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Modeling and Estimation of Covariance of Replicated Modulated Cyclical Time Series

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2 Author(s)
Sofia C. Olhede ; Department of Statistical Science, University College London, London, UK ; Hernando Ombao

This paper introduces the novel class of modulated cyclostationary processes, a class of nonstationary processes exhibiting frequency coupling, and proposes a method of their estimation from repeated trials. Cyclostationary processes also exhibit frequency correlation but have Loève spectra whose support lies only on parallel lines in the dual-frequency plane. Such extremely sparse structure does not adequately represent many biological processes. Thus, we propose a model that, in the time domain, modulates the covariance of cyclostationary processes and consequently broadens their frequency support in the dual-frequency plane. The spectra and the cross-coherence of the proposed modulated cyclostationary process are first estimated using multitaper methods. A shrinkage procedure is then applied to each trial-specific estimate to reduce the estimation risk.

Published in:

IEEE Transactions on Signal Processing  (Volume:61 ,  Issue: 8 )