A Comparison of the Smoothing Constant Values Among Exponential Smoothing Methods in Commodity Prices Forecasting

Commodity prices forecasting is one of the business functions to estimate future demand based on past data trend. This study aims to implement a trial and error technique of the constant (alpha α) value in the exponential smoothing method. Dealing with confusion that often researchers find in selecting an alpha (α) value among exponential smoothing families, which suits characteristics of the investigated case. As selection of the constant value precisely contributes to reduce the forecasting deviation. This paper used the alpha (α) value in the range 0,1 to 0,9 and utilized the mean absolute percentage error (MAPE) and Mean Absolute Error (MAE) as the parameter to know the grade of prediction. In data training, the authors used Single Exponential Smoothing (SES) and Brown’s Double Exponential Smoothing (B-DES) as methods to compare the results of prediction. It is addressed that forecasting with alpha (α) 0,1 is the most optimal values for Single Exponential Smoothing (SES) in this case with margin error 0,00036 of MAPE and 16,84 of MAE.


Introduction
Commodity prices forecasting is an important part of decision-making activities. The main benefits in forecasting is ease in predicting future demand. One of forecasting method is the time series. Analysis of time series is used to data collected over time such as: daily, weekly, monthly, as well as annually data [1]. To model data in the time series, exponential smoothing is used. Besides being simple in solving problems, it can be used in all domain data in the form of time series [2] to forecast future data [3]. Two popular methods in exponential technique includes Single Exponential Smoothing (SES) and Brown's Double Exponential Smoothing (B-DES). The basis for applying both methods is due to the exponential smoothing provides a larger weight in the current data and calculates all prior observations [4]. To get accurate results in predictions, exponential smoothing required a constant value denoted by alpha (α), where alpha is a smoothing constant in range zero and one [5] [6].
Many works have been using exponential smoothing constant application for forecasting. Such as forecasting for electricity load demand with alpha 0,9 [7]. Meanwhile, studied with alpha 0 to 1 have been carried out such as fish inventory prediction [8], rice price forecasting [9], liquefied petroleum gas [10] and prediction of monthly cargo weight [11] food commodity prices [12], forecasting Palm Oil real production [13] and wind energy predictions [14]. Furthermore, some researchers tried to integrate the Brown's Double Exponential Smoothing (B-DES) method with other methods such as predicting stock exchange composite index [15], and prices prediction [16] compared with Weighted Moving Average. Then predicted the number of batik cloth requests [17] and consumer price index [11] with alpha between 0-1. However, those previous works have not been discussed the comparison of these methods.
Selection of the constant value precisely is very important, as it contributes to reduce the forecasting deviation, or conversely elevates the deviation. In fact, researchers often find a confusion in selecting an alpha (α) value among exponential smoothing families that suits characteristics of the investigated case. Realize the importance of the constant values selection, the authors conducted a study to find the best alpha (α) value in forecasting commodity prices. In this paper the authors . For this study, we used trial & error method to test alpha value from 0,1 to 0,9. The aim of the research is to find best alpha value in reducing the error measurement as well as to obtain the best method which is suitable with the training data. The proposed method will be implemented in the Modern Market of Makassar city, with case study of Chicken sales.

Dataset Structure
The study took place in Makassar city, South of Sulawesi, Indonesia. The dataset consists of three months' chicken meat process history. For simulation, we used chicken prices commodity dataset starting from August to October, 2019 as shown in Table I.  [18]. It presents an advantage for short-term forecasting [19]. The general model for SES is written in formula (1) [20].
is single exponential smoothed value in period t+m, y is the actual value at time period t. While α is the smoothing constant (α) between 0 to 1, and F is the forecast made in period t.
Furthermore, another method using in this research is Brown's Double Exponential Smoothing (B-DES). This method was developed by Brown to overcome difference between actual data and forecast values. B-DES is usually used for loading data linear trend [21] as presented in formula (2) to (6) [17].
Symbol is the smoothing constant (α) between 0 to 1, + is forecasting result for period t+m, ′ is the value of single exponential smoothing for period t. While " is the value of double exponential smoothing for period t, and a , b are smoothing constant. Stages how this research conducted as presented in Figure 2, as well as the pseudocode in Figure 3.

Forecasting Error Measurements
In testing forecasting accuracy, it is needed to calculate the percentage error that occurs between the actual values and the predicted results. We use Mean Absolute Percentage Error (MAPE) and Mean Absolut Error (MAE) as measurement tools, where the best value is obtained from the smallest error value. MAPE is a prediction accuracy calculated using the absolute error [22]. It explains that how much error in forecasting data compared with the real values using formula (7) [17].
Where n is number of data, shows the actual data, indicates the forecasted data. Meanwhile, MAE is the absolute value of the actual data minus the forecast result. The equation of MAE as shown in formula (8) [23].

Results and Discussions
Historical data in Table I indicate significant fluctuation of chicken meat prices. As shown by irregular alternation of the increasing and decreasing sales pattern trends. Due to unstable, it is necessary to predict the chicken meat prices in certain periods in the future. The SES and B-DES methods are suitable for price forecasting in both short and long term. Both methods require the alpha (α) parameter. The input value (α) is to minimize the sum of squared and the absolute error number in forecasting [24]. In this study, we used a trial and error method to get the best alpha parameters to optimize the comparison of both methods. The estimation results of the model with alpha parameters are presented in Table 2.
Based on the result recapitulated in Table II Fig.1 to Fig.4 respectively.   Table 2.
Furthermore, Fig. 6 Table 3 recapitulates the whole comparison aspects including two additional evaluation models (MFE and MSE) as an enrichment.