Forecasting Ginger Harvest Yields: A Comparative Study of Double Exponential Smoothing and Long Short-Term Memory Models

2.1 Literature review

The crop yield forecasting literature is quite extensive. Therefore, it is possible to find forecasting methods for systematic and pragmatic prediction through previous relevant data. Forecasting methods can be used to recognize the elements of data that affect the amount of deviation due to unexpected factors. Many studies have compared several forecasting models to find a suitable model to predict crop yields, such as least squares [11, 12], SES [13], winter exponential smoothing [14], weight moving average [15], and ARIMA [16]. However, these models are not accurate at predicting variables. In 2022, Asrul [17] used the DES method to predict potato vegetable yields, which met the annual potato crop production as a material for consideration and the amount of potato production for subsequent market demand was recommended. Therefore, this method can improve forecasting by smoothing the average previous value of time series data in a decreasing (exponential) way. This can provide accurate short-term forecasting, and is easily adapted to changes in data without requiring a lot of data [18].

In addition to the DES method, the LSTM method also has advantages in forecasting time series data, which can be used to overcome long-term dependencies on the input [19]. In addition, LSTM also has a memory block that determines which value is selected as the output, which is relevant to the given input [20]. Several studies have been conducted in the domain of agricultural forecasting, specifically ginger yield prediction. Elpawati et al. [21] analyzed the relationship between ginger-exporting countries, such as Indonesia, China, India, and the Netherlands, using the Value at Risk/Vector Error Correction Model (VaR/VECM) method. It was found that Indonesia's ginger exports increased by 92%, followed by the Netherlands (7%), China (0.2%), and India (0.8%). Apart from that, Das et al. [22] forecasted ginger production in Bangladesh, and tested the performance of eight trend models using the coefficient of determination (R²) and adjusted R². This research shows that the compound growth rate of ginger production is 1.019 per year.

This study tries to compare the accuracy of the DES and LSTM methods in predicting ginger yields based on the nature of the composition, forecasting time, and data patterns. The MAPE and RMSE approaches are used to measure accuracy. The best forecasting result is based on the level of prediction error. The smaller the error rate, the more precise a method is in prediction [23].

2.2 Data collection

This study uses the data on ginger crop yields in the Madura Region in 2015-2019, which was obtained from the Department of Agriculture and Food Security in Pamekasan, Madura, after determining the quantity of the ginger harvest through observation. The ginger harvesting process in Madura is carried out once a week from January to December each year so that approximately 250 datasets are obtained, as shown in Table 1. The yield of the ginger commodity fluctuates from year to year, as shown in Figure 1. This original data consists of yields, years and names of the ginger-producing areas. Before data processing, the data was plotted first to determine the pattern of data flow, making forecasting easier. This data processing aims to ensure that the raw data obtained can be analyzed and conclusions can be drawn easier. Based on the data plot in Figure 1, which shows actual harvest data, it can be concluded that the data distribution is seasonal. In this research, raw data was obtained before analysis. Therefore, the data was preprocessed first, aiming to clean the data from distorted and missing values. This process is highly valid for providing accurate output for forecasting ginger harvest yields.

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Figure 1. Data on ginger commodity yields

Table 1. Sample dataset of ginger plant harvesting

To predict ginger yields, a time-series forecasting method was used. This means that the data is presented based on the time of occurrence without indicating the factors that influence it. The time series method is a quantitative prediction, which is based on the analysis of the pattern of relationships between the variables to be searched (dependent) and the variables that affect them (independent), and changes from time to time, such as weeks, months, quarters, semesters, and years. According to the study of Estiningtyas et al. [24], ginger production is influenced by the abiotic environment, including all living things, such as pests, pathogens, and weeds, which interfere with ginger cultivation. Furthermore, the collected data was analyzed by comparing forecasting methods.

2.3 Forecasting method

Forecasting is an approach to predicting the possibilities for future situations by testing data that occurred in the past [25]. It predicts event history data or events in the business sector. The importance of forecasting is that it influences someone in making decisions and can also be used as a basis for long-term planning efforts in an organization [26]. Forecasting is usually divided into three types, such as short-term, medium-term, and long-term [27]. Short-term forecasting is usually used to predict events using periods of the next day, week, or month [28]. Medium-term forecasting is a forecasting approach that utilizes time data from one year to two years into the future [29]. Finally, long-term forecasting aims to find out events more than two years in the future. Usually, this forecasting uses a time series method which is based on historical data and predicts future event data as output [30]. The purpose of forecasting is to reduce the risk in conditions of uncertainty about something that might happen in the future, thereby minimizing this uncertainty. According to the study of Wang and Chaovalitwongse [31], the approach through forecasting or forecasting methods is divided into two parts, i.e., quantitative and qualitative methods. Qualitative methods are used when no sufficient previous data is available. In other words, this method can be used as a basis for consideration in making decisions for forecasting cases with previous data. However, if a lot of previous data is available and meets the criteria, then forecasting with quantitative methods is more effective than qualitative ones [32]. Forecasting using quantitative methods has several requirements. For example, previous data is available, can be quantified, and has the same trend as future data [33]. To find patterns in the past series and extrapolate these patterns in the future by analyzing the data, this study compares the DES and LSTM methods as a reference for predicting future values.

