An ARIMA model approach to forecasting and comparing black gram, green gram, and red gram production in Tamil Nadu

Introduction

Tamil Nadu, one of the prominent agricultural states in southern India, places great emphasis on pulse cultivation as part of its farming and food systems. Pulses play a crucial role in the agricultural economy of the state as well as in the nutritional intake of its population. Among the key pulses grown in the region, blackgram (urad dal), greengram (moong dal), and redgram (pigeon pea or thuvaram paruppu) stand out for their dual benefits. These crops not only support food and nutritional security but also play a crucial role in soil enrichment and sustainable agricultural practices, thanks to their ability to fix atmospheric nitrogen and thrive with minimal inputs. In Tamil Nadu, where vegetarian diets are predominant, these pulses act as a major source of plant-based protein, fiber, and essential micronutrients. Their cultivation supports low-input agriculture and serves as a climate-resilient option for farmers operating in varied agro-climatic zones, including rainfed and drought-prone areas. Their role in biological nitrogen fixation further enhances their agricultural value by reducing the dependence on chemical fertilizers and enriching soil quality. Blackgram, a short-duration and high-value pulse crop, holds a prominent place in the agricultural landscape of Tamil Nadu. It is extensively cultivated across several districts, including Thanjavur, Kallakurichi, Ramanathapuram, Cuddalore, Thiruvannamalai, and Thoothukudi. Due to its quick maturity, blackgram fits well into both kharif and rabi seasons, making it highly suitable for multiple cropping patterns. It is often grown as a catch crop between major crops, offering flexibility to farmers. For many small and marginal farmers, blackgram serves as a reliable source of income, thanks to its adaptability and relatively low input requirements. In recent years, blackgram has been cultivated on an estimated 2.5 to 4.0 lakh hectares, yielding around 1.5 to 2.5 lakh metric tonnes annually. Its increasing popularity is linked to several agronomic advantages, such as low water and nutrient requirements, faster maturity, and resistance to common diseases. Farmers in Tamil Nadu benefit from improved seed varieties like VBN 8, which offers resistance to Yellow Mosaic Virus (YMV); VBN 6, adaptable to both rainfed and irrigated conditions; CO 6, suited for short growing seasons; and ADT 5, known for its nutritional quality. These varieties contribute to stable yields and make blackgram cultivation economically attractive, especially in areas with limited resources. Greengram, known for its nutritional value and rapid growth, is a key pulse crop widely grown across Tamil Nadu. Its high digestibility and rich protein content make it a vital part of the local diet. Greengram is especially well-suited to shortduration cropping windows, allowing farmers to cultivate it efficiently between major crops. It is extensively grown in both coastal and inland regions, particularly in districts like Cuddalore, Thiruvarur, Nagapattinam, Mayiladuthurai, Thoothukudi, and Thiruvallur. Due to its adaptability, greengram is often used in intercropping systems or sown immediately after the paddy harvest, making it an excellent choice for enhancing farm productivity and sustainability. Tamil Nadu grows greengram on approximately 1.5 to 2.0 lakh hectares, producing 0.6 to 1.5 lakh metric tonnes annually. It thrives under both irrigated and rainfed conditions, making it versatile for diverse farm settings. Popular seed varieties include VBN 3, which resists YMV and powdery mildew; VBN 4, valued for early maturity and bold grains; CO 8, suitable for intercropping; and KM 2, known for its drought tolerance and early harvest. These improved varieties have supported better adoption rates and yield stability across the state. Redgram, or pigeon pea, is a resilient, drought-tolerant pulse that plays a crucial role in supporting dryland farming systems across Tamil Nadu. As a long-duration crop, it is well adapted to regions with limited rainfall and is primarily cultivated in Dharmapuri, Krishnagiri, Vellore, Thirupathur, and Madurai districts. The crop makes efficient use of monsoon rains and residual soil moisture, thriving in areas where water resources are scarce. Redgram is typically grown on around 0.5 to 1.0 lakh hectares, yielding an annual production of 0.3 to 0.8 lakh metric tonnes. Its deep-root system not only aids in moisture extraction but also helps in soil conservation, making it an important component of sustainable agriculture in dry zones. Its deep root system allows it to extract moisture from lower soil layers, making it suitable for soil conservation and water management in drought-prone regions. Redgram also plays an essential role in local diets, providing a rich source of protein. Improved varieties such as VBN 3 (wilt-resistant), CO(Rg), ICPL 87119 (Asha) (a drought-tolerant hybrid with bold grains), and CO 6 (a short-duration, determinate variety) are popular among farmers for their resilience and productivity. The combined agronomic and economic importance of blackgram, greengram, and redgram cannot be overstated. From an agronomic perspective, these crops are highly beneficial to the farming ecosystem. Their nitrogen-fixing capabilities reduce fertilizer use and enhance soil fertility, supporting long-term sustainability. They also require fewer resources, such as water and fertilizers, making them suitable for regions affected by climate variability. From an economic standpoint, pulses are a profitable crop choice for smallholder and marginal farmers. They generate consistent income due to their steady market demand, both in domestic consumption and trade. Additionally, the availability of high-yielding, disease-resistant seed varieties has improved productivity and made pulse cultivation a viable income source, especially in rural and economically weaker areas. Furthermore, the inclusion of these pulses in crop rotation and intercropping systems helps improve land use efficiency and reduce pest and disease build-up, thus reducing reliance on chemical inputs. This holistic role in nutrition, income generation, soil health, and climate resilience underlines the centrality of pulses in Tamil Nadu's agricultural development strategy.

