Forecasting of Carbon Emissions in India Using Bayesian ARIMA and BSTS Approaches: Evidence from Environmental Sustainability

Abstract

This work uses a completely Bayesian method to analyse and forecast CO₂ emissions in India by comparing the performance of the Bayesian Autoregressive Integrated Moving Average (ARIMA) and Bayesian Structural Time Series (BSTS) models. This study intends to show that the Bayesian formulation of the ARIMA model can provide better predictive performance in specific situations, even though prior research has frequently emphasised the advantages of the BSTS model particularly in capturing intricate structures in environmental and economic time series. This investigation, which focusses on long-term historical CO₂ emissions data from 1858 to 2023, takes a different modelling approach and comparison framework than previous studies. Based on the Leave-One-Out Information Criterion (LOOIC), choosing the best ARIMA model order is an important initial step. The rstan package is used to perform parameter estimates for the ARIMA and BSTS models using the Hamiltonian Monte Carlo technique. Bayesian criteria, including the Widely Applicable Information Criterion (WAIC) and the Leave-One-Out Information Criterion (LOOIC), are used to assess the performance of the model. The findings show that, in terms of forecast accuracy for India's CO₂ emissions, the Bayesian ARIMA model routinely beats the BSTS model, even with its more straightforward structure.