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On A Class Of Nonstationary Processes

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  • H. L. Gray
  • Nien Fan Zhang

Abstract

. In this paper a class of nonstationary processes, referred to as multiplicative stationary processes, is investigated. It is shown that although these processes are not stationary with regard to an additive binary operation, i.e. in the classical sense, they are stationary with respect to a multiplicative binary operation. This property is then exploited in such a way as to guarantee essentially the same structure as is available for stationary processes. In particular, suitable definitions for the autocorrelation, power spectrum and linear processes are given. In addition, the Euler process is introduced as the nonstationary or multiplicative stationary dual of the classical autoregressive processes. Some ergodic theorems are also obtained and numerous examples are given.

Suggested Citation

  • H. L. Gray & Nien Fan Zhang, 1988. "On A Class Of Nonstationary Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 9(2), pages 133-154, March.
    • Handle: RePEc:bla:jtsera:v:9:y:1988:i:2:p:133-154
    DOI: 10.1111/j.1467-9892.1988.tb00460.x
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    Cited by:

    1. Jiang, Huiping & Gray, Henry L. & Woodward, Wayne A., 2