Application of long short term memory to forecast tomato prices

Introduction

Agriculture holds immense significance in the Indian economy, with over two-thirds of the population directly or indirectly reliant on it, and over 70% of rural households deriving their livelihood from it. India ranks second globally in agricultural commodity production, contributing nearly 18% to the GDP. Price stability in agriculture is crucial for social sustainability, as sharp fluctuations impact producers, consumers, government policies, and national food security. (Guo et al., 2022) [1] . Forecasting agricultural commodity prices is vital for farmers, policymakers, and administrative bodies to make informed decisions. Knowing future prices enables farmers to plan their crop selection and government agencies to implement schemes effectively. With increasing demand and diminishing agricultural land, forecasting is essential for the sustainability of future generations and the agricultural sector. (Mahto et al., 2021) [4] . Agricultural price fluctuations pose challenges, affecting people's food expenditure and the entire supply chain from production to consumption. These fluctuations are influenced by various factors, both internal (production costs) and external (market environment, alternative prices), resulting in large, non-stationary, and nonlinear price changes. This uncertainty heightens risks for stakeholders, hindering the healthy development of agriculture and the national economy. (Li et al., 2010) [3] . Scientific data mining methods aid in understanding price patterns and predicting fluctuations, benefiting producers, consumers, processors, and rural development planners. However, despite various forecasting models, including statistical methods, no single efficient solution exists due to the complexity of price changes, which include both abrupt and gradual shifts. (Paul et al., 2022) [5] . In addressing this complexity, machine learning models, particularly Long Short-Term Memory (LSTM) networks, have gained prominence. LSTMs, as recurrent neural networks, excel in learning sequence dependencies, offering the potential to predict time series data accurately by understanding contextual patterns. This departure from predefined assumptions in traditional models makes LSTMs particularly effective in nonlinear cases, offering promise in improving agricultural price forecasting methodologies for better decision-making and risk management. (Shin et al. 2018) [8] .

Methodology

Data: For study purpose the prices of tomato were used for forecasting. The average weekly prices of tomato of Kolar market was collected from January 2011 to December 2020. The data was collected from the Krishimaratavahini. The monthly prices of tomato in the Kolar are predicted using www.extensionjournal.com ARIMA, Holt-Winter's Seasonal method, and LSTM neural network. The performance of these models was evaluated for fitting the best model.

Proposed Techniques:

Here, a model is fit for predicting the prices of Tomato. The performance of classical timeseries models like Holt-Winter's Seasonal Method, ARIMA model and Machine learning model-LSTM were compared for finding out the most parsimonious model. Exploratory analysis indicated the presence of trend and seasonality in the time-series data of prices. ARIMA and Holt-Winter's seasonal method is the commonly used statistical method in forecasting data with trend and seasonality. These models are capable of producing forecasts with relatively well Performance. LSTM model was selected as it has the ability to capture the non-linear dependence of the data points that makes it favorable for time-series forecasting (Sabu and Kumar, 2020) [6] .

ARIMA: ARIMA (Auto-Regressive Integrated Moving Average) model is a variation of Box Jenkins models used for predicting or understanding stationary or non-stationary time-series data. The Box Jenkins model plays a vital role in the area of time-series analysis and forecasting. ARIMA consists of three parts-the AR part, lag-difference (integrated), and the MA part, denoted as ARIMA (p, d, q) where p is the number of AR terms, d is the order of lag difference, and q is the number of MA terms (Jadhav et al., 2017) [2] .

Autoregressive process of order (p) is,

Moving Average process of order (q) is,

and the general form of ARIMA model of order (p, d, q) is

Where, 𝑌𝑡 is tomato prices, 𝑒𝑡 '𝑠 are independently and normally distributed with zero mean and constant variance for t = 1, 2,... n; d is the fraction differenced while interpreting AR and MA and Ø𝑝 and 𝑞𝑞 are coefficients to be estimated. The seasonal variation model of ARIMA is the SARIMA denoted as SARIMA (p, d, q) (P, D, Q), used for data with trend and seasonality. Also, it consists of seasonal AR, seasonal lag difference, and seasonal MA terms. Here P is the number of seasonal AR terms, D is the order of seasonal lag difference, and Q is the number of seasonal MA terms. SARIMA model equation is written as follows: (𝐵)(𝐵)𝐻 𝐷𝑑𝑋𝑡 = + 𝜃(𝐵)𝜃(𝐵)𝑍𝑡 Holt-Winter Seasonal Method: Holt-Winter Seasonal Method is one of the variations of Exponential Smoothing used for seasonal data. It consists of a forecast equation and three smoothing equations:

Where, * and are smoothing parameters and m is the frequency of seasonal (Choon and Chuin 2008)

Long Short Term Memory (LSTM): LSTM Introduced by Hochreiter & Schmidhuber. LSTM is a type of RNN that can learn the order dependence between items in a sequence. It is able to learn the context required to make predictions in time series forecasting problems, rather than having this context pre-specified and fixed. Its capable of learning long-term dependencies. It is trained using Back propagation through time and overcomes the vanishing gradient problem. (Sherstinsky, 2020) [7] .

Stationary analysis: Augmented-Dickey Fuller test was used to check the stationarity. It is a hypothesis test in which the null hypothesis is that the series is non-stationary, and the alternate hypothesis is set to series is stationary. Based on the test, the p-value was found to be, the alternate hypothesis implying the stationarity is rejected.

Model Fitting:

The dataset was divided into training and test set. The training set consists of first two third of observations and the remaining observations were taken as the test set.

Loss function

Root Mean Square Error (RMSE): is a metric commonly used to measure the accuracy of a forecasting model. It calculates the square root of the average of the squared differences between the predicted values and the actual (observed) values. RMSE is a popular choice because it penalizes larger errors more heavily, making it sensitive to outliers. The formula for calculating RMSE is as follows:

RMSE=n1∑i=1n(yi-yi^)2

Where:  n is the number of data points.  yi is the actual value of the dependent variable for the ith data point.  yi^ is the predicted value of the dependent variable for the ith data point.

Mean Absolute Error (MAE):

Mean Absolute Error (MAE) is another metric used to assess the accuracy of a forecasting model. It computes the average of the absolute differences between the predicted values and the actual (observed) values.

The formula for calculating MAE is as follows: www.extensionjournal.com

MAE=n1∑i=1n|yi-yi^|

 n is the number of data points.  yi is the actual value of the dependent variable for the ith data point.  yi^ is the predicted value of the dependent variable for the ith data point.

Mean Absolute

 n is the number of data points.

 yi is the actual value of the dependent variable for the ith data point.  yi^ is the predicted value of the dependent variable for the ith data point.

Results and Discussion

The implementation of proposed LSTM model, SARIMA and Holt Winters using python. Figure 1 As the variability in tomato prices increases, the task of forecasting becomes more challenging. To address this, the study employs three different forecasting methods: SARIMA, Holt Winters, and LSTM. The primary objective is to compare these methods and determine which one yields the most accurate predictions.

To conduct the comparison, the tomato price data is split into two segments: a training set comprising 60% of the data and a testing set containing the remaining 40%. This division allows for assessing the accuracy of predictions made by SARIMA, Holt Winters, and LSTM on unseen data. Due to the presence of seasonality in tomato prices, the Holt Winters method proves to be the most suitable approach for effectively capturing both trends and season In Figure 3, we observed the forecast of tomato prices using the Holt Winters method. The blue line represents the training data, while the orange line represents the data used for testing the model, and the green line represents the predicted data. It is noticeable that there is a considerable variation between the tested and predicted data, indicating potential areas for improvement in the forecasting model. (Yin et al. 2020) [9] Considering the seasonality in tomato prices, the SARIMA method emerges as the most appropriate approach for effectively capturing trends and seasonal patterns. In Figure 4, we can examine the forecast of tomato prices generated using the SARIMA method. The blue line corresponds to the training data, the orange line reflects the data utilized for testing the model, and the green line represents the predicted data. Notably, there exists a significant variation between the tested and predicted data. These metrics are commonly used to assess the accuracy of forecasting models.

Conclusion

This study aimed to assess tomato price forecasting methods in the Kolar market, crucial for India's agricultural sector. SARIMA, Holt Winters, and LSTM were evaluated due to their significance for farmers, policymakers, and consumers. The analysis revealed the complexity and seasonality of tomato price data, posing challenges for accurate forecasting. LSTM emerged as the most accurate method, surpassing SARIMA and Holt Winters, as evidenced by lower RMSE, MAE, and MAPE values.

References

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