Space-time forecasting and evaluation of wind speed with statistical tests for comparing accuracy of spatial predictions

High-quality short-term forecasts of wind speed are vital to making wind power a more reliable energy source. Gneiting et al. (2006) have introduced a model for the average wind speed two hours ahead based on both spatial and temporal information. The forecasts produced by this model are accurate, and subject to accuracy, the predictive distribution is sharp, i.e., highly concentrated around its center. However, this model is split into nonunique regimes based on the wind direction at an off-site location. This work both generalizes and improves upon this model by treating wind direction as a circular variable and including it in the model. It is robust in many experiments, such as predicting at new locations. This is compared with the more common approach of modeling wind speeds and directions in the Cartesian space and use a skew-t distribution for the errors. The quality of the predictions from all of these models can be more realistically assessed with a loss measure that depends upon the power curve relating wind speed to power output. This proposed loss measure yields more insight into the true value of each model's predictions. One method of evaluating time series forecasts, such as wind speed forecasts, is to test the null hypothesis of no difference in the accuracy of two competing sets of forecasts. Diebold and Mariano (1995) proposed a test in this setting that has been extended and widely applied. It allows the researcher to specify a wide variety of loss functions, and the forecast errors can be non-Gaussian, nonzero mean, serially correlated, and contemporaneously correlated. In this work, a similar unconditional test of forecast accuracy for spatial data is proposed. The forecast errors are no longer potentially serially correlated but spatially correlated. Simulations will illustrate the properties of this test, and an example with daily average wind speeds measured at over 100 locations in Oklahoma will demonstrate its use. This test is compared with a wavelet-based method introduced by Shen et al. (2002) in which the presence of a spatial signal at each location in the dataset is tested.