This paper is concerned with a nonparametric regression problem in which the input variables and the errors are autocorrelated in time. The motivation for the research stems from modeling wind power curves. Using existing model selection methods, like cross validation, results in model overfitting in presence of temporal autocorrelation. 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 Gaussian process (GP)-based method to tackle the temporal overfitting problem. Our model is partitioned into two parts -- a time-invariant component and a time-varying component, each of which is modeled through a GP. We modify the inference method to a thinning-based strategy, an idea borrowed from Markov chain Monte Carlo sampling, to overcome temporal overfitting and estimate the time-invariant component. We extensively compare our proposed method with both existing power curve models and available ideas for handling temporal overfitting on real wind turbine datasets. Our approach yields significant improvement when predicting response for a time period different from the training time period. Supplementary material and computer code for this article is available online.
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