Testing for separability of spatial–temporal covariance functions

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Tests for separability in nonparametric covariance operators of random surfaces (2015, background): “This is opposed to assuming a parametric separable form with only few unknown parameters, which is usually too restrictive in many applications, something that has led to separability being rightly criticised and viewed with suspicion in the spatio-temporal statistics literature [Gneiting (2002), Gn”
A likelihood ratio test for separability of covariances (2006, background): “Recently, Fuentes [ 8 ] proposes a test using properties of the spectral domain.”
Separable approximations of space‐time covariance matrices (2007, background): “Matsuda and Yajima (2004), Scaccia and Martin (2005), and Fuentes (2006) suggested a test for separability of covariances based on spectral methods.”
Geostatistical Space-Time Models, Stationarity, Separability, and Full Symmetry (2007, methodology): “For tests of stationarity we point to Fuentes (2005b) and references therein.”