Wavelet Estimation of Nonstationary Spatial Covariance Function

This work proposes a new procedure for estimating the non-stationary spatial covariance function for spatio-temporal deformation. The proposed procedure is based on a monotonic function approach. The spatio-temporal deformation functions are expanded as a linear combination of wavelet bases. The estimate of the deformation guarantees an injective transformation, such that two distinct locations in the geographic plane are not mapped into the same point in the deformation plane. Simulation studies have shown the effectiveness of this procedure. An application to historical daily maximum temperature records exemplifies the flexibility of the proposed methodology when dealing with real datasets.