A MODEL SELECTION FOR PRICE FORCASTING OF CRUDE PALM OIL AND FRESH FRUIT BUNCH PRICE FORECASTING

1) Department of Agricultural Socio-Economics, Faculty of Agriculture, University of Bengkulu 2) Department of Soil Science, Faculty of Agriculture, University of Bengkulu Correspondent Author: ksukiyono@unib.ac.id ABSTRACT This study was aimed to determining a fitted forecasting method for the forecasting of crude palm oil prices at international and domestic market as well as fresh fruit bunch prices at collecting merchant and farmer level in Bengkulu Province market by considering three models, namely, double exponential smoothing, autoregressive integrated moving average, and classical decomposition. The data used were monthly data of crude palm oil prices at domestic and world markets from January 2012 – October 2016 and January 2012 – April 2017, while the fresh fruit bunch data at collecting merchant and farmers in Bengkulu Province were also monthly data from 2007 – 2014. The result showedthat the most accurate method was ARIMA for all prices at all market levels. This decision was based on all criteria used to determine the best model including MAPE, MAD, and MSD.


INTRODUCTION
The palm oil industry plays a significant role in Indonesian export. The total exports of palm oil commodities throughout 2016 reached IDR 240 trillion or nearly 14 % of non-oil and gas export with the production of 25.67 million tons. Indonesia is one of the world's largest suppliers of crude palm oil (CPO) at 34 metric tonslast season, or 54% of the global supply (10). This industry also involved 1.5 million households (24). Therefore, due to high dependence on the international market, the Indonesian palm oil industry hasbeen barely impacted by a decrease in CPO demand and price. With a continuous decline in the price and demand of CPOin the world market in 2015, for example, selling prices of fresh fruit bunch (FFB) of oil palm in different districts in Indonesia might have encountered wildprice distortions within the last five years (14). The adverse effects hit not only CPO producers andexporters, but also farmers. A study by Sukiyono, Cahyadinata, Purwoko, Widiono, Sumartono, Arianti, & Mulyasari (28) concluded that both plasma and non-plasma oil palm households were most impacted by the frequently decreasing FFB price, in whichplasma oil palm growers were more sensitive than non-plasma. The study also discovered that oil palm farmers with limited palm oil area were more vulnerable compared to larger oil palm growers. This discussion suggestedthat due to the significant effect of price fluctuations on producers and consumers, they should recognize and understand the pattern of price volatility to avoid the risk of loss. Hence, the existence of CPO price forecasting information will facilitate producers and consumers in handling loss risk. Forecasting the price of valuable commodities, such as oil palm, is essential for all stakeholders involvedin palm oil industries. Unquestionably, price forecast is also useful for policymakers to design and formulate macroeconomic policies including supporting the agricultural sector as noted by Bowman & Husain (3) and Xin & Can (32). In addition, Jha & Sinha (15) stated that agricultural price forecasts help farmers strategize their production and marketing on the predicted prices. For palm oil farmers, appropriate forecasting changes in FFB prices would guide them in the production and marketing of their products as well as prepare themselves economically in facing a decline in FFB prices. Therefore, the research aimed at forecasting prices of CPO and FFB is of great significance. Price forecasting can be defined as an attempt to predict the future of price based on previous data references. Various forecasting techniques have been applied to forecast price depending on the availability of data, time horizon, and objectives. Broadly, two basic approaches to forecasting can be classified, namely, qualitative and quantitative (5,6,12). Qualitative approaches are forecasting techniques based on the judgment of consumers or experts. Thus, these approaches are subjective and appropriate in the absence of previous data. Quantitative forecasting method, on the other hand, can be used when two conditions are met (a) the availability of previous numerical data; and (b) assumption that the existence of some past patterns in the futurewill prevail (13). Compared to qualitative approaches, also known as judgemental methods, quantitative techniques based on statistical techniques are better in terms of their accuracy. Numerous quantitative forecasting methods are available, from a simple model (trend forecasting model) to a more complex model (suh as Autoregressive Integrated Moving Average=ARIMA). Each method has its properties, accuracies, and costs. These properties must be taken into account when choosing a specific method.
Quantitative methods are grounded in statistical and mathematical concepts. They are categorized into (a) Time series forecasting, i.e., the forecasted variables behave according to a particular pattern in thepast and that trend will continue in the future; and (b) Causal forecasting, i.e., cause and effect relationship between the predicted variable and another or a series of variables. Among forecasting models, time series forecasting method is popular among forecasters because it is easy to understand and explain. The simplest forecasting models are a naive model, assumingthat recent period is the best forecaster of the future.This technique is understandable, takes nocalculations, and cheap.
Forecasting techniques are then 481 developed and designed to be more complex along with an increasing need for accuracy in forecasting. Among those techniques are an exponential smoothing model (30), ARIMA models and composite models (17,25,27,29,31,32). Three-time series forecasting methods were used in this paper, namely, double exponential smoothing, ARIMA, and classical decomposition. This article was intended to determine the best forecasting method for the world and domestic CPO prices and FFB price in Bengkulu Province.  (19). Kalekar (16) noted that exponential smoothing with a trend workssubstantially like basic smoothing, but the level andpattern components must be revised each period. The data at the end of each period were smoothed,estimated as the level. At the end of each period, the average growth that had been smoothed indicated the trend.An approach used to handle a lineartrend is called the Holt's two-parameter method (25). Three equationsused are as follows: where t = 1, 2, 3 ... T t  is an uncorrelated process with mean zero, i  and i  are coefficients (to be determined by fitting the model) The Box-Jenkins methodology consists of identifying, selecting, and assessingconditional mean models and univariate time series data (21). The first step is to check the data stationarity since theestimation procedure is only for stationarydata. Data are stationary if the mean and the autocorrelationstructures of the variables are constant over a time series data period. If the stochastic trendexists, it is removed by differencing and variance stabilization is conducted by applying the logarithmic transformation. Decomposition Forecasting Model Decompositionmethods involve decomposing time series data into 4 components, i.e.,trend, seasonal, cyclical anderrorcomponent (23).The model is