2.4 DES (Holt)

DES is a linear model proposed by Afiyah et al. [18]. In the DES method, the smoothing process is carried out twice. In principle, Holt's linear and exponential smoothing methods use the multiple smoothing formulae directly [34]. Instead, Holt decides on a seasonal value with parameters different from the two used in the original series. The trend is a smoothed estimate of the average growth at the end of each period [35]. Forecasting Holt's linear and exponential smoothing has several steps [36]:

(i) The first smoothing value is determined.

$S_t^{\prime}=\alpha X_t+(1-\alpha) S_t^{\prime}$                (1)

(ii) The second smoothing value is determined.

$S_t^{\prime \prime}=\alpha S_t^{\prime}+(1-\alpha) S_t^{\prime \prime}$              (2)

(iii) The constant value (α_t) is determined.

$\alpha_t=S_t^{\prime}+\left(S_t^{\prime}-S_t^{\prime \prime}\right)=2 S_t^{\prime}-S_t^{\prime \prime}$            (3)

(iv) The slope value (β_t) is determined.

$\beta_t=\frac{\alpha}{1-\alpha}\left(S_t^{\prime}-S_t^{\prime \prime}\right)$               (4)

(v) The forecasting value is determined.

$F_{t+m}=S_t^{\prime}+t_t m$                (5)

where, $x_t$ is the demand data in period $t, S_t^{\prime}$ is the SES value, $t_t$ is the trend value in $t, \alpha$ and $\beta$ are the intermediate smoothing parameters ranging between $0-1, F_{t+m}$ is the forecasting of $m$ periods, and $m$ is the number of future periods to be forecast.

The $S_t^{\prime}$ parameter is a basic and pragmatic technique used for forecasting with time series anticipation that estimates only the level components. Meanwhile, $S_t^{\prime \prime}$ is specifically for trends in univariant time series which can help change trends over time in different ways, either in a linear trend or an exponential trend. $\alpha_t$ is the level smoothing factor and $\beta_t$ is the trend smoothing factor with the best trend estimate at time $t$.

2.5 Deep learning LSTM

Deep learning is a branch of machine learning that uses a deep neural network to solve problems [37]. Neural networks are inspired by how neurons work in the human brain. Each neuron in the human brain is interconnected and information flows from and between each of these neurons [38]. In deep learning, the network consists of several layers which are collections of nodes [39]. A node becomes the place where calculations occur. Compared to neural networks, deep learning has more hidden layers, such as more than three (including input and output), or even up to hundreds. LSTM is often used to overcome deficiencies found in RNNs, which are the phenomenon of the magnitude of the gradient disappearing [40]. LSTMs use larger data sets and all data information as input to build deep networks. LSTM has three gates that control the use and updating of past text information, namely, the input gate, forget gate, and output gate [41]. There are several steps in LSTM among others [42]:

(i) Calculation of forget gates $\left(f_t\right)$. The value of the forget gate is between 0 and 1, as shown in Eq. (7). Information that is not needed for the cases being managed is removed using the sigmoid function $(\sigma)$;

(ii) Calculation of cell states $\left(c_t\right)$. The tanh activation function is used, which forms a new context candidate, as shown in Eq. (8);

(iii) Calculation of the gate output $\left(o_t\right)$. Sigmoid $(\sigma)$ is used to generate output values and process cell state $\left(c_t\right)$ on tanh activation, as shown in Eq. (9).

$f_t=\sigma\left(W_f .\left[h_{t-1}, x_t\right]+b_t\right)$               (7)

$\begin{gathered}i_t=\sigma\left(W_i\left[h_{t-1}, x_i\right]+b_i\right. \\ \widehat{c_t}=\tanh \left(W_c .\left[h_{t-1}, x_t\right]+b_c\right.\end{gathered}$                    (8)

$\begin{gathered}c_t=f_t * c_{i-1}+i_t * \hat{c}_t \\ o_t=\sigma\left(W_0 \cdot\left[h_{t-1}, x_t\right]+b_0\right. \\ h_t=o_t \tanh \left(c_t\right)\end{gathered}$               (9)

Before the model was trained, the parameters needed for the LSTM model were determined. The hidden state process in LSTM goes through four gates, namely, the forget gate, the input gate, the cell state and the output gate. The forget gate is the first gate that the input passes through using a sigmoid activation function or a sigmoid gate. The hidden state determines the gate input value. At the input gate, the value of the new candidate cell state is calculated and obtained using the tanh activation function. Meanwhile, the gate output uses the sigmoid activation function. The gate output value is used to generate a new hidden state value along with the cell state value.

