A1 Refereed original research article in a scientific journal
Modeling temporally uncorrelated components of complex-valued stationary processes
Authors: Lietzén Niko, Viitasaari Lauri, Ilmonen Pauliina
Publisher: VTEX
Publication year: 2021
Journal: Modern Stochastics: Theory and Applications
Journal name in source: MODERN STOCHASTICS-THEORY AND APPLICATIONS
Journal acronym: MOD STOCH-THEORY APP
Volume: 8
Issue: 4
First page : 475
Last page: 508
Number of pages: 34
ISSN: 2351-6054
DOI: https://doi.org/10.15559/21-VMSTA190
Self-archived copy’s web address: https://research.utu.fi/converis/portal/detail/Publication/68193907
A complex-valued linear mixture model is considered for discrete weakly stationary processes. Latent components of interest are recovered, which underwent a linear mixing. Asymptotic properties are studied of a classical unmixing estimator which is based on simultaneous diagonalization of the covariance matrix and an autocovariance matrix with lag tau. The main contributions are asymptotic results that can be applied to a large class of processes. In related literature, the processes are typically assumed to have weak correlations. This class is extended, and the unmixing estimator is considered under stronger dependency structures. In particular, the asymptotic behavior of the unmixing estimator is estimated for both long-and short-range dependent complex-valued processes. Consequently, this theory covers unmixing root T and unmixing estimators that produce non Gaussian asymptotic distributions. The presented methodology is a powerful preprocessing tool and highly applicable in several fields of statistics.
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