Modeling temporally uncorrelated components of complex-valued stationary processes

Niko Lietzén*, Lauri Viitasaari, Pauliina Ilmonen

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

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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 usualT 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.

Original languageEnglish
Pages (from-to)475-508
Number of pages34
JournalModern Stochastics: Theory and Applications
Issue number4
Publication statusPublished - Nov 2021
MoE publication typeA1 Journal article-refereed


  • Asymptotic theory
  • Blind source separation
  • Long-range dependency
  • Multivariate analysis
  • Noncentral limit theorems


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