A nonparametric regression cross spectrum for multivariate time series

  • Authors:

  • Jan Beran;Mark A. Heiler

  • Affiliations:

  • Department of Mathematics and Statistics, University of Konstanz, Germany;Department of Mathematics and Statistics, University of Konstanz, Germany

  • Venue:
  • Journal of Multivariate Analysis
  • Year:
  • 2008

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Abstract

We consider dependence structures in multivariate time series that are characterized by deterministic trends. Results from spectral analysis for stationary processes are extended to deterministic trend functions. A regression cross covariance and spectrum are defined. Estimation of these quantities is based on wavelet thresholding. The method is illustrated by a simulated example and a three-dimensional time series consisting of ECG, blood pressure and cardiac stroke volume measurements.