This paper is concerned with a nonparametric regression problem in which the independence assumption of the input variables and the residuals is not valid. The motivation for the research stems from modeling wind power curves where the data are temporally autocorrelated. Using existing model selection methods, like cross validation, the presence of temporal autocorrelation in the input variables and the error terms leads to model overfitting. This phenomenon is referred to as temporal overfitting, which causes loss of performance while predicting responses for a time domain different from the training time domain. We propose a new method to tackle the temporal overfitting problem. Our nonparametric model is partitioned into two parts -- a time-invariant component and a time-varying component, each of which is modeled through a Gaussian process regression. The key in our inference is a thinning-based strategy, an idea borrowed from Markov chain Monte Carlo sampling, to estimate the time-invariant component. In our numerical studies, we extensively compare our proposed method with both existing power curve models and available ideas for handling temporal overfitting. Our approach yields significant improvement in prediction when predicting response for a time period different from the training time period.

翻译：本文涉及一个非参数回归问题, 输入变量和剩余值的独立假设是无效的。 研究的动机来自模拟风力曲线, 数据是暂时自动相关的。 使用现有的模型选择方法, 如交叉验证, 输入变量和错误术语中存在时间自动关系, 导致模型过大。 这种现象被称为时间过度, 造成性能损失, 同时预测一个与培训时间范围不同的时间范围。 我们提出了解决时间过长问题的新方法。 我们的非参数模型分为两个部分 -- -- 一个是时间变异部分,一个是时间变异部分,一个是时间变数部分,每个部分都是通过高斯进程回归模型。 我们推论中的关键是一种基于稀薄的战略, 一种从Markov 链 Monte Carlo 取样中借用的想法, 来估计时间变异部分。 在我们的数字研究中, 我们广泛比较了我们提出的方法, 与现有的电力曲线模型以及处理时间过长的可用想法。 我们的方法在预测不同时期的反应时会大大改进。