We consider a complex-valued linear mixture model, under discrete weakly\nstationary processes. We recover latent components of interest, which have\nundergone a linear mixing. We study asymptotic properties of a classical\nunmixing estimator, that is based on simultaneous diagonalization of the\ncovariance matrix and an autocovariance matrix with lag $\\tau$. Our main\ncontribution is that our asymptotic results can be applied to a large class of\nprocesses. In related literature, the processes are typically assumed to have\nweak correlations. We extend this class and consider the unmixing estimator\nunder stronger dependency structures. In particular, we analyze the asymptotic\nbehavior of the unmixing estimator under both, long- and short-range dependent\ncomplex-valued processes. Consequently, our theory covers unmixing estimators\nthat converge slower than the usual $\\sqrt{T}$ and unmixing estimators that\nproduce non-Gaussian asymptotic distributions. The presented methodology is a\npowerful prepossessing tool and highly applicable in several fields of\nstatistics. Complex-valued processes are frequently encountered in, for\nexample, biomedical applications and signal processing. In addition, our\napproach can be applied to model real-valued problems that involve temporally\nuncorrelated pairs. These are encountered in, for example, applications in\nfinance.\n