Comparison the Error Rate of Autoregressive Distributed Lag ( ARDL ) and Vector Autoregressive ( VAR ) ( Case study : Forecast of Export Quantities in DIY )

Forecasting is estimating the size or number of something in the future. Regression model that enters current independent variable value, and lagged value is called distributed-lag model, if it enters one or more lagged value, it is called autoregressive. Koyck method is used for dynamic model which the lagged length is unknown, for the known lagged length it is used the Almon method. Vector Autoregressive (VAR) is a method that explains every variable in the model depend on the lag movement from the variable itself and all the others variable. This research aimed to explain the application of Autoregressive distributed-lag model and Vector Autoregressive (VAR) method for the forecasting for export amount in DIY. It takes export amount in DIY and inflation data, kurs, and Indonesia’s foreign exchange reserve. Forecasting formation: defining Koyck and Almon distributed-lag dynamic model, then the best model is chosen and distribution-lag dynamic forecasting is performed. After that it is performed stationary test, co-integration test, optimal lag examination, granger causality test, parameter estimation, VAR model stability, and performs forecasting with VAR method. The forecasting result shows MAPE value from ARDL method obtained is 0.475812%, while MAPE value from VAR method is 0.464473%. Thus it can be concluded that Vector Autoregressive (VAR) method is more effective to be used in case study of export amount in DIY forecasting.


Introduction
Forecasting is estimating the size or number of something in the future according to the lag that is analyzed naturally, especially using statistic method (Sudjana, 1986).Time series data are often used as input or output data for performing forecasting process.Some forecasting method that can be applied to perform forecasting according to the time series data include: naïf approach method, moving average, exponential smoothing method, and trend projection method.
The data used in this research is the historical data of export amount in DIY.
Therefore, it will be performed a linear also the previous movement of the whole variable inside the system.In VAR analysis, the system model sought between time series variables in vector form to be used to determine the causality relationship (interrelation) of the variables (Gujarati, 2003).This

Stationarity Test of Time Series Data
In  (Rosadi, 2012).

Optimal Lag Examination
Optimal Lag Examination is used to determine optimal lag length which be used to determine the parameter estimation of VAR model.This can be caused by causal relationship and VAR model which are sensitive toward the lag length, so it is necessary to determine the proper optimal lag length (Widarjono, 2007) The optimal lag is on the smallest value obtained in calculation (Widarjono, 2007).

Model
Dynamic model is a model that describes the movement of the dependent variables which is influenced by the value from the past.The required time for independent variable X in influencing dependent variable Y is called time difference or lag or time-lag.
There are 2 kinds of linear regression model that pays attention to the time influence, there are:

Distributed Lag Model
When a dependent variable is influenced by the independent variable in the current time, and if it is also influenced by the independent value in the previous time, then it is called distributed lag model.There are 2 kinds of distributed lag:

Autoregressive Model
If the dependent variable is affected by the independent variable in the current time, and also affected by dependent variable itself in the previous time, so it called autoregressive model.

This
is the example of autoregressive model, which is also known as dynamic model, because it is figure out the timeline from the dependent variable with the value from the previous time (Gujarati, 2003).3) He define that the value of β's is a sum of limited long term (Gujarati, 2003).

Almon Method
Almon method used to determine the estimated of dynamic distributedlag, which the length of the lag is known.The model that used in the almon method is finite lag (3) method as follow: Based on the mathematics theory which is well known as Weir-Strass's Theorem, Almon assumed that βi can be approached by a certain polynomial in the i which has degree, With i is the length of the lagged.That Polynomial degree could be 0, 1, 2, … etc.For example, if β i was following polynomial of second degree of the model, so it can be written as: By distributing equation ( 2) to (1), obtained If defined: = ∑ So it will be: Equation ( 11) can be predicted by OLS Procedure.The probability of ̂ and ̂ that will be possess the desired properties if only the error full filled the classic assumption.After all ̂ predicted from equation ( 10), coefficient can be calculated using equation ( 9) as follow: So the estimation of distributed lag model is:

Koyck Model Formation
In order to makes analysis become easier the researcher using software Eviews 10.

VAR Model Formation
Based on the optimal lag test it is obtained the value of optimal lag on the lag 1.
of export amount in DIY according to its error value.The variables used are inflation, exchange rate and foreign exchange reserve because it is suspected to have an effect towards the export amount in DIY.
Method usually used to determine the estimated dynamic distributed lag model, which the length of the lag is unknown (3) as follow: , k = 0,1, … dan 0 < λ <1 (6) Eksakta: Jurnal Ilmu-ilmu MIPA p. ISSN: 1411-1047 e. ISSN: 2503-2364 Comparison the Error Rate of Autoregressive Distributed Lag (ARDL) and Vector Autoregressive (VAR) ...... (Dewi Kusumaningrum, Sugiyarto Surono) 171 Where λ is the decreasing of distributed-Lag, Koyck Model was written as follow: assuming the value of λ is not important, Koyck tooe a side of β's by the change the sign;2) By assuming the value of λ<1 , He gave small integrity to β's which is far from now;

Figure 1
Figure 1 Graphic Forecasting of ARDL and VAR Conclusion Based on the test it is concluded that Autoregressive distributed-Lag model cannot be used because the Koyck assumption does not fulfilled.So to overcome the calculation of Autoregressive Distributed Lag method used Autoregressive distributed-Lag Almon method with the length of lagged is three and polynomial degree 14)

Table 4 .
VAR parameters estimation (Continued) 176 more effective to be used in case study of export amount in DIY forecasting.The forecasted result of 2018 and the comparison of MAPE value can be seen on the table 5: Comparison the Error Rate of Autoregressive Distributed Lag (ARDL) andVector Autoregressive (VAR) ......(Dewi Kusumaningrum, Sugiyarto Surono)

Table 5 .
Forecasted result of 2018

Table 6 .
The Comparison of MAPE Value