MATERIALS AND METHODS Data and source of data
This model assumes that t Y the actual time series value atperiod t, is a function of four components: seasonal (S), cyclical (C), trend (T) anderror (e). These components are combined to generate theobserved values of the time series dependingon their relationship whetherit is an additive or a multiplicative decomposition model (22). An additive decomposition model has the following form: 482 the time series that other elements in the modelare unable to explain. A multiplicative decomposition model can be written as: In this model, trend, cyclic, seasonal and irregular components are multiplied to generate thevalue of time series.

Model Selection
In many forecasting situations, Makridakis & Wheelwright (20) stated that measuring forecasting error for a given set of data and a given forecasting technique has become critical concerns. Error testing, i.e., the difference between the value of forecasting and the actual value, is seen as a way of looking at the precision of a forecasting method. In this study, three criteria for measuring accuracy were chosen to assess the six forecasting models, namely Mean Absolute Deviation(MAD), Mean Squared Deviation (MSD), and Mean Absolute Percent Error (MAPE). The first accuracy measurement used in this paper was MAD. MAD is the absolute average value of error regardless of whether the error is an overestimate or underestimate (18). The second measurement was MSD. MSD is similar to Mean Squared Error (MSE), a commonly-used measure of the accuracy of time series models (8). This method avoids positive and negative deviations from each other by squaring the error. The average squared difference between the predicted andthe actual values of y is MSD. MSD is used to assess how close a regression model matches the real data; a lower MSD indicates acloser fit. Finally, MAPE is the mean of the sum of all of the percentage errors for a given data set taken regardless of sign in order to avoid problems of positive and negative values canceling out one another (20). MAPE is calculated by subtracting the actual value from theforecast value and then dividing by the real value. The absolute value of the division is multipliedby 100 and divided by the number of observations. Similar to MAD and MSE, the smaller the MAPE, the better the forecasting model.   Figure 1, it seems that both world price and domestic price hadsimilar data pattern. The domestic and world CPO price data were not stationary, and the price fluctuations were not of fixed period meaning that they are cyclical, not seasonal. The cyclic component was seen with the increasing and decreasing fluctuations in the CPO price data in the non-fixed period. Cyclical data components are difficult to separate from trends and are often considered a part of trends (11), even though from Figure 1 it is difficult to recognize the presence of trend. The world and domestice prices of CPO tendedto be non stationary because of many factors, namely exchange rate, the price of soybean and coconut oil as alternative products of CPO that 483 tend to fluctuate, demand and supply of CPO in areas where the price tends to be low.

