Goodness-of-fit tests for the spatial spectral density

Detection and modeling the spatial correlation is an important issue in spatial data analysis. We extend in this work two different goodness-of-fit testing techniques for the spatial spectral density. The first approach is based on a smoothed version of the ratio between the periodogram and a parametric estimator of the spectral density. The second one is a generalized likelihood ratio test statistic, based on the log-periodogram representation as the response variable in a regression model. As a particular case, we provide tests for independence. Asymptotic normal distribution of both statistics is obtained, under the null hypothesis. For the application in practice, a resampling procedure for calibrating these tests is also given. The performance of the method is checked by a simulation study. Application to real data is also provided.