<![CDATA[This article proposes Drift-Adaptive Non-Crossing Quantile Regression (DAN-CQR), a methodological framework for modeling conditional distributions under nonstationary and tail-sensitive data. Conventional quantile regression can describe heterogeneous effects across the response distribution, but it often treats all observations as equally relevant, may produce crossing quantile curves, and usually relies on global conformal corrections that are less efficient under distributional drift and local heteroscedasticity. DAN-CQR integrates four components: memory-weighted composite quantile loss, residual-adaptive robustness, non-crossing rearrangement, and local conformal calibration. A simulation study with nonlinear structure, heteroscedasticity, heavy-tailed asymmetric errors, outliers, and regime changes was conducted to assess its behavior. The preliminary results show that DAN-CQR achieves calibrated coverage of 0.950 with a narrower average interval width of 11.460 and lower median absolute error than the global conformalized linear and polynomial quantile regression baselines. These findings suggest that the proposed framework can provide coherent quantile estimates and adaptive prediction bands for dynamic data. The method offers a promising direction for robust and interpretable distributional regression in economics, finance, environmental risk, health, education, and public policy.]]>
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