2.6 Evaluation method

According to the study of Peñaloza et al. [43], the accuracy of the forecasting results can be seen from the large difference between the actual and estimated values of the forecasting. The accuracy value is the difference between the actual and forecast results. The residual value is obtained by measuring the accuracy of forecasting results, i.e., MAPE and RMSE. MAPE is the absolute average percentage error for evaluation calculations in measuring the precision or accuracy of a prediction [44]. MAPE is calculated using the absolute error for each period divided by the real observed value for that period. The general formula for MAPE can be seen in Eq. (10) [45]. The smaller the MAPE value, the more accurate the forecasting model [46]. RMSE is the root result of the average square of the difference between actual and predicted data, as shown in Eq. (11) [7].

$M A P E=\sum_{t=1}^n\left|\frac{y_i-\hat{y}_i}{\hat{y}_i}\right| x 100 \%$                 (10)

where, $\hat{y}_1$ is the forecasting result, $y_1$ is the actual value, $X_t$ is the actual value in $t$ data, $F_t$ is the forecast value on $t$ data, and n is the number of data periods.

$R M S E=\sqrt{\frac{1}{n} \sum_i^n\left(\dot{y}_l-y_i\right)^2}$                     (11)

where, $n$ is the amount of data, $y_i$ is the predicted data, and $y_i$ is the actual data.

This study uses actual data from ginger yields from 2015 to 2019 to produce precise and accurate predictions for the future A comparison between the DES and LSTM methods shows that both methods have the same advantage in forecasting, i.e., high accuracy. Before making predictions, the actual data was converted into a time series by preprocessing the data. Then ginger yields were predicted using both DES and LSTM. Several trials were carried out, including testing the DES model in two stages, i.e., testing the $\alpha$ value when the $\beta$ value was fixed and vice versa to find the best $\alpha$ and $\beta$. This is shown in Table 3. The test results show that the MAPE value tends to be smaller when the $\alpha$ parameter value is large and the $\beta$ parameter value is small. This shows that the DES method has the advantage on relatively little data. However, the weakness is that it should be maintained continuously, checked routinely and updated if there are bugs or new important features are added. Meanwhile, the tests carried out by the LSTM model in this study are shown in Table 6, where there are several parameters, including learning rate, epoch, and LSTM units. The initial weight at each LSTM gate was determined randomly and the initial bias was updated to achieve a loss function at a local minimum with the learning rate. Meanwhile epoch and LSTM units were used to indicate the number of iterations and dataset size in LSTM training to produce a smaller MAPE. The analysis results using the LSTM model show that LSTM can be carried out for long-term time series data because it has memory to store information that will be reused in the calculation process for the next gate. In addition, the prediction results cannot be sufficiently compared with the original data. However, LSTM has a weakness, i.e., reliance on gradient values, where the weights cannot be updated for the next process if the gradient value is lost.

Table 9. Comparison between the results of the DES and LSTM methods and the actual data

According to the results of the trial scenarios, the yield prediction data produced by the ginger yield forecasting system in Table 9 is higher predicted with DES than predicted with LSTM. The forecasting results can also be seen in Figure 5, with actual ginger yield data shown on the graph with a yellow line, DES prediction data with a blue line and LSTM prediction data with a red line. This shows that the LSTM method provides very good performance in this crop yield prediction model, even better than DES. However, LSTM in data processing requires quite a long time, as is evidenced in Table 8, where LSTM has a gate to regulate the entry and exit of processes that work with entry and exit gates. This shows that LSTM has a high complexity. After processing the data, the model was evaluated using MAPE and RMSE. The evaluation results of the LSTM model show that 38.99% takes 8.726145 seconds while the DES model produces an error rate of 43.49% with 0.00004 seconds, as shown in Table 3. Apart from that, it can be seen from the graph that the ginger harvest in July-December has increased, i.e., in the range of 31,000 tons. Meanwhile, the lowest demand occurs in January-June, with around 27,000 tons for both methods. Therefore, farmers are advised to plant ginger before June so that it can be harvested in July to meet market demand. According to the results of the trials, it can be concluded that this forecasting system provides more information for ginger farmers about the estimated future ginger harvest, thereby enabling farmers to handle the ginger planting in certain months more effectively.

According to the trial results in this study and literature review, it can be found that statistical and deep learning methods can be used to process time series data. Each has a relative effectiveness level, depending on the complexity of the data used. The difference between both methods is the use of time in processing data. In addition, deep learning methods tend to require more time than statistical methods. Therefore, further research could utilize several statistical methods to predict data with a short processing time. The LSTM and DES deep learning algorithms are two different prediction models and are suitable for performing time series analysis to improve performance and accuracy in forecasting.

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Figure 5. Graph of forecasting result comparison using the DES and LSTM methods with the actual data