Comparison tests for the spectra of dependent multivariate time series

  • René A. Carmona
  • Andrea Wang
Part of the Progress in Probability book series (PRPR, volume 39)

Abstract

Statistical test procedures are proposed to compare the spectra of multivariate time series. We are mostly concerned with the general case of dependent series. The study was motivated by physical oceanography problems for which daily satellite measurements of drifter positions are readily available. Within the mathematical models used for the velocity field at the surface of the ocean, the Lagrangian velocities (time series of the velocities of the drifters along their trajectories) are realizations of stationary stochastic processes having the same one-dimensional marginal distributions. The theory leads to the conjecture that they also should have the same spectra. The tools presented in this paper were intended to test this hypothesis on real data and on data obtained from numerical simulations of transport properties in a two dimensional incompressible Gaussian velocity field.

Keywords

Covariance Coherence Rene 

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References

  1. [1]
    D.R. Brillinger (1973): The Frequency Analysis of Vector-valued Time Series. Holt New York, N.Y.Google Scholar
  2. [2]
    R. Carmona (1994): Ornstein-Ulhenbeck Stochastic Flows. (in preparation)Google Scholar
  3. [3]
    R. Carmona and S. Grishin (1994): Massively Parallel Simulations of Motions in a Gaussian Velocity Field. (preprint)Google Scholar
  4. [4]
    D.S. Coates and P.J. Diggle (1986): Test for Comparing Two Estimated Spectral Densities. J. of Time Series Analysis, 1, 7–20.MathSciNetCrossRefGoogle Scholar
  5. [5]
    P.J. Diggle and N.I. Fisher (1991): Nonparametric Comparison of Cumulative Periodograms. Appl. Statist. 40, 423–434.MathSciNetMATHCrossRefGoogle Scholar
  6. [6]
    S.C. Port and C.J. Stone (1976): Random Measures and their Applications to Motion in an Incompressible Fluid. J. Appl. Prob. 13, 498–506.MathSciNetMATHCrossRefGoogle Scholar
  7. [7]
    M. Rosenblatt (1988): Stationary Sequences and Random Fields. Birkhaüser, Boston, MA.Google Scholar
  8. [8]
    y A.M. Yaglom (1987): Correlation Theory of Stationary and Related Random Functions. vol. I: Basic Results. Springer Verlag. New York, N.Y.Google Scholar
  9. [9]
    z C.L. Zirbel (1993): Stochastic Flows: Dispersion of a Mass Distribution and Lagrangian Observations of a Random Field. Ph. D. Princeton Univ.Google Scholar

Copyright information

© Birkhäuser Boston 1996

Authors and Affiliations

  • René A. Carmona
    • 1
  • Andrea Wang
    • 2
  1. 1.Department of MathematicsUniversity of California at IrvineUSA
  2. 2.Department of StatisticsUniversity of California at BerkeleyUSA

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