This correspondence focuses on the asymptotic performance analysis of general direction of arrival (DOA) finding algorithms under the stochastic model assumption in which source and noise signals are possibly non-Gaussian and possibly temporally correlated. We prove, in particular, that all the covariance-based DOA estimators are sensitive to the temporal correlation of the sources when the noise is temporally correlated; otherwise, most of them are insensitive to the temporal correlation of the sources except for the Toeplitzation and the augmentation techniques.