Provincial FFB Price
The data at the provincial level were also monthly price data of FFB both atfarmers and collecting merchants level from January 2007 to December 2014 or 96 observations. Since January 2015, the provincial plantation office no longer recorded these data. The provincial data of FFB prices were likely to follow the data pattern of the domestic and world prices of CPO. Cyclical pattern was dominated by the FFB prices at the provincial level. This finding is not surprising because the FFB pricing at the provincial level was also based on the world prices of CPO. Since 1998, the FFB pricing policy is determined by a Team established by the local government and referring to the Decree of the Minister of Forestry and Estate Crops 627/1998. However, the Decree was subsequently replaced by Regulation of the Minister of Agriculture (Permentan) No. 395 of 2005, but the contents did not change significantly.

Figure 2. FFB price series at Collecting Merchants and Farmers in Bengkulu Province Forecasting Model Estimation and Model Selection
Double Exponential Smoothing: This double exponential smoothing method uses two smoothing coefficients, namely,  (smoothing constant) and  (smoothing trend). These smoothing coefficients are determined by trial and error to produce the smallest error value (26). An indicator used to select the fitted  and  value is Root Mean Square Error (RMSE)in which the best value of  and  is indicated by the smallest value of RMSE. The result of the forecasting models of CPO and FFB prices is presented in Table 1.

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ARIMA Stationary test: It should be noted that most time series data are nonstationary yetAR and MA aspects of ARIMA model require stationary periodical series. Stationarity means that data must roughly be horizontal along the time axis. In other words, the fluctuation of data is a constant average value, independent of the time and variance of the variation remains constant at all times. Non-stationary time series data must be converted into stationary data by differencing, calculatingthe change or the difference in the value of observation. The value of the difference obtained is then rechecked to find out whether it is stationary or not. If nonstationary, then another differencing is performed. If the variance is nonstationary, then a logarithmic transformation is performed. Thus, the first step is to determine the data stationarity as shown by autocorrelation and partial autocorrelation calculations as illustrated in Figure 3 and 4.

. Partial Autocorrelation Function for CPO and FFB Prices
The graphs of autocorrelation and partial autocorrelation function as in Figure 3 and 4 showed that the formed autocorrelation function was rapidly falling into a sinusoidal pattern while the formed partial autocorrelation function exhibitedinsignificant.

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Furthermore, the model checking done with Augmented Dickey-Fuller (ADF) unit root test on CPO and FFB prices confirmedthat the series was stationary, except for the CPO prices at the world market. After the firstdifference, the CPO prices at global market became stationary. Table 2 presents stationary test for the data used in this paper. all the parameters were significant with respective significant levels as presented in Table 5. Similar steps were also conducted for the domestic prices of CPO. It is found that the best ARIMA model for domestic prices was ARIMA (1,0,4). The parameters of ARIMA (1,0,4) with their respective significance levelsaregivenin Table 3.

