  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.
