Estimation and testing for covariance-spectral spatial-temporal models

In this paper we explore a covariance-spectral modelling strategy for spatial-temporal processes which involves a spectral approach for time but a covariance approach for space. It facilitates the analysis of coherence between the temporal frequency components at different spatial sites. Stein (J R Stat Soc Ser B (Statistical Methodology) 67:667–687, 2005) developed a semi-parametric model within this framework. The purpose of this paper is to give a deeper insight into the properties of his model and to develop simpler and more intuitive methods of estimation and testing. A very neat estimation for drift direction is proposed while Stein assumes it is known. An example is given using the Irish wind speed data. Stein constructed various plot to assess the goodness of fit of the model, we use similar plots to estimates the parameters.