A nonlinear regression framework is proposed for time series and panel data for the situation where certain explanatory variables are available at a higher temporal resolution than the dependent variable. The main idea is to use the moments of the empirical distribution of these variables to construct regressors with the correct resolution. As the moments are likely to display nonlinear marginal and interaction effects, an artificial neural network regression function is proposed. The corresponding model operates within the traditional stochastic nonlinear least squares framework. In particular, a numerical Hessian is employed to calculate confidence intervals. The practical usefulness is demonstrated by analyzing the influence of daily temperatures in 260 European NUTS2 regions on the yearly growth of gross value added in these regions in the time period 2000 to 2021. In the particular example, the model allows for an appropriate assessment of regional economic impacts resulting from (future) changes in the regional temperature distribution (mean AND variance).

翻译：本文针对某些解释变量以高于被解释变量的时间分辨率可得的情况，提出了一种适用于时间序列与面板数据的非线性回归框架。核心思想是利用这些变量的经验分布矩来构建具有正确时间分辨率的回归因子。由于这些矩可能呈现非线性边际效应与交互效应，我们采用人工神经网络回归函数进行建模。相应模型在传统随机非线性最小二乘框架内运行，具体通过数值黑塞矩阵计算置信区间。通过分析2000至2021年间260个欧洲NUTS2地区的日温对年度总增加值增长的影响，我们验证了该方法的实际效用。在该具体案例中，该模型能够合理评估因区域温度分布（均值与方差）的（未来）变化而产生的区域经济影响。