Modeling temporally uncorrelated components of complex-valued stationary processes
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A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
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Date
2021-11
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Language
en
Pages
34
475-508
475-508
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Modern Stochastics: Theory and Applications, Volume 8, issue 4
Abstract
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 τ.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 estimators that converge slower than the usual√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.Description
Funding Information: N. Lietzén gratefully acknowledges financial support from the Emil Aaltonen Foundation (Grant 180144 N) and from the Academy of Finland (Grant 321968). Funding Information: The authors would like to thank Katariina Kilpinen for providing the photographs to Section 5. The authors would like to thank the two anonymous referees for their insightful comments that helped to improve this paper greatly.N. Lietzen gratefully acknowledges financial support from the Emil Aaltonen Foundation (Grant 180144 N) and from the Academy of Finland (Grant 321968). Publisher Copyright: © 2021 The Author(s). Published by VTeX. Open access article under the CC BY license.
Keywords
Asymptotic theory, Blind source separation, Long-range dependency, Multivariate analysis, Noncentral limit theorems
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Citation
Lietzén, N, Viitasaari, L & Ilmonen, P 2021, ' Modeling temporally uncorrelated components of complex-valued stationary processes ', Modern Stochastics: Theory and Applications, vol. 8, no. 4, pp. 475-508 . https://doi.org/10.15559/21-VMSTA190