Clustering and Regime Analysis of Global Black Carbon Emission Pathways: Robustness, Historical Context, and Forecast Benchmarks

This study investigates whether long-term country-level pathways of per-capita black carbon (BC) emissions can be adequately represented by a single global trajectory and determines when the emerging pathway types experienced major structural changes. The study analyzes a balanced panel of 190 countries observed annually over the period 1800–2022. Log-transformed per-capita BC series are standardized within each country and clustered according to pathway shape using normalized L2 Dynamic Time Warping with a 22-year Sakoe–Chiba window and average linkage. Both average silhouette width and DTW-consistent gap statistics based on 200 reference simulations under a one-standard-error rule select the two-cluster solution. Cluster 1 comprises 30 countries, displaying a relatively high early-period pathway followed by a marked decline after 1958. Cluster 2 comprises 160 countries, exhibiting a long-term upward pathway associated with structural shifts in 1878 and 1949, before declining toward the end of the sample period. Country-level PELT results provide stronger support for the 1958 and 1949 break dates than for the 1878 break. Resampling stability analyses yield median Adjusted Rand Indices of 0.645 and 0.723 for ordinary bootstrap and 80% subsampling, respectively. The solution shows high agreement under closely related DTW specifications but remains sensitive to certain alternative representations and linkage choices. Contemporary external development indicators overlap substantially across clusters, although regional compositions differ descriptively. Historical fossil energy and industrial series provide plausible context for the identified shifts without establishing causal mechanisms. Auxiliary forecasting comparisons demonstrate that Long Short-Term Memory models are not uniformly superior to naive, ARIMA, or ETS models, confirming that forecast performance should not be interpreted as validation of cluster membership.