Review of Literature

Widely recognized for its capabilities in statistical computing, R programming has become a preferred platform for time series forecasting. Its adaptability and extensive library support enable effective implementation of models such as ARIMA (Auto Regressive Integrated Moving Average). The ARIMA modeling framework was originally developed by Box and Jenkins (1970) [4] in their pioneering publication Time Series Analysis: Forecasting and Control, which introduced a comprehensive procedure for selecting, estimating, and validating time series models. This work remains the gold standard for time series forecasting. Complementing this, Gupta and Kapoor (2001) [7] provided a broader statistical perspective in their book Fundamentals of Applied Statistics, offering essential knowledge that has supported the application of ARIMA and related models in various practical domains. The ARIMA model has been particularly effective in agricultural forecasting. Mandal (2005) [8] demonstrated the utility of ARIMA in forecasting sugarcane production in India, which highlighted the model's role in facilitating better agricultural decision-making and policy planning. Likewise, Ramakrishna and Vijayakumari (2017) [9] used the ARIMA model to forecast rice production trends in India. Their study underscored the model's capacity to handle seasonality and variability in agricultural data. Ramesh Reddy et al. (2017) [10] applied ARIMA to analyze monthly rainfall patterns in the Rayalaseema region. Their work showed the model's ability to manage climatic time series data, which is essential for water-dependent crop planning. Further agricultural applications of ARIMA include the study by Sakuntala Deka et al. (2022) [6] , who used it to forecast tea production in India. Their findings supported the model's robustness and long-term forecasting reliability in agricultural sectors. Although Bhattacharyya et al. (2021) [3] employed linear regression instead of ARIMA, their study on the influence of weather variables on crop yields in Manipur complements time series analysis by highlighting the interdependencies between climate and crop production, which ARIMA can also model effectively. In the domain of economic and financial forecasting, ARIMA has been widely applied. Ayık and Erkal (2021) [2] used ARIMA to predict unemployment and economic growth in Turkey, demonstrating its effectiveness in modeling economic indicators. Al-Qazzaz and Yousif (2022) [1] adopted the Auto ARIMA variant for forecasting Brent crude oil prices. Their results showed that ARIMA models can manage highvariance financial datasets with reasonable accuracy. Hybrid models have also emerged to enhance forecasting performance. Camara et al. (2016) [5] combined seasonal ARIMA with artificial neural networks to forecast energy consumption, and the hybrid model outperformed standalone ARIMA in terms of accuracy. This reflects the growing trend of integrating classical statistical models with machine learning to capture both linear and nonlinear patterns. Finally, Tharwat and Hassanien (2023) [11] provided a comprehensive review comparing ARIMA with machine learning approaches. Their study concluded that while machine learning models may outperform ARIMA in complex, nonlinear data settings, ARIMA remains valuable due to its interpretability, transparency, and strong performance with structured, linear, or seasonal datasets particularly when data availability is limited.

Overview of the Dataset

This study makes use of data obtained from the Department of Economics and Statistics, Government of Tamil Nadu, specifically extracted from the 'Season and Crop Report'. This comprehensive 59 years dataset spans the period from 1966 to 2024 and offers detailed insights into the cultivation and production of three major pulse crops in Tamil Nadu: black gram, green gram, and red gram. Over nearly six decades, Tamil Nadu's agricultural scenario has experienced considerable shifts, shaped by climatic factors, agronomic innovations, and changing land-use patterns. Among these pulses, black gram emerges as the most prominently cultivated crop, both in terms of area and total output. On average, black gram covers approximately 232,873 hectares, with an average annual production of 114,607 tonnes, making it a staple component of the state's pulse cultivation. Green gram ranks second, with an average area of about 117,624 hectares and an average annual production of 48,706 tonnes. Although red gram occupies the least area approximately 66,350 hectares it contributes significantly to overall pulse output, with an average production of 44,255 tonnes per year. Despite its smaller scale of cultivation, red gram demonstrates the highest productivity among the three crops, indicating better yield efficiency. This productivity is estimated at about 0.67 tonnes per hectare, compared to 0.49 tonnes for black gram and 0.41 tonnes for green gram. From the 1960s to the mid-2010s, a general upward trend is observed in both the area under cultivation and total output across all three crops. The period between 2014 and 2017 was particularly notable, marking peak production and cultivation levels. For example, black gram reached its historical high in 2015 with a production volume of 358,895 tonnes. During the same year, green gram and red gram also attained their highest outputs, at 180,726 tonnes and 90,950 tonnes respectively. These record-breaking figures could be attributed to a combination of favorable climatic conditions, the adoption of high-yielding seed varieties, improved irrigation practices, and the implementation of supportive agricultural policies. However, this positive trend has not been consistent. Post-2017, there has been a noticeable decline in both cultivated area and production levels, especially in red gram. A sharp drop in red gram production was recorded in 2009, falling to just 16,703 tonnes, underscoring the crop's vulnerability to adverse weather and agronomic instability. In more recent years, particularly by 2024, all three pulses recorded significant reductions in both area and yield. Black gram production decreased to 179,261 tonnes from its 2020 high of over 317,000 tonnes. Green gram and red gram also followed this downward trend. The findings underscore the central role of black gram in Tamil Nadu's pulse economy while drawing attention to the need for stabilizing and enhancing the output of green and red gram. Focused interventions, such as introducing climate-resilient varieties, promoting efficient water management practices, and ensuring timely policy support, are vital for sustaining pulse production. Long-term strategies must emphasize increasing productivity, minimizing yield variability, and fostering sustainable agricultural practices to strengthen food security and rural livelihoods in Tamil Nadu. Figure 1 illustrates the expansion and contraction trends in the cultivation area of three major pulse crops in Tamil Nadu. The area under black gram cultivation rose significantly from 44,000 hectares in 1966 to a peak of 429,784 hectares in 2017, before declining to 354,917 hectares by 2024. Green gram area expanded from 42,779 hectares to a maximum of 238,842 hectares in 2016, although it exhibited considerable fluctuations, particularly after the year 2000. Red gram, which peaked at 125,028 hectares in 1990, has since stabilized within a narrower range of 40,000 to 60,000 hectares. All three crops reached their highest cultivation areas during the mid-2010s. Figure 2 presents corresponding production trends: black gram production climbed from 14,100 tonnes in 1966 to a high of 358,895 tonnes in 2015, before falling to 179,261 tonnes by 2024. Similarly, green gram and red gram peaked in 2015, then declined sharply. These trends reflect the sensitivity of pulse production to environmental and policy changes.

Methods and Forecasting Models 3.1 Box-Jenkins methodology -Time Series

The Autoregressive Integrated Moving Average (ARIMA) model is a widely recognized technique for time series forecasting particularly suited for analyzing and predicting the behavior of a single variable over time. Often referred to as the Box-Jenkins model after its originators Box and Jenkins (1970) [4] ARIMA effectively captures the underlying structures in temporal data. In the present study, the Box-Jenkins methodology was utilized to apply the ARIMA model in assessing the production trends of black gram, green gram, and red gram. The ARIMA model is expressed as ARIMA (p, d, q), where p denotes the number of autoregressive terms, d signifies the order of differencing required to achieve stationarity, and q represents the number of moving average terms. The modeling process involves a structured sequence of steps to identify, estimate, and validate the most suitable model

and the Moving Average part: Box & Jenkins (1970) [4] The initial step in ARIMA model development involves assessing whether the time series is stationary. A stationary series exhibits a constant mean and variance over time, along with consistent, predictable patterns of fluctuation. To assess this, the Augmented Dickey-Fuller (ADF) test was applied to the production data for black gram, green gram, and red gram. Results indicated non-stationarity in all three series. Since the data includes zero values, a logarithmic transformation was not feasible. Therefore, to induce stationarity, first differencing (d=1) were performed. Following differencing, the series were further examined using the autocorrelation function (ACF) and partial autocorrelation function (PACF) plots to confirm stationarity. Figure 3 (correlograms) presents the ACF and PACF plots of the differenced series, providing insights into selecting appropriate ARIMA parameters for each crop. The correlogram and the values of the ACF and PACF (Figure 3) indicate that a first-order seasonal differencing is adequate to achieve stationarity. Thus, a single differencing (d = 1) is sufficient for the given time series. Prior to model development, confirming the stationarity of the differenced series is crucial. This is achieved by conducting the Augmented Dickey-Fuller (ADF) test, which assesses the presence of a unit root. Confirming stationarity at this stage ensures that the series is suitable for ARIMA modeling.

ARIMA model development

ADF Test for Stationarity of Pulses Production Series

In order to test whether the time series data for black gram, green gram, and red gram production were stationary, the hypotheses outlined below were proposed:  H₀: The production time series of all three crops are nonstationary.  H₁: The production time series of all three crops are stationary.

Using the Augmented Dickey-Fuller (ADF) test on the firstdifferenced data (d = 1), the hypothesis was assessed. The test statistics are summarized as follows: Since the p-values are all below the 0.05 significance threshold, the null hypothesis is rejected for each crop, indicating that the first-differenced series (d = 1) is stationary in both mean and variance. With stationarity confirmed at this level of differencing, no further differencing is required. The subsequent stage in ARIMA model development is to determine the appropriate non-seasonal orders: p (autoregressive order) and q (moving average order). This is achieved by examining the autocorrelation function (ACF) and partial autocorrelation function (PACF) plots of the stationary series. Accordingly, the preliminary model for all three crops is specified as ARIMA (p, 1, q).

Selecting the Appropriate Model for Forecasting:

Preliminary ARIMA models were developed for each pulse crop by examining the ACF and PACF plots of the differenced production data. Seven candidate models were initially selected, as shown in Table 1. To determine the best model, each candidate was evaluated using the Akaike Information Criterion (AIC) and Schwarz Bayesian Information Criterion (SBIC). The model with the lowest AIC and SBIC values was chosen as the optimal fit. The provisional models along with their final best-fitting ARIMA versions are summarized in Tables 1 and2, respectively.

The Green gram ARIMA (1,1,1) model includes one autoregressive and one moving average term:

Similar to black gram, Red gram follows the ARIMA (0, 1, 1) model:

These results confirm that the selected ARIMA models are suitable for capturing production trends and can support future forecasting efforts for pulse crops in Tamil Nadu. Furthermore, to assess the presence of autocorrelation among successive forecast errors, the fit of the ARIMA models was evaluated using the Box-Ljung test. This diagnostic test checks whether the residuals from the fitted models resemble white noise. The outcomes of these tests for each model are summarized below.

Test for Autocorrelation in Model Residuals

The presence of autocorrelation in the residuals was examined using the Box-Ljung test on the lag values of the ACF and PACF. The test results are presented below. Investing in storage and processing infrastructure can help reduce post-harvest losses and stabilize market prices. Encouraging crop diversification through intercropping pulses with cereals can also enhance soil health and farmer income. Lastly, ensuring accessible minimum support prices and updating forecasting models using advanced statistical tools will support better planning, policy-making, and resilience in pulse production across the state.

Acknowledgement

AcknowledgementI sincerely thank the Department of Economics and Statistics, Government of Tamil Nadu, for providing the vital datasets essential to this research. I am especially grateful to the Principal Secretary/Commissioner for their support and encouragement throughout the study. I also extend heartfelt thanks to my family and friends for their unwavering support and motivation during the preparation and completion of this paper.

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