Principal Component Analysis of CO2 Emissions Drivers in BICS EconomiesCovariance Structure, Singular Value Decomposition, and Principal/Independent Axis Analysis

Abstract

This study refines and extends the Principal Component Analysis (PCA) of CO₂ emissions drivers in the BICS economies (Brazil, India, China, South Africa) over 1990–2013, building on the Grey System Theory forecasting framework of Ahmed et al. (2020). I present the full computational machinery: standardized covariance matrices, complete Singular Value Decomposition (SVD) tables (singular values, eigenvalues, explained variance), and explicit direction vectors for the principal axis (V₁, highest-magnitude singular value) and the orthogonal independent axis (V₂). Country-level PCA confirms a dominant Development Intensity Index (88.6–98.9% of variance). Pooled BICS SVD yields three interpretable latent structures: a high-carbon industrialization axis, a clean-growth axis, and an innovation diffusion axis. The independent axis analysis reveals that South Africa’s V₂ is unique in loading positively on both CO₂ and fossil fuels, while India’s V₂ captures a technology-vs-fossil tension absent in other members. These findings sharpen differentiated climate policy prescriptions across the BICS group.