Analysis Monthly Import of Palm Oil Products Using Box-Jenkins Model

The palm oil industry has been an important component of the national economy especially the agriculture sector. The aim of this study is to identify the pattern of import of palm oil products, to model the time series using Box-Jenkins model and to forecast the monthly import of palm oil products. The method approach is included in the statistical test for verifying the equivalence model and statistical measurement of three models, namely Autoregressive (AR) model, Moving Average (MA) model and Autoregressive Moving Average (ARMA) model. The model identification of all product import palm oil is different in which the AR(1) was found to be the best model for product import palm oil while MA(3) was found to be the best model for products import palm kernel oil. For the palm kernel, MA(4) was found to be the best model. The results forecast for the next four months for products import palm oil, palm kernel oil and palm kernel showed the most significant decrease compared to the actual data.


Introduction
The objectives of this study are to identify the pattern of import of palm oil products, to model the time series and to forecast the monthly import of palm oil products. The most important tropical vegetable oils in the global market for oils and fats markets is palm oil [4]. In order to fill the gap and the demand, Malaysia has to imports crude palm oil mostly from Indonesia. The import of palm oil has increased to 1.1 million from 2010 compared to the previous year [4,8]. Due to insufficient crude palm oil for local activities, Malaysia has to import crude palm oil [1,11]. The way to support local supply of palm oil, Malaysia has to import products of palm oil [3]. About 80% of palm oil and palm kernel oil are used in food applications [5].

Method
The stationary of time series data could be determined by plotting the time series plot or autocorrelation function (ACF) plot. The series is considered to be stationary if the ACF plot of the time series value dies down quickly and then the series considered to be non stationary if the ACF plot of the time series value dies down extremely slowly [1,7]. There are three basic model which are autoregressive (AR) model, moving average (MA) model and autoregressive moving average model (ARMA). There are 4 phases in Box-Jenkins methodology which are model identification, parameter estimation, diagnostic checking and forecasting [6,12]. There are few studies that use forecasting as a stepping stone in order to get preliminary results and use it with other mathematical or statistical methods [9,10]. There are other quite considerable studies were carried out to use statistical techniques in Malaysia and other countries [13,14,15]. Whereas the concept of time series have been studied by [16] and [17]. The study will forecast the variable of interest using a linear combination of past values of the variable in an autoregressive (AR) model [2,12].
Moving average (MA) uses past forecast errors in a regression-like model.
The order of the ARMA model is found by examining the autocorrelations and partial correlations of the stationary series.
The Box-Ljung test was used to test the lack of fit of a time series model. If the p-value associated with the Q statistic is small (p-value < 0.05), the model considered inadequate [2]. If the model is inadequate, the analysis continued until the level of satisfactory for model achieved. Once an adequate model has been selected, it was used to forecast for one period or several periods into the future. Once the best model is obtained, the next step is forecast using estimated model equation.

Result & Discussion
The results obtained by analyzing the import of palm oil products data using the Box-Jenkins approached. The stationary mean is 81650. To identify whether the graph is stationary or non-stationary, it can be determined by the autocorrelation function (ACF) and partial autocorrelation function (PACF).  The time series value dies down exponentially fast in Figure 2. The ACF plot shows the data was stationary. Hence, differencing is not necessary.  (1), MA(2) and ARMA(2,1). We determined the best parameter by testing the parameter significant and Ljung-Box Chi Square statistic. Next, to determine the best model we choose the smallest value of mean square error (MSE). Therefore, the model that satisfied all the test is AR(1). The model can be estimated as in equation (4).     The stationary mean is 23712. To identify whether the graph is stationary or non-stationary, it can be determined by the autocorrelation function (ACF) and partial autocorrelation function (PACF).  The time series value dies down exponentially fast in Figure 6. The ACF plot shows the data was stationary. Hence, differencing is not necessary.  3). We determined the best parameter by testing the parameter significant and Ljung-Box Chi Square statistic. Next, to determine the best model we choose the smallest value of mean square error (MSE). Therefore, the model that satisfied all the test is MA(3). The model can be estimated as in equation (5). 75  70  65  60  55  50  45  40  35  30  25  20  1     The stationary mean is 2549. To identify whether the graph is stationary or non-stationary, it can be determined by the autocorrelation function (ACF) and partial autocorrelation function (PACF). The time series value dies down exponentially fast in Figure 10. The ACF plot shows the data was stationary. Hence, differencing is not necessary.

Partial Autocorrelation Function for Products Import Palm Kernel Oil
(with 5% significance limits for the partial autocorrelations) Figure 11. The ACF and PACF plot for Product Import Palm Kernel.
The model identified by reading the plot of ACF and PACF to determine whether the model is AR, MA or ARMA. Figure 11, shows there are three different model to be selected which are AR(2), MA(4) and ARMA (2,4). We determined the best parameter by testing the parameter significant and Ljung-Box Chi Square statistic. Next, to determine the best model we choose the smallest value of mean square error (MSE). Therefore, the model that satisfied all the test is MA(4). The model can be estimated as in equation (6).