Modeling the determinants of CO₂ emissions from drained organic soils in Denmark: A robust PCA and HAC covariance analysis

The drainage management in organic soils is critical for climate resilience.This study investigates the determinants of  Υ: Drained organic soils (CO₂) (kt) utilizing annual FAO data from 1990 to 2019 in Denmark. The regressors include Χ₁: Net exports of forest products (thousands USD) (UNECE), X₂: Emissions CH₄ - (kt CO₂ equivalent) (European Environment Agency (EEA)), Χ₃: Emissions SF₆ - (t CO₂ equivalent) per capita (EEA), X₄: Urban population (% of total population) (World Bank Group), X₅: Yearly Average Surface Temperature (°C) (Global Data Lab). The methodological approach incorporated an Ordinary Least Squares (OLS) model in python JupyterLab with Heteroskedasticity and Autocorrelation Consistent (HAC) standard errors to address serial correlation, Durbin-Watson (DW) for autocorrelation, Breusch-Pagan (BP) for  heteroskedasticity, Variance Inflation Factor (VIF) for multicollinearity, and Shapiro-Wilk (SW) for normality of the residuals. Moreover, a two-step Engle-Granger cointegration analysis was implemented, while Principal Component Analysis (PCA) ensured robustness against multicollinearity.

Results from the OLS model with HAC standard errors demonstrate a high explanatory power (R² =0.936), with all five variables presenting statistical significance (p < 0.05), while passing all diagnostic tests (DW = 2.136, BP= 0.5426, VIFmax < 7.52, Kolmogorov-Smirnovmin= 0.17). Variables  X1, Χ2,  Χ4,  Χ5   exhibit a negative effect, whereas X₃ is positively connected to CO₂ emissions from drained organic soils.  A stable long-term equilibrium was confirmed by the Engle-Granger method, with the Error Correction Term (ECT) being negative and statistically significant (ECT = -0.7847, p = 0.0008), indicating a 78.47% correction of short-term deviations towards the long‑run equilibrium within a year. Finally, the PCA analysis revealed that the first three principal components explain 90.7% of the total variance.

The study concludes that the five variables are key components associated with CO₂ emissions from drained organic soils in Denmark.