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Stationary Processes With A Finite Number Of Non‐Zero Canonical Correlations Between Future And Past

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  • K. L. Vaninskii
  • A. M. Yaglom

Abstract

. The spectral densities f(γ) are determined for stationary random processes X(t) with continuous time which have the property that the number of non‐zero canonical correlations between the past X(t) (t≤ 0) (more accurately the present and the past) and the future X(t) (t≥θ) is finite (equal to N) at any θ≥τ for some r > 0. A method for finding all the corresponding canonical correlations P1, …, PN and the canonical variables X1‐, …, XN‐ and X1+, …, XN+ is given. Similar results related to processes X(t) with discrete (integral) time are briefly considered.

Suggested Citation

  • K. L. Vaninskii & A. M. Yaglom, 1990. "Stationary Processes With A Finite Number Of Non‐Zero Canonical Correlations Between Future And Past," Journal of Time Series Analysis, Wiley Blackwell, vol. 11(4), pages 361-375, July.
    • Handle: RePEc:bla:jtsera:v:11:y:1990:i:4:p:361-375
    DOI: 10.1111/j.1467-9892.1990.tb00064.x
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    Cited by:

    1. Dauxois, Jacques & Nkiet, Guy Martial, 2002. "Measures of Association for Hilbertian Subspaces and Some Applications," Journal of Multivariate Analysis, Elsevier, vol. 82(2), pages 263-298, August.
    2. Bhansali, Rajendra J., 2020. "Model specification and selection for multivariate time series," Journal of Multivariate Analysis, Elsevier, vol. 175(C).

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