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Comparison tests for the spectra of dependent multivariate time series. (English) Zbl 0864.76072

Adler, Robert J. (ed.) et al., Stochastic modelling in physical oceanography. Boston, MA: Birkhäuser. Prog. Probab. 39, 69-88 (1996).
Summary: Statistical test procedures are proposed to compare the spectra of multivariate time 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.
For the entire collection see [Zbl 0836.00049].

MSC:

76M35 Stochastic analysis applied to problems in fluid mechanics
86A05 Hydrology, hydrography, oceanography
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
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