A Hybrid Mathematical Modelling Framework for Forecasting India's Economic Growth: Comparative Evidence from Logistic, Gompertz, Polynomial, ARIMA and ARIMA-Random Forest Hybrid Models (2014–2026)

DOI- https://doi.org/10.5281/zenodo.21096925

Abstract

India's gross domestic product (GDP) growth has been choppy, but on the whole has been positive between 2014 and 2026, witnessing continued expansion before the pandemic in financial year (FY) 2020-21, a steep decline in the middle of the pandemic, and a strong recovery thereafter. This study quantitatively and comparatively analyses the real GDP growth of India using the following six complementary mathematical modelling approaches: Exponential Growth Model, Logistic (Verhulst) Growth Model, Gompertz Growth Model, Polynomial Regression Models (degree 2 and 3), Auto-Regressive Integrated Moving Average (ARIMA) time-series forecasting, and a novel hybrid modelling approach called the ARIMA-Random Forest (ARIMA-RF). Data on real GDP (at 2011-12 prices) for FY2014-15 to FY2024-25 have been prepared using data from Ministry of Statistics and Programme Implementation (MOSPI), Government of India and cross checked with the national accounts data from the World Bank, IMF, RBI and Press Information Bureau (PIB). The non-linear least squares (Exponential, Logistic, Gompertz) and ordinary least squares (Polynomial Regression) methods along with the maximum likelihood (ARIMA) method were used to estimate the model parameters and the Akaike Information Criterion (AIC) was used as the base for selecting the best model. The goodness of fit was evaluated with the coefficient of determination (R²), root mean square error (RMSE) and mean absolute percentage error (MAPE). The structural break tests by Chow were used to study the effect of the major policy shocks such as the Goods and Services Tax (GST) rollout in 2017 and the COVID-19 pandemic in 2020. The results suggest that the cubic polynomial model is the best model in terms of the in-sample level of fit (R² = 0.979, AIC = 35.83); the Exponential model is the best of the theory-based growth curves in terms of the AIC (AIC = 40.66) and the bounded Logistic model and the Gompertz model do not suggest that there is a horizon for the growth to reach a plateau within the past 20 years. However, the Chow test results for the COVID shock or the GST rollout do not attain conventional significance at the 5 per cent level for the limited annual sample size, although the former test result is quite high, reflecting the larger size of its visual impact relative to the other tests conducted. The novel ARIMA-RF hybrid model performs significantly better in terms of in-sample forecasting accuracy than the pure ARIMA(0,1,1) model (with in-sample R² = 0.708 and MAPE = 20.8% against R² = −0.204 and MAPE = 50.6% for the same evaluation window) by capturing the residual non-linearity associated with the pandemic shock, and projects real GDP growth in FY2025-26 at approximately 6.7% per cent, which is very close to the actual provisional outcome reported by MOSPI/NSO of 7.6-7.8 per cent, for the same year. The study provides a reproducible framework for macroeconomic forecasting for emerging economies in the short-to-medium timeframe that is multi-model and hybrid, and suggests implications for fiscal policy, investment policy, and the Government of India's vision of high-income ‘Viksit Bharat' by 2047.

Keywords: Real GDP; Exponential Growth Model; Logistic Growth Model; Gompertz Model; Polynomial Regression; ARIMA; Random Forest; Hybrid Forecasting; Structural Break; Chow Test; Indian Economy; Mathematical Modelling