The temporal overfitting problem with applications in wind power curve modeling

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.