuels, electricity Chemical and Plastic products Leather and leather manufactures Wood manufactures and articles of paper Textile and footwear Construction materials and metals Machineries, equipments and spare parts Others Figure 3. Monthly exports by group of commodities The Albanian exports were oriented mainly to European Union countries, mostly to Italy. During year 2015, exports to European Union countries were 75.2% of total exports, more specifically exports to Italy were 50.9%, to Spain 5.2%, to Greece 3.9% and to Germany 3.1% of total exports of goods. Exports to Kosovo were 8.6%, to Turkey 2.8% and to China 2.7% of total exports. The natural logarithm transformation of the exports data is used to stabilize the variability of the original data. The ACF and PACF plots of the transformed exports series, in figure 1 in Appendix, show that the series is not stationary and the series has not seasonality pattern. The ADF test statistics for the transformed series was found to be 2.02 (lag order = 5), p = 0.57, so the null hypothesis of unit root cannot be rejected at 5% level, indicating that the series is not stationary. To achieve the stationarity of the series, a differencing at lag 1 is applied. The ADF test statistics for the differenced series was found to be 6.37 (lag order = 5), p < 1%, so the series is stationary. The ACF and PACF plots of the differenced series are shown in figure 2 in Appendix. Many possible models are considered. In the table 1 are shown several estimated model and their respective AICc value. Table 1. Some SARIMA estimated models and their respective AICc value Model AIC c SARIMA(0,1,1)x(3,0,0) SARIMA(0,1,1)x(2,0,0) SARIMA(0,1,2)x(2,0,0) SARIMA(1,1,0)x(2,0,0) SARIMA(0,1,1)x(1,0,0) SARIMA(0,1,1)x(0,0,3) SARIMA(0,1,1)x(0,0,2) P a g e

5 The best fitted model is the SARIMA (0,1,1)x(3,0,0) 12 model with an AIC c value of , and Log likelihood = The results of the best model are shown in table 2. Table 2. Results of the best fitted SARIMA (0,1,1)x(3,0,0) 12 model Variable Coefficient Standard error MA Seasonal AR Seasonal AR Seasonal AR The results of ADF test for the best fitted model residuals indicated a ADF value of -5.4, lag order = 5 and p- value < 1%, so the residuals series is stationary. The ACF and PACF plots of the residuals up to 35 lags, shown in figure 3 in Appendix, indicated that none of the autocorrelations was significant at 5% level. This confirms that the selected SARIMA model was an appropriate model. The results of Ljung-Box test indicated a value of statistics of (df = 36), and p-value = > 5%, that is the residuals of the model are random, and the model is appropriate for the data. The Q-Q normality plot shows that the residuals of the best fitted model are approximately normally distributed. The results of Lagrange Multiplier (LM) test for autoregressive conditional heteroscedasticity (ARCH) test, with null hypothesis: no ARCH effects of best fitted model, indicated a chi-squared value of 10.8, df = 12 and p-value = 0.54 > 5%. To evaluate the performance of the best fitted model, are found the values of MAE = 0.074, RMSE = 0.1, and MAPE = 0.79%. The forecasted values of monthly exports for year 2016, and their corresponding lower and upper 95 per cent confidence interval limits are given in table 3. Table 3. Predicted monthly exports for February-December 2016 Year 2016 Forecast Lower limit Upper limit Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec The forecasted values of exports from February to December 2016 are lower than the respective values of the period February-December The exports value is predicted to decrease on average by 7.34% per month or 1620 Million ALL per month for year 2016 compared to the respective months of the year P a g e

6 IV. CONCLUSIONS Exports are a very important factor to reach a sustainable economic development. The importance of increasing exports is not related only with the reduction of trade balance, but also with the improvement of the quality of products and the increase of the production capacity, new jobs, and wellbeing. The increase of quality of Albanian products will have a positive impact on exports growth. This study is an attempt to model the monthly exports in Albania for the period January January 2016 The results of the descriptive analysis indicated that the value of exports is increased year to year and that three group of commodities had dominated the others: textile and leather manufactures; minerals, fuels, and electricity; and construction materials and metals. The exports time series indicated a positive trend and no seasonality. The natural-logarithm of monthly exports series is found to follow the SARIMA(0,1,1)x(3,0,0) 12 with an AIC c value of This model was used to forecast the monthly exports values for January December The exports values are predicted to decrease on average by 7.34% per month or 1620 Million ALL per month for year 2016 compared to the respective months of the year To increase exports is necessary to improve the infrastructure that obstructs the arrival of products to the market, to increase the level of loans for investments, and to achieve the Europian Union standards of products. Increasing the quality of products is the most important factor for improving the competiveness, and the improvement of the infrastructure reduces the cost. Technological advancement and new methods for management of production systems will encourage the growth of production. Domestic and foreign investment will be beneficial to improving productivity, encouraging capacity expansion, improving quality and competitiveness in term of cost. The policies of government of Albania should support and encourage the exports. In the future research, the relationships between exports, imports, foreign direct investments and exchange rate ALL/euro can be studied using econometric models. REFERENCES [1] E. Bezhani, The economic impact of agricultural products in the Albanian products, Academic Journal of Interdisciplinary Studies, 2(1), 2013, [2] M. Shitam, M.M. Hossian, and M. Rajeb, A re-analysis of time series modeling of Bangladesh Export values, International Journal of Statistical Sciences, 12, 2012, [3] R.K. Paul, S. Panwar, S.K. Sarkar, A. Kumar, K.N. Singh, S. Farooqi, and V.K. Choudhary, Modelling and Forecasting of Meat Exports from India. Agricultural Economics Research Review, 26(2), 2013, [4] A.Farooqi, ARIMA model building and forecasting on Imports and Exports of Pakistan, Pakistan Journal of Statistics and Operations Research, X(2), 2014, [5] Sh. Mehmood, Forecasting Pakistan s Exports to SAARC: an Application of univiriate ARIMA mode, Journal of Contemporary Issues in Business Research, 1(3), 2012, [6] T.J. Sankar, Forecasting Fish Product Export in Tamilnadu A Stochastic Model Approach, Recent Research in Science and Technology, 3(7), 2011, P a g e

7 [7] A. Ghafoor, and S.Hanif, Analysis of the Trade Pattern of Pakistan: Past Trends and Future Prospects. Journal of Agriculture and Social Science, 1(4), 2005, [8] P.J. Brockwell, and R.A. Davis, Introduction to time series and forecasting (Springer-Verlag, New York, 2002). [9] H.R. Shumway, and S.D. Stoffer, Time series analysis and its applications with R examples (Springer- Verlag New York, 2006). [10] Albania Institute of Statistics, Database. Accessed APPENDIX Figure 1. The ACF and PACF of the transformed exports series Figure 2. The ACF and PACF plots o the lag 1 differenced transformed series Figure 3. The ACF and PACF of residuals series 21 P a g e