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Error Covariance Matrix Estimation of Noisy and Dynamically Coupled Time Series

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Abstract

We estimate the covariance matrix of the errors in several dynamically coupled time series corrupted by measurement errors. We say that several scalar time series are dynamically coupled if they record the values of measurements of the state variables of the same smooth dynamical system. The estimation of the covariance matrix of the errors is made using a noise reduction algorithm that efficiently exploits the information contained jointly in the dynamically coupled noisy time series. The method is particularly powerful for short length time series with high uncertainties.

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Acknowledgements

This research was supported by the grant MTM2009-12672 given by the Spanish government’s Ministerio de Ciencia e Innovación.

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  1. Dpto. de Fundamentos del Análisis Económico I, Universidad Complutense, 28223, Madrid, Spain

    Maria Eugenia Mera & Manuel Morán

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  1. Maria Eugenia Mera
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  2. Manuel Morán
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Correspondence to Maria Eugenia Mera.

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Mera, M.E., Morán, M. Error Covariance Matrix Estimation of Noisy and Dynamically Coupled Time Series. J Stat Phys 150, 375–397 (2013). https://doi.org/10.1007/s10955-012-0683-7

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