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A characterization of the pareto process among stationary stochastic processes of the form Xn = c min(Xn-1, Yn)

Author

Listed:
  • Arnold, Barry C.
  • Hallett, J. Terry

Abstract

Let {Yn} be a sequence of i.i.d. non-negative extended real valued random variables. For c > 0, consider stationary stochastic processes of the form Xn = c min(Xn-1, Yn). Subject to a regularity condition related to the behavior of FYn(y) in a neighborhood of 0, it is verified that the associated level crossing processes, Zn(t) = I(Xn > t), are Markovian for every t if and only if {Xn} is a Pareto process.

Suggested Citation

  • Arnold, Barry C. & Hallett, J. Terry, 1989. "A characterization of the pareto process among stationary stochastic processes of the form Xn = c min(Xn-1, Yn)," Statistics & Probability Letters, Elsevier, vol. 8(4), pages 377-380, September.
    • Handle: RePEc:eee:stapro:v:8:y:1989:i:4:p:377-380
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    Cited by:

    1. Yeh, Hsiaw-Chan, 2011. "A multivariate semi-logistic autoregressive process and its characterization," Statistics & Probability Letters, Elsevier, vol. 81(9), pages 1370-1379, September.
    2. Debasis Kundu, 2021. "Stationary GE-Process and its Application in Analyzing Gold Price Data," Papers 2201.02568, arXiv.org.
    3. Debasis Kundu, 2022. "Stationary GE-Process and its Application in Analyzing Gold Price Data," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(2), pages 575-595, November.

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