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Reducing non-stationary stochastic processes to stationarity by a time deformation

Author

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  • Perrin, Olivier
  • Senoussi, Rachid

Abstract

A necessary and sufficient condition is given to reduce a non-stationary random process to stationarity via a bijective differentiable time deformation [Phi] so that its correlation function r(t,t') depends only on the difference [Phi](t')-[Phi](t) through a stationary correlation function R: r(t,t')=R([Phi](t')-[Phi](t)).

Suggested Citation

  • Perrin, Olivier & Senoussi, Rachid, 1999. "Reducing non-stationary stochastic processes to stationarity by a time deformation," Statistics & Probability Letters, Elsevier, vol. 43(4), pages 393-397, July.
    • Handle: RePEc:eee:stapro:v:43:y:1999:i:4:p:393-397
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    Cited by:

    1. Kleiber, William, 2016. "High resolution simulation of nonstationary Gaussian random fields," Computational Statistics & Data Analysis, Elsevier, vol. 101(C), pages 277-288.
    2. Rachid Senoussi & Emilio Porcu, 2022. "Nonstationary space–time covariance functions induced by dynamical systems," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(1), pages 211-235, March.
    3. Valerie Girardin & Rachid Senoussi, 2020. "Filling the gap between Continuous and Discrete Time Dynamics of Autoregressive Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(4), pages 590-602, July.
    4. Perrin, Olivier & Senoussi, Rachid, 2000. "Reducing non-stationary random fields to stationarity and isotropy using a space deformation," Statistics & Probability Letters, Elsevier, vol. 48(1), pages 23-32, May.
    5. A. E. Madrid & J. M. Angulo & J. Mateu, 2016. "Point Pattern Analysis of Spatial Deformation and Blurring Effects on Exceedances," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 21(3), pages 512-530, September.

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