Forecasting Foreign Trade of Bosnia and Herzegovına for Wood and Articles of Wood , Wood Charcoal by Seasonal ARIMA Model

In this study, it is aimed that the analysis of export and import values of Bosnia and Herzegovina for wood and articles of wood, wood charcoal with seasonal ARIMA model and forecasting of export and import values for next term by the best appropriate seasonal ARIMA model. The data used in this study were obtained from Trade statistics for international business development (TRADEMAP) and monthly data covering the period of January 2007 and December 2015. Augmented Dickey-Fuller test was used for the stationarity test. Temporary model that have smallest values of forecasting accuracy measurement was determined. The appropriateness of the model (whether plot of autocorrelation has white noise) was determined by using the Box-Ljung test. As a result, ARIMA (3,1,0)(0,1,2)12 model was found as the best forecasting model for both export and import series. It was estimated that export value of Bosnia and Herzegovina for wood and articles of wood, wood charcoal is approximately 531 million$, while import value is 160 million$ in 2020.


Introduction
Export provides to remain in the balance of foreign trade by supply the amount of foreign currency going abroad.In addition, companies are becoming more powerful in global competition by expanding the market network with export and as well negative trend of exports in the future.Export / import that are in a close relationship with GDP, interest rates, inflation, etc. may affect the country's economy.Therefore, the forecasting of accurately value of export/import is very important.
There are many forecasting techniques that including qualitative and quantitative for predicting the future.Quantitative methods are contained in the method of time series analysis [1].There are many methods for analyzing time series.Box-Jenkins method is one of the most used methods.This method is called as ARIMA (autoregressive integrated moving average) analysis.ARIMA model is divided into two.These are nonseasonal and seasonal ARIMA models.ARIMA model combine differencing with autoregression (AR) and a moving average (MA) models.This model can be expressed as w t =c+ϕ 1 w t-1 +……+ϕ p w t-p +θ 1 ε t-1 +… +θ q ε t- q + ε t .Here, w t is the differenced series, p is order of the autoregressive part and q is order of moving average part.Also, we said this an ARIMA (p,d,q), where, d is a degree of difference [2].General process of ARIMA model is as follows [2]; 1. Plot the data.Identify unusual obversations.ARIMA model was applied many studies [3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19].In this study, it is aimed that the analysis export and import values of Bosnia and Herzegovina for wood and articles of wood with SARIMA model.In addition, the best appropriate SARIMA model estimated export and import values.

Material
In this study, it was used that export and import values of Bosnia and Herzegovina for wood and articles of wood, wood charcoal.The monthly data was used for examine the seasonal and trend components.This data covers the period of January 2007 and December 2015.Data were obtained from Trade statistics for international business development [20].Data was taken as $1000.Minitab 16 was used for determine the best model while Eviews-8 was used for the analysis of stationary.

Seasonal ARIMA model
The seasonal ARIMA (SARIMA) model is similar to the ARIMA model which known as a linear approximation for predicting future.This model consists of stages such as identification, estimation, diagnostic checking and forecasting.Accurate predictive models can improve with this model by removing the characteristics of seasonal variation through seasonal differences [21].
The SARIMA model consists of seasonal autoregressive term (P), seasonal integrated term (D), and seasonal moving average term (Q) as well as autoregressive term (p), integrated term (d), and moving average term (q).Generally, the SARIMA model represents as SARIMA (p, d, q)(P, D, Q) and is expressed by equations in follow Here, y t is the observation value at time t, α t is the lagged error at time t, B is the lag operator defined by B k y t = y t-k ; φ p (p=1,2,…p), Φ P (P=1,2,…,P), θ q (q=1,2,..q) and Θ Q (Q=1,2,…Q), p and q are the order of non-seasonal autoregressive and non-seasonal moving average, P and Q is the order of seasonal autoregressive and seasonal moving average, d is order of regular difference, D is order of seasonal difference and S is a seasonal length [21,22].

Forecasting Accuracy Measurements
For the series, forecasting values are calculated and compared with the actual values of the series.There are several criteria for forecasting accuracy measurement.Forecasting accuracy measurements used in this study were given as follows: Mean Absolute Percentage Error; (MAPE)= ( 6) Here, is the forecasting value of model, is the actual value of model and n is the number of observations [19,23].The criteria of MAPE for model evaluation were in Table 1.

Results
Firstly, it must be provided to export and import series of stationary condition.For this, the stationary of export and import series were analyzed with Augmented Dickey-Fuller (ADF) unit root test and results shown in Table 2.It was seen that series is stationary in the 5% significance level according to ADF test when taken difference of the natural logarithm series.The 1stdifference of series was taken.Distribution graph of natural logarithm and differenced of export and import series were shown in Figure 1 and 2. According to Figure 1 and 2, the mean and variance of export and import series are a constant.But, series comprise seasonality.For this, natural logarithm and differenced of export and import series were taken seasonal difference (12st difference).After obtaining these series of stationary conditions, a variety of ARIMA (p,d,q)(P,D,Q) 12 models has been tested by autocorrelation and partial autocorrelation graphics of the export and import series.Autocorrelation and partial autocorrelation graphics of stationarized these series were shown in Figure 3, 4, 5 and 6.As a test results, ARIMA (3,1,0)(0,1,2) 12 model which have smallest values of the error sum of squares (SSE) and the mean square error (MSE) was determined as temporary model for both export and import values of Bosnia and Herzegovina for wood and articles of wood, wood charcoal.The results related to the model were given in Table 3 and 4. The suitability of models were tested with Ljung-Box Q statistic and results shown in Table 5 and 6.While the actual and forecasting export values for wood and articles of wood, wood charcoal were shown in Figure 7, actual and forecasting export values in Figure8.In addition, the forecasting values for export and import were given in Table 7 and 8.

Conclusions
The export and import values of Bosnia and Herzegovina for wood and articles of wood, wood charcoal with seasonal ARIMA model were estimated with seasonal ARIMA model.The natural logarithm, regular difference and seasonal difference of the series were taken.ACF and PACF graphics of the series for determine the appropriate models were examined.Q statistics were calculated for the appropriateness of the model.ARIMA (3,1,0)(0,1,2) 12 model was found as the best forecasting model for both export and import series.It was found that MAPE value of model for export is 8.12%, while MAPE value for import is 7.54%.It was estimated that export value of Bosnia and Herzegovina for wood and articles of wood, wood charcoal is approximately 531 million$, while import value is 160 million$ in 2020.

2 . 3 . 5 . 6 .
If necesarry, transform the data to stabilize the variance.If the data are non-stationary, take first difference the data until the data are stationary.4. Plot the autocorrelation function (ACF)/partial autocorrelation function (PACF) of the differenced data and try to determine possible candidate models.Try your chosen model(s) and use the akaike information criterion (AIC) to search for better model.Check the residuals from your chosen model by plotting the ACF of the residuals and doing a Ljung-Box test of the residuals.If model has not white noise, determine model again.

7 .
If model has white noise, calculate forecasts.