In this paper we assess the security performance of key-less physical layer authentication schemes in the case of time-varying fading channels, considering both partial and no channel state information (CSI) on the receiver's side. We first present a generalization of a well-known protocol previously proposed for flat fading channels and we study different statistical decision methods and the corresponding optimal attack strategies in order to improve the authentication performance in the considered scenario. We then consider the application of machine learning techniques in the same setting, exploiting different one-class nearest neighbor (OCNN) classification algorithms. We observe that, under the same probability of false alarm, one-class classification (OCC) algorithms achieve the lowest probability of missed detection when a low spatial correlation exists between the main channel and the adversary one, while statistical methods are advantageous when the spatial correlation between the two channels is higher.