🤖 AI Summary
本文提出新的统计方法来分析人为因素与温度分布长期变化的关系，解决了传统回归方法无法区分不同影响路径的问题。
📝 Abstract
Anthropogenic forcing components follow different long-run paths, while persistent temperature change can involve distributional changes beyond the mean. Scalar regressions aggregate these components and retain only mean temperature, obscuring how distinct forcing paths relate to persistent distributional change. We develop new testing, estimation, and inference methods for long-run relations between an integrated predictor vector and a density-valued response. These comprise a residual-based test of between-cointegration (whether predictor trends account for all stochastic trends in the response density), a fully modified least-squares estimator of predictor-specific functional responses, and simulation-based inference for interpretable projections. We apply the methods to densities of observed local temperature anomalies and anthropogenic effective radiative forcing divided into CO$_2$ and non-CO$_2$ portfolios. The test results are consistent with persistent movements in these portfolios statistically accounting for the persistent evolution of the anomaly distribution, with no additional stochastic trend detected in the residual. A joint test rejects the common-response restriction imposed by aggregating the two portfolios. The fitted CO$_2$ response mainly shifts mass toward warmer anomalies and increases central concentration, whereas the non-CO$_2$ response produces a smaller shift but greater dispersion and off-center reshaping. Positive fitted mean responses for both portfolios conceal these contrasts, demonstrating the information lost through scalar aggregation.