Estimation of FFB Prices Model
The data of fresh fruit bunch prices, both at collecting merchant and farmer level were already stationary, so they did not need a differencing. From the estimation, it is found that the best model for the FFB prices at collecting merchant and farmer level was the same, i.e., ARIMA (1, 0, 2).

Decomposition Model World and Domestic Prices of CPO
Based on the classical decomposition methods, the world CPO price forecasting results are presented in Figure 5 (Table 5). MAPE value for both decomposition forecasting model was 19.70 %, and MAD value for both models was 156.6. These inconclusive results imply that forecasters can use either additive or multiplicative to predict the world CPO prices. However, if looking at MSD value, the additive hada smaller MSD value than multiplicative. The MSD value of additive decomposition model was 35,731.8 while the MSD value of multiplicative was 35,740.6. This result concludes that additive is more accurate than commutative in forecasting the world CPO prices. Based on this discussion, it is better to apply an additive decomposition model to forecast the world CPO prices for the period of January 2007 -October 2016.

c) Additive Decomposition Model d) Multiplicative Decomposition Model Figure 5. Forecasting Results of World and Domestic CPO Prices
The forecasting result of the domestic CPO prices is presented in Figure 5 (c) and (d). This figure also indicates that the forecasting results from additive and multiplicative have similar patterns and accuracies. The plots tend to have an upward trend and similar cyclical patterns. The upward trend of both additive and multiplicative has positive and quite similar slope described by its fitted trend equation. These results also imply that both forecasting models have a similar degree of forecasting accuracy. This means that,regardless of what decomposition models are used, they will produce identical results. This conclusion is more convincing when viewed from the forecasting accuracy measurements, namely, MAPE and MAD (Table 5). MAPE and MAD value for both additive and multiplicative were similar, i.e., 13 % and 938 respectively. Also, examining the MSD value, additive decomposition model was less accurate than multiplicative because its MSD value was higher than that of multiplicative, i.e., 1 370 177 for additive and 1 369 277 for multiplicative.
For these reasons, it is better to apply a multiplicative decomposition model for estimating the future domestic prices of CPOin Indonesia.

FFB Prices at Collecting Merchant and Farmer Level
The FFB prices at collecting merchant level behave similarly to domestic CPO prices. Thedecomposition plot of the FFB prices at collecting merchant level also showedcyclical and upward trend patterns as shown in Figure  6 (a) and (b). The estimation results using an additive and a multiplicative decomposition model showed that both models had similar fitted trend equation. By looking at the MAPE value, both additive and multiplicative had the same value, i.e., 16.50 % (Table 6). Thus, using either additive or multiplicative to forecast FFB prices at collecting merchant level showed no difference. They produced similar accuracies. However, considering the MAD and MSD values, both accuracy measurements producedthe opposite conclusions. Based on the MAD value, the multiplicative produced more accurate forecasting than additive. However, referring to the MSD value, the additive was more accurate because its MSD value was lower than that of multiplicative. Based on these findings, there is an inconclusive conclusion regarding the best decomposition forecasting method used to forecast the FFB prices at collecting merchant level. Forecasters can use either an additive or a multiplicative decomposition model.    Table 7 shows the differences in theMAPE, MAD and MSD values for each forecasting method. As can be seen, all the accuracy indicator values of ARIMA were the lowest among those of the other methods, which means that the ARIMA model can be used as the best forecasting tool in time series analysis.

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To conclude, the primary goal of this study was to select the most appropriate forecasting technique for the future prices of CPO prices, both at domestic and world markets, and FFB prices at collecting merchant and farmer level in Bengkulu Province. Three types of forecasting methods were used in this study, namely, double exponential smoothing, ARIMA, and classical decomposition methods. The forecasting method was selected by least forecasting errors, that is, minimum values of MAPE, MAD, as well as MSD. Even though some decision is not always unanimous, it is found that the ARIMA model provides the most accurate prediction for CPO and FFB prices based on most of the accuracy measures.