Forecasting area, production and productivity of fieldpea (Pisum sativum) in India: A comparative assessment of polynomial, ARIMA and ANN models

Introduction

Pulses are important components of the Indian food system and are major sources of dietary protein, particularly for populations relying substantially on plant-based foods. The thesis notes the continuing importance of pulses for food security and identifies fieldpea (Pisum sativum) as an important cool-season crop. It also highlights the need for better planning of pulse production in the context of variability in agricultural production. Agricultural area, production and productivity are interrelated but do not necessarily exhibit identical temporal patterns. Long-term changes may arise from changes in cultivated area, productivity, technological progress and crop-management practices. Consequently, a forecasting framework should be able to represent both systematic trend and temporal dependence. Previous studies summarized in the thesis have applied ARIMA and ANN methods to agricultural production, prices and yields. The thesis also cites comparative work showing that model performance can differ by crop, location and time-series structure. This provides a rationale for evaluating alternative models rather than assuming that one forecasting method is universally superior. The objective of the present paper is therefore to synthesize and publish the thesis analysis as a focused comparison of polynomial trend, ARIMA and ANN models for Indian fieldpea area, production and productivity. The specific objectives are to: (i) characterize the longterm trends; (ii) identify suitable ARIMA and ANN forecasting models; (iii) compare predictive performance using the reported error measures; and (iv) provide five-year postsample forecasts based on the selected models. For publication, the exact source attribution and unit convention should be checked against the original statistical tables/data files before journal submission because the thesis uses different unit descriptions in different sections.

Trend models

Linear, quadratic and cubic polynomial models were fitted to describe the temporal trend. The general forms reported in the thesis were: Yt = a + bt + et; Yt = a + bt + ct² + et; and Yt = a + bt + ct² + dt³ + et, respectively. Model suitability was assessed using R², RMSE and MAE. The quadratic model was selected for area, while cubic models were selected for production and productivity. The selected equations reported in the thesis were: area, Yt = 341.91 + 25.746t -0.37362t²; production, Yt = 145.17 + 52.205t -1.9073t² + 0.02665t³; and productivity, Yt = 453.16 + 84.969t -4.5628t² + 0.073114t³.

ARIMA modelling

ARIMA models were developed following the Box-Jenkins framework. Stationarity was examined using the Augmented Dickey-Fuller (ADF) test. The thesis reports that all three original series were non-stationary and became stationary after first-order differencing, giving d = 1. Candidate p and q orders were considered using ACF and PACF diagnostics, followed by parameter estimation and comparison of candidate models using AIC and forecasting-error measures. The selected models were ARIMA(0,1,0) for area, ARIMA(0,1,1) for production and ARIMA(0,1,0) for productivity. The thesis reports MAPE, MAE and RMSE for the selected models and uses these measures, together with AIC and R² where reported, to assess performance.

Artificial Neural Network modelling

ANN models were developed as multilayer feed-forward networks using back-propagation learning. The thesis reports use of a sigmoid activation function in the hidden layer and comparison of alternative network structures. The best-performing architectures were selected using reported error measures and R². Fitted values are generated from the quadratic equation reported in the thesis. Fitted values are generated from the cubic equation reported in the thesis.

ARIMA results

The ADF results reported in the thesis indicate nonstationarity in the original area, production and productivity series. First-order differencing produced stationary series. Forecasts for 2022-2026 as reported in the thesis. Forecasts for 2022-2026 as reported in the thesis.

ANN results

The ANN comparison identified architecture 5-5-1 as the best model for area, 4-4-1 for production and 4-2-1 for productivity.

Comparative model performance

The direct comparison reported in the thesis shows that ARIMA produced lower MAE and RMSE than the selected ANN model for area and production, and a higher R² for all three variables. For productivity, the ANN RMSE (104.51) was lower than the ARIMA RMSE (117.67), but the ARIMA model had lower MAE (95.60 versus 110.23) and substantially higher R² (0.87 versus 0.74). On the combined comparison reported by the thesis, ARIMA was therefore identified as the forecasting approach.

Discussion

The results demonstrate that Indian fieldpea area, production and productivity exhibit distinct temporal behaviour. The quadratic area trend suggests a nonlinear change in cultivated area over the study period, whereas cubic specifications provided the strongest fit for production and productivity. The difference among selected trend orders is important because it indicates that production and productivity cannot be adequately represented solely by changes in cultivated area.

The ARIMA results further indicate that the three annual series contain substantial persistence or trend-related nonstationarity that can be reduced through first-order differencing. The selected specifications are relatively parsimonious: ARIMA(0,1,0) for area and productivity and ARIMA(0,1,1) for production. This parsimony, together with the reported error measures, contributed to the stronger performance of ARIMA in the thesis comparison. ANN models were able to represent nonlinear patterns and produced competitive fits. However, the selected ANN models did not outperform ARIMA on the overall set of comparison measures. This finding is consistent with the thesis interpretation that conventional time-series models can be advantageous when annual agricultural series have relatively stable temporal structure. At the same time, ANN remains potentially useful as a complementary model when stronger nonlinear behaviour or additional explanatory variables are introduced. The five-year forecasts illustrate meaningful differences between the modelling approaches. Because the study is based on annual observations and the thesis uses a univariate forecasting framework, these forecasts should be interpreted as model-based projections conditional on historical patterns rather than as forecasts incorporating weather, prices, policy changes or other external shocks.

Conclusion

This study compared polynomial trend, ARIMA and ANN approaches for forecasting fieldpea area, production and productivity in India using annual data from 1980 to 2021. Area was best represented by a quadratic trend, whereas production and productivity were best represented by cubic trends. After first-order differencing, ARIMA(0,1,0), ARIMA(0,1,1) and ARIMA(0,1,0) were selected for area, production and productivity, respectively. The selected ANN architectures-5-5-1 for area, 4-4-1 for production and 4-2-1 for productivity-also provided useful predictive performance. Nevertheless, the thesis comparison identified ARIMA as the more reliable overall forecasting framework for the annual fieldpea series. The results support the use of ARIMA as a practical baseline for agricultural planning, while ANN can be retained as a complementary method for nonlinear modelling. For applied planning, the forecasts can provide an initial quantitative reference for future fieldpea area, production and productivity. However, future studies should validate the models using an explicitly defined hold-out period and, where data permit, compare univariate ARIMA and ANN with hybrid or exogenous-variable models incorporating weather, prices, input use and other agronomic factors.

Study limitations and publication notes

The manuscript is derived directly from the submitted thesis and therefore preserves its reported data, models and results. Before journal submission, the following items should be checked against the original analysis files: (i) exact units of area and production; (ii) the precise data source and retrieval dates for each series; (iii) the train/test or validation design used for ANN; (iv) residual diagnostic statistics for the selected ARIMA models; (v) exact definitions of the reported R² values; and (vi) the apparently inconsistent wording in the thesis describing some ARIMA parameter components. These checks are important for reproducibility and should be completed before submission. The paper also intentionally avoids adding new empirical claims or external references that were not established in the thesis. Journal-specific formatting, reference verification, figure preparation and plagiarism/similarity screening should be performed as a separate final submission stage.

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