Adaptive radar detection and estimation schemes are often based on the independence of the training data used for building estimators and detectors. This paper relaxes this constraint and deals with the non-trivial problem of deriving detection and estimation schemes for joint spatial and temporal correlated radar measurements. In order to estimate these two joint correlation matrices, we propose to use the Vector ARMA (VARMA) methodology. The estimation of the VARMA model parameters are performed with Maximum Likelihood Estimators in Gaussian and non-Gaussian environment. These two joint estimates of the spatial and temporal covariance matrices leads to build Adaptive Radar Detectors, like Adaptive Normalized Matched Filter (ANMF). Their corresponding performance are analyzed through simulated datasets. We show that taking into account the spatial covariance matrix may lead to significant performance improvements compared to classical procedures ignoring the spatial correlation.