  We consider a complex-valued linear mixture model, under discrete weakly
stationary processes. We recover latent components of interest, which have
undergone a linear mixing. We study asymptotic properties of a classical
unmixing estimator, that is based on simultaneous diagonalization of the
covariance matrix and an autocovariance matrix with lag $\tau$. Our main
contribution is that our asymptotic results can be applied to a large class of
processes. In related literature, the processes are typically assumed to have
weak correlations. We extend this class and consider the unmixing estimator
under stronger dependency structures. In particular, we analyze the asymptotic
behavior of the unmixing estimator under both, long- and short-range dependent
complex-valued processes. Consequently, our theory covers unmixing estimators
that converge slower than the usual $\sqrt{T}$ and unmixing estimators that
produce non-Gaussian asymptotic distributions. The presented methodology is a
powerful prepossessing tool and highly applicable in several fields of
statistics. Complex-valued processes are frequently encountered in, for
example, biomedical applications and signal processing. In addition, our
approach can be applied to model real-valued problems that involve temporally
uncorrelated pairs. These are encountered in, for example, applications in
finance.
