Price forecasting models for rice in West Bengal, India

Introduction

Rice plays a pivotal role in ensuring food security and sustenance for a significant portion of the global population, especially in India, where it is a staple food crop. West Bengal, one of the prominent states in India, is renowned for its substantial rice production and consumption. The state's agricultural landscape is characterized by a rich diversity of rice varieties and a dynamic market that constantly adapts to various economic and environmental factors. Accurate forecasts of food prices could be helpful to farmers, policymakers and agribusiness industries (Jha & Sinha, 2023) [16] . Accurate forecasting in rice market is crucial to make informed decisions and mitigate potential food security concerns. Choosing rice crop and the Burdwan market in West Bengal for rice price forecasting is a strategically sound decision driven by a compelling set of factors. To begin with, India's ranking as the second-largest rice producer globally (Annon, 2022(b)) emphasizes the economic and cultural significance of this staple crop. Within India, West Bengal holds the distinction of being the largest rice producer with 16.91 MT production (Annon, 2022(b)) which is 12.87 per cent to all-India (Annon, 2022(a)). Within this rice-producing state, Burdwan district known as 'Rice bowl of West Bengal' is the foremost contributor to this vital crop, as rice is cultivated in all the three seasons (viz. Aus or Autumn rice, Aman or Winter rice and Boro or Summer rice) in the district (Ali & Ahmad, 2018) [2] . This regional proficiency extends to the Burdwan Market, recognized as the largest rice market in the area. As such, the Burdwan market becomes the prime source for gathering reliable and comprehensive price data, making it an ideal location for accurate rice price forecasting. This paper focuses on the development and evaluation of price forecasting models for rice in the major market of West Bengal, India. The primary aim is to provide a comprehensive analysis of various time series forecasting methods, including AutoRegressive Moving Average (ARMA), AutoRegressive Integrated Moving Average (ARIMA), Recurrent Neural Networks (RNN), Artificial Neural Networks (ANN), Gated Recurrent Unit (GRU), Long Short-Term Memory (LSTM), and Stacked Long Short-Term Memory (SLSTM). These models are applied to historical price data to forecast future rice prices accurately and efficiently. The choice of forecasting models considered in this study reflects the diverse range of methodologies available, catering to both traditional statistical approaches and modern deep learning techniques. ARMA and ARIMA models are well-established statistical models, while RNN, ANN, GRU, LSTM, and SLSTM are part of the contemporary machine learning and deep learning arsenal. The comparison and evaluation of these models allow us to assess their respective strengths and weaknesses in the context of rice price forecasting, which is subject to seasonality, trends, and external factors like government policies, weather conditions, and global market dynamics. The significance of this research extends beyond academic interest, as it addresses real-world issues of economic importance and food security. Accurate price forecasts can assist farmers in making informed planting and selling decisions, traders in managing their stocks and pricing strategies, and policymakers in formulating agricultural and trade policies. Furthermore, consumers benefit from more stable and predictable rice prices, contributing to their overall economic well-being. In the following sections, we will delve into the methodologies of each forecasting model, present the data sources and preprocessing techniques, and discuss the results of our experiments. By the end of this study, we aim to provide valuable insights into which forecasting models perform best for rice price forecasting in the major markets of West Bengal, India, and offer recommendations for their practical implementation.

Materials and Methodology Database

For this study, we gathered daily rice price data from the Burdwan market in Burdwan district, West Bengal, covering the period from 2003 to 2022, from secondary sources available on the official website Agmarknet (https://agmarknet.gov.in/). Choosing rice crop and the Burdwan market in West Bengal for rice price forecasting is a strategically sound decision driven by a compelling set of factors. To begin with, India's ranking as the second-largest rice producer globally emphasizes the economic and cultural significance of this staple crop.

Methodology

The analytical models utilized in the present study are as follows:

Statistical Models

Statistical models are essential tools in data analysis and decision-making. These models utilize mathematical relationships, probability theory, and historical data to describe and understand the underlying patterns and trends in data. They are widely employed in fields such as economics, epidemiology, and social sciences to draw meaningful insights and make informed predictions based on empirical evidence. In the present study we will consider following statistical models:

ARMA (AutoRegressive Moving Average) Model

ARMA is a statistical model used for time series forecasting. It combines two components: AutoRegressive (AR) and Moving Average (MA) introduced by Yule (1926) [8] and Slutsky (1937) [25] respectively. The AR component models the relationship between a variable and its lagged values, while the MA component models the relationship between a variable and the lagged forecast errors. ARMA models are effective for capturing linear dependencies in time series data. Mathematically it can be expressed as, Where, is the value of the time series at time are the coefficients of the past values, is the order of the autoregression and is the error term at time . are the coefficients of the past errors, is the order of moving average.

ARIMA (Auto-Regressive Integrated Moving Average)

ARIMA model is a famous time series prediction method proposed by Box and Jenkins in the early 1970s (Box et al., 1994) [10] . The ARIMA model transforms the nonstationary time series into stationary time series and then regresses the dependent variable due to the lag value of its independent variable and the present value and lag value of its random error term (Luo et al., 2013) [6] . The parameters p, d, and q represent the autoregressive term, the times of differences when the time series becomes stationary, and the number of moving average terms, respectively. Mathematically it can be expressed as, i. e., Here p, d and q are integers greater than or equal to zero.

Machine Learning Models

Machine learning techniques are a subset of artificial intelligence that empower computers to learn from data and improve their performance on specific tasks without being explicitly programmed. By leveraging algorithms and statistical models, machine learning enables computers to identify patterns, make predictions, and provide insights across various domains, from image recognition and natural language processing to financial forecasting and healthcare diagnostics. These techniques have revolutionized the way businesses and researchers extract valuable information from large datasets, driving advancements in automation, decision-making, and problem-solving. In the present study we will consider following machine learning models:

ANN (Artificial Neural Network) Model

ANN is a versatile machine learning model inspired by the human brain. In time series forecasting, it can be used as a feed forward network with input features relevant to the prediction task. ANN can handle non-linear relationships and adapt to various data patterns. The ANN architecture (Fig. 1 A set of neurons between input and output layers. There can be single or multiple layers. (c) output layer: Usually it has one neuron, and its output ranges between 0 and 1, that is, greater than 0 and less than 1 (Kukreja, 2016) [17] . But multiple outputs can also be present (Shukla & Abdelrahman, 2004) [24] . The processing ability is stored in inter-unit connection strengths, called weights (Kuldeep & Anitha, 2015) [18] .

RNN (Recurrent Neural Network) Model

Recurrent Neural Networks (RNNs) are neural networks that employ recurrence, which basically uses information from a previous feedforward pass over the neural network (Fig. 2) (Kumar et al., 2018) [29] RNN is a kind of neural network used to process sequential data (Williams & Zipser, 1989) [27] . RNNs have been incredibly successful when applied to problems where the input data are in the form of a sequence for which predictions are to be made (Gamboa & Borges, 2017,) [11] . The basic idea of RNN is that the network will memorize the previous information and apply it to the calculation of the current output, i.e., the nodes between the hidden layers are connected, and the input of the hidden layer includes not only the output of the input layer but also the output of the hidden layer at the last moment. Based on the idea of graph expansion and parameter sharing, we can design various kinds of RNN (Weng et al., 2019) [26] .

GRU (Gated Recurrent Unit) Model

The GRU is a variant of the LSTM and was introduced by K, Cho (Chung et al., 2014) [8] . The GRU was inspired by the LSTM unit but is considered simpler to compute and implement. It retains the LSTM's resistance to the vanishing gradient problem, but its internal structure is simpler and therefore easier to train since fewer computations are needed to make update to its hidden state. The update gate defines how much previous memory to keep around and the reset gate defines how to combine the new input with the previous memory. The major difference is that the GRU fully exposes its memory content using only integration (but with an adaptive time constant controlled by the update gate) (Kumar et al., 2018) [29] .

LSTM (Long Short-Term Memory)

In the mid-90s, Sepp Hochreiter & Juergen Schmidhuber, 1997) [15] proposed a variation of existing RNN having Long Short-Term Memory units, or LSTMs (Bengio et al., 1994) [5] . However, the full gradient can instead be calculated with backpropagation through time (Graves & Schmidhuber, 2005) [12] . LSTMs help preserve the error that can be back propagated through time and layers. LSTMs contain information in a gated cell. The cell makes decisions about what to store, and when to allow reads, writes and erases, via gates that open and close. The cells learn when to allow/leave/delete the data, through the iterative guesses, back propagating errors, and adjusting weights. The structure of the LSTM network is shown in Fig. 4. A Stacked LSTM architecture can be defined as an LSTM model comprised of multiple LSTM layers (Fig. 5). An LSTM layer above provides a sequence output rather than a single value output to the LSTM layer below. Specifically, one output per input time step, rather than one output time step for all input time steps. These models represent a mix of traditional statistical approaches (ARMA, ARIMA) and modern machine learning techniques (RNN, ANN, GRU, LSTM, SLSTM). Each model has its strengths and weaknesses, and their performance may vary depending on the specific characteristics of the rice price data in West Bengal's major markets. The paper aims to compare these models to determine which one is best suited for accurate rice price forecasting in this context. Root Mean Square Error (RMSE): it is defined as the square root of mean square error which is the sum of squared errors divided by total numbers of observations (Salman et al., 2018) [23] . The formula for RMSE is:

Mean Absolute Percentage Error (MAPE):

It is a measure of accuracy of a method for constructing fitted time series values in statistics, specifically in trend estimation (Mitra & Paul, 2017) [20] . It usually expresses accuracy as a percentage and is defined by the formula:

Results and Discussion Dataset Description

The secondary data on daily prices of cumin for Burdwan market, Burdwan, West Bengal for present study was collected for 2003 to 2022 from official website (https://agmarknet.gov.in/) and the dataset were divided inti training set which comprised 85% per cent of the data and a testing set which consisted of the remaining 15 per cent of the data to evaluate the accuracy. Table 1 presents the mean value of the dataset for cumin prices ₹ 7305/quintal. The first and third quartile are ₹ 1280/quintal and ₹ 2450/quintal respectively, which suggests that the data distribution is not normal. The rice price has a high degree of variation ranging from a minimum of ₹ 930/quintal to a maximum of ₹ 3300/quintal. The skewness of the dataset is -0.01, indicating a slightly negative skewness which means that the data is slightly skewed to left. The kurtosis of the dataset is -1.32, which indicates that the distribution of the data is slightly flatter than the normal distribution.

Performance of the Forecasting Models

To precisely assess the performance of the models, the dataset of each model was partitioned into two distinct sets, namely training and testing data. Subsequently, each model was executed on the testing data during the testing phase and the resulting values were compared with their corresponding actual values.

The models were subjected to performance evaluation using the testing dataset. The main approach involved comparing the predicted values with the actual values to ascertain the model's efficacy. The study aimed to determine the RMSE and MAPE values as the primary evaluation metrics (Table 2). A visual comparison of the RMSE values of all the models under study is depicted in Fig. 7 with the help of bubble diagram. The Stacked LSTM models marked the lowest RMSE value and thus, showed the highest accuracy among all the models under study. The graph clearly depicted that the predicted prices very closely coincided with the actual prices. The Stacked LSTM model was chosen for its ability to handle long-term dependencies in time series data, making it suitable for predicting future prices of rice. Makama et al. (2016) [19] have highlighted that in India, market prices of rice fall during the harvest period and it rises through the lean season due to law of demand applied. It is observed that price rate of rice fluctuates from months to months and year to year due to production of rice crops, carryout from earlier year, climatic circumstance, local entrepreneurial management, and sells to other countries or another state (Dey & Mistri, 2019) [9] .

Model Accuracy

The evaluation metrics including Root Mean Square Error (RMSE) and Mean Absolute Percentage Error (MAPE) values on the test data was generated to test model performance (Table 2). [21,22] . The LSTM, GRU, ANN and RNN models followed the Stacked LSTM model respectively. In contrast, the ARIMA and ARMA displayed the highest RMSE and relatively high MAPE values respectively, indicating its inferior predictive performance compared to other models. ARIMA model performs well for average monthly data but not fare as well for daily data; whereas, the neural network approaches were effective at forecasting the daily trends in price fluctuation (Weng et al., 2019) [26] .

Conclusion

The results of the study indicated that when it comes to forecasting rice prices, machine learning models such as Stacked LSTM, LSTM, GRU, ANN and RNN outperformed the traditional statistical models ARMA and ARIMA. These ML models exhibited greater accuracy and efficiency in capturing the intricate patterns and dynamics present in rice price data. Their capacity to learn from historical patterns and adjust to evolving market conditions played a key role in their superior forecasting capabilities. These findings suggested that leveraging advanced machine learning algorithms can significantly improve the accuracy of price forecasts and offer valuable insights for decision making within the rice market. The Stacked LSTM model demonstrated the lowest values for evaluation metrics such as RMSE (18.718) and MAPE (0.010) establishing it as the most suitable and reliable approach for accurate forecasting of rice prices for the year 2023. The market prices of rice fall during the harvest period and it rises through the lean season. It is observed that price rate of rice fluctuates from months to months and year to year due to various factors. These insights are valuable for farmers as they can optimize their production to coincide with periods of high prices. Additionally, traders and policymakers can leverage this information for making profitable decisions and formulating effective policies.

References

1. Agriculture Marketing website; c2023. Retrieved from https://agmarknet.gov.in/. Accessed October 2023.
2. Ali SA, Ahmad A. Economic feasibility of integrated farming: A study from West Bengal. J Reg. Dev Plan. 2018;7(1):45-60.
3. Anonymous. Area, Production & Yield -Reports. Directorate of Economics and Statistics, Department of Agriculture and Farmers Welfare, Ministry of Agriculture and Farmers Welfare, Government of India. Retrieved from DES | Area, Production & Yield -Reports (desagri.gov.in). Accessed October 2023.
4. Anonymous. Press Information Bureau. Ministry of Agriculture & Farmers Welfare, Government of India. Retrieved from doc2022920106001.pdf (pib.gov.in). Accessed October 2023.
5. Bengio Y, Simard P, Frasconi P. Learning long-term dependencies with gradient descent is difficult. Neural Networks, IEEE Trans. 1994;5(2):157-166.
6. Luo CS, Zhou LY, Wei QF. Application of SARIMA model in cucumber price forecast. Appl Mech Mater. 2013;373:1686-1690.
7. Cho K, Merrienboer BV, Gulcehre C, Bahdanau D, Bougares F, Schwenk H, et al. Learning phrase representations using RNN encoder-decoder for statistical machine translation. Retrieved from https://arxiv.org/abs/1406.1078. Accessed October 2023.
8. Chung J, Gulcehre C, Cho K, Bengio Y. Empirical evaluation of gated recurrent neural networks on sequence modeling. In: NIPS 2014 Workshop on Deep Learning.
9. Dey CK, Mistri T. Changing trends of market prices of rice in Burdwan and Memari markets of Purba Bardhhaman district, West Bengal, India. J Inf. Comput Sci. 2019;9(8):492-508.
10. Box GEP, Jenkins GM, Reinsel GC. Time Series Analysis: Forecasting and Control. Holden-day Series in Time Series Analysis. 1994;199-201.
11. Gamboa J, Borges JC. Deep Learning for Time-Series Analysis. 2017. Retrieved from https://arxiv.org/abs/1701.01887. DOI: https://doi.org/10.48550/arXiv.1701.01887.
12. Graves A, Schmidhuber J. Framewise phoneme classification with bidirectional LSTM and other neural network architectures. Neural Networks. 2005;18:602-610.
13. Hochreiter S, Schmidhuber J. Long short-term memory. Neural Comput. 1997;9(8):1735-1780.
14. Jha GK, Sinha K. Agricultural price forecasting using neural network model: An innovative information delivery system. Agric Econ Res Rev. 2013;26(2):229-239.
15. Kukreja H, Bharath N, Siddesh CS, Kuldeep S. An introduction to artificial neural network. Int J Adv Res Innov Ideas Educ. 2016;4(5):27-30.
16. Kuldeep S, Anitha GS. Neural network approach for processing substation alarms. Int J Power Electron Controllers Converters. 2015;1(1):21-28.
17. Makama SA, Amrutha TJ, Lokesha H, Koppalkar BG. Analysis of seasonal price variation of rice in India. Res J Agric For Sci. 2016;4(6):1-6.
18. Mitra D, Paul RK. Hybrid time-series models for forecasting agricultural commodity prices. Model Assist Stat Appl. 2017;12(3):255-264.
19. Muzaffar S, Afshari A. Short-term load forecasts using LSTM networks. Energy Procedia. 2019;158:2922-2927.
20. Sabu KM, Kumar TM. Predictive analytics in agriculture. Forecasting prices of arecanuts in Kerala. Procedia Comput Sci. 2020;171:699-708.
21. Salman N, Lawi A, Syarif S. Artificial neural network back propagation with particle swarm optimization for crude palm oil price prediction. J Phys Conf Ser. 2018;1114(1):012088.
22. Shukla M, Abdelrahman M. Artificial Neural Networks based steady state security analysis of power systems. In: Proceedings of the Thirty-Sixth Southeastern Symposium on System Theory; c2004. p. 266-269. DOI:10.1109/SSST.2004.1295661.
23. Slutsky E. The summation of random causes as the source of cyclic processes. Econometrica. 1937;5:105-146.
24. Weng Y, Wang X, Hua J, Wang H, Kang M, Wang FY. Forecasting horticultural products price using ARIMA model and neural network based on a large-scale data set collected by web crawler. IEEE Trans Comput Soc Syst. 2019;6(3):547-553.
25. Williams RJ, Zipser D. A learning algorithm for continually running fully recurrent neural networks. Neural Comput. 1989;1(2):270-280.
26. Yule GU. Why do we sometimes get nonsense-correlations between time series? A study in sampling and the nature of time series. J R Stat Soc. 1926;89:1-64.
27. Kumar S, Stecher G, Li M, Knyaz C, Tamura K. MEGA X: molecular evolutionary genetics analysis across computing platforms. Molecular biology and evolution. 2018 Jun 1;35(6):1547-1549.