This paper proposes tds mgtwr, a multiscale geographically and temporally weighted regression (MGTWR) model with covariate-specific spatial and temporal scales. The approach combines a separable spatio-temporal kernel with a Top-Down Scale (TDS) calibration scheme, where spatial and temporal bandwidths are selected for each covariate through a coordinate-wise search over ordered grids guided by the corrected Akaike Information Criterion (AICc). By avoiding unconstrained multidimensional optimization, this strategy extends to the spatio-temporal setting the stabilizing properties of TDS calibration scheme Geniaux (2026). The multiscale backfitting procedure combines the Top-Down Scale calibration scheme with an adaptive, importance-driven update schedule that prioritizes covariates according to their current scale-normalized contribution to the fitted signal, thereby limiting the number of local recalibrations required and accelerating convergence while maintaining estimator fidelity. We also introduce a generic prediction method for MGWR and MGTWR based on kernel sharpening. Monte Carlo experiments show that modeling both space and time improves coefficient recovery and predictive accuracy relative to purely spatial multiscale models when temporal variation is present and sufficiently supported by the data. Gains increase with sample size and signal-to-noise ratio. Two empirical applications illustrate the method under contrasting regimes. For Beet Yellows severity, a plant epidemiology and pest management problem, multiscale spatial modeling is essential, while spatio-temporal extensions yield additional gains when temporal information is rich. In modeling house prices, MGTWR consistently outperforms spatial local and STVC models. In both cases, predictive performance rivals flexible machine-learning benchmarks while preserving interpretable spatio-temporal scales.

翻译：本文提出tds mgtwr——一种基于协变量特定空间和时间尺度的多尺度地理与时间加权回归（MGTWR）模型。该方法将可分离的时空核函数与自顶向下尺度（TDS）校准方案相结合，通过基于修正Akaike信息准则（AICc）引导的有序网格坐标搜索，为每个协变量选择空间和时间带宽。通过避免无约束的多维优化，该策略将TDS校准方案（Geniaux，2026）的稳定性特性推广至时空场景。多尺度反向拟合过程将自顶向下尺度校准方案与自适应重要性驱动更新策略相结合，根据各协变量当前尺度归一化对拟合信号的贡献权重进行优先级排序，从而限制局部重新校准次数，在保持估计量精度的同时加速收敛。我们还引入了一种基于核锐化的MGWR与MGTWR通用预测方法。蒙特卡洛实验表明，当数据存在足够时间变化支持时，相较于纯空间多尺度模型，对空间和时间的联合建模能提升系数恢复精度与预测准确性，且增益随样本量和信噪比增加而提高。两项实证应用展示了该方法在不同场景下的表现：在甜菜黄化病严重度这一植物流行病学与害虫管理问题中，多尺度空间建模至关重要，而时空扩展方法在时间信息丰富时能产生额外增益；在房价建模中，MGTWR持续优于空间局部模型与STVC模型。两种场景下，其预测性能均可与灵活的机器学习基准模型媲美，同时保持时空尺度的可解释性。