Estimation of Indonesian Beef Price Forecasting Model

: The need for beef in Indonesia tends to increase along with fluctuated beef prices. The existence of price fluctuations will be a risk for producers and consumers. Therefore, price information is necessary, especially the future beef price and price forecasting is the answer to need. The purpose of this study is to analyze and identify the best forecasting models for domestic and international beef prices. The data used is monthly retail price data for domestic and international beef from 2013:1-2017:12. Four models used in this study, namely decomposition models, ARIMA, moving averages, and Single Exponential Smoothing are applied. The best forecasting method for forecasting domestic and international beef prices is the ARIMA model based on the lowest values of MAD, MAPE, and MSD .


INTRODUCTION
Data published by Pusdatin (2016) informs the development of beef prices at the consumer level from 1983 to 2016 fluctuating and tending to increase. During this period, the price of beef at the consumer level increased by 13.17% /year. The price of beef for the last five years (2012)(2013)(2014)(2015)(2016) also has a tendency to increase from the price of Rp.76,925,751, -with a 5-year growth of 11.08%. The phenomenon of a high increase in meat prices occurred in the last five years where the highest price reached Rp.116,751 / kg in 2016. This price increase is usually due to high meat consumption on religious holidays and national holidays. However, the beef price from Eid Al-Fitr until September 2016 has never returned to its initial level. The increase in consumption which is not offset by increased production of beef causes an increase in the number of beef imports. This will cause uncertainty and instability in domestic beef prices. With the price volatility of beef, it is important to forecast to find out the estimated price for the next period to be analyzed from the previous price. The choice of forecasting method must be with the right model in order to get accurate results. Therefore it is important to forecast the price of beef using the best model.

MATERIALS AND METHODS
The data used in this article is the monthly price data for world/international beef from 2013: 1-2017: 12 obtained from Index Mundi. While the monthly (retail) price data for domestic / Indonesian beef from 2013:1-2017:12 was obtained from the Food and Agriculture Organization (FAO).
There are 4 (four) models used to forecast the prices of Indonesian beef and international beef. In detail these models will be explained as follows:

Decomposition Model
In the decomposition method, there are two models, namely additive and multiplicative decomposition. Additive and multiplicative decomposition models can be used to predict the trend, seasonal and cycle factors. where Yx= periodic data period x, Tx= period trend data x, Sx= seasonal factor (index ) period x, Cx = cyclic period x, Ix= error factor x.
Several studies have used decomposition models for forecasting research, such as Indira's research (2018) for forecasting the number of aircraft passengers.

ARIMA Model
The Autoregressive Integrated Moving Average (ARIMA) is often also called the Box-Jenkins time series method. ARIMA is very good for shortterm forecasts, while for long-term forecasts the accuracy of its estimates is not good. Usually, it will tend to be flat for a fairly long period. ARIMA can be interpreted as a combination of two models, namely the autoregressive (AR) model which is integrated with the Moving Average (MA) model. The ARIMA model is generally written with ARIMA notation (p, d, q). P is the degree of AR process, d is the differentiation order and q is the degree of MA process (Nachrowi, 2006

Moving Average Model
The model Moving Average (MA) is an indicator that is often used in technical analysis that shows the average value of data over a given period. The averaged data is time-dependent data. Moving Average is usually used in stock/forex technical analysis, price to measure momentum and determine the possible area of support and resistance. The MA method can be formulated as follows: Where = Time series data (data series), N = Total average number of periods, = prediction in period t + 1.

Single Exponential Smoothing Model
Exponential smoothing model is a procedure that repeats continuously calculation that uses the latest data. Each data is given a weight, where the weight used is symbolized by α. The α symbol can be determined freely, which reduces forecast error. The smoothing constant value, α, can be selected between the values of 0 and, because it applies: 0 <α <1 (Garpersz, 2005). The model Exponential Smoothing was used by Suryani & Wahono (2015) in his research on forecasting gold prices.
Mathematically, the exponential writing equation is as follows: Where St + 1 = Forecast value for the next period, α = Writing constant (0-1), Xt = Data in period t, St = Old writing value or starting average until t-1 period.

Model Selection
The forecasting method aims to produce optimum predictions that do not have a large error rate. If the error rate is getting smaller, the forecasting results will be closer to the actual value. Accurate projection results are predictions that can minimize forecasting errors. The best model is selected from the model that has the smallest MAPE, MSE and MAD values.

Mean Absolute Percentage Error (MAPE)
This approach is very useful if the forecasting variable size is an important factor in evaluating the accuracy of the forecasting.
MAPE provides an indication of how much forecasting error is compared to the actual value of the data series. where: At=Actual Demand in a period -t, Ft=Demand forecasting (Forecast) in period-t, n=Amount forecasting period involved.

The average Absolute Deviation (MAD)
MAD is the average absolute error over a given period regardless of whether the forecasting results are greater or smaller than the reality. Mathematically, MAD is formulated as follows (Nasution & Prasetyawan, 2008): where: At=Actual Request in a period -t, Ft= Demand forecasting (Forecast) in period-t, n=Number of forecasting periods which are involved.

Description of Beef Prices
Prices of beef prices used are domestic beef retail prices and international beef prices from 2013:1-2017: 12 (60 observations). Descriptively domestic and international beef prices can be seen in Table 1, while graphically can be seen in Figure 1.
From   Table 2 as follows: In Table 2, the results of the decomposition analysis on domestic beef prices decomposition of the best models are models additive decomposition with MSD values smaller than MSD from multiplicative decomposition models, while the MAPE and MAD values of each model are the same. From this additive decomposition model, forecasting the price of dominate beef in the next period (61st period) is Rp. 121,327, -.
For the results of decomposition analysis on international beef prices, the best decomposition model is an additive decomposition model. This conclusion is based on the smaller MAPE, MAD and MSD values that are owned by the Additive decomposition model. From this additive decomposition model, forecasting international beef prices in the next period (61st period) is $ 4.38.

ARIMA Model
The Arima model will first see data that is used stationary or not.data can Time series not be separated from autocorrelation which causes data to be not stationary. Therefore the data to be analyzed must be ensured to be stationary both for variety and average. To find out the stationary data on the variety, transformation needs to be done by using Box-Chox Transformation, where the value of the Rounded Value must be equal to 1. If the Rounded Value value is not equal to 1 then the transformation of the Rounded Value is 1.
For seeing the stationary data on the average can be seen in the autocorrelation and partial autocorrelation functions in figure 4 and 5 as follows:

In
Autocorrelation Function (ACF) and Partial Autocorrelation Function (PACF), Domestic and International Beef Prices after data has experienced differencing 1 time. This shows that the ACF and PACF data is stationary because the lag that comes out of the line confidence interval does not exceed 3 and the data can be continued to be estimated using the ARIMA model.
The price of domestic beef is obtained by the Arima model (5,1,0) with the forecast price for the 61st period amounting to Rp.117,729. Results of the estimation of Arima models can be seen in Table 3. For international beef prices, the results of the estimation of the Arima model can be seen in Table 4 with the Arima model (2,1,3) with the forecast price for the 61st period amounting to $ 4,26.

Moving Average
On the Moving Average model at the price of domestic beef and international beef prices can be seen from the estimation results in table 5. For the price of MA 1 domestic beef type is the best type with MAPE values (1%), MAD (907) and MSD (1701792) with estimated meat prices domestic cattle in the 61st period is Rp. 116,680, -. Similar to the price of domestic beef, the best price of MA type international beef is type 1 with MAPE values (3.3159%), MAD (0.1500) and MSD (0.0408) with estimated beef prices international in the 61st period was $ 4.28.

Methods single Exponential smoothing
In a single exponential smoothing method is performed using a value of 0<α<1. The comparison of the estimation results from the method is single exponential smoothing used for the value of α ranging from 0.1 to 0.9 can be seen in table 6 as follows:  Smoothing (α=0,9) 3,4214 0,1550 0,0445 From Table 7 it can be seen that the selection of the best model for price data ( retail) Domestic is the ARIMA model (5,1,0) and world beef is the ARIMA model (2,1,3) with the smallest comparison of MAPE, MAD, MSD values between other models. This is in line with Sukiyono et al (2018) 's study of accurate cocoa price forecasting models, where the best model of the study is the ARIMA model. In addition to the research of Novanda et al (2018) regarding the forecasting of the world and domestic coffee prices, the Arima model is also the best model with the smallest MAPE, MAD, MSD values delivered by other models.

CONCLUSION
The best model for forecasting (retail) domestic and global beef prices is the ARIMA model. This is because the model has the lowest MAPE, MAD, MSD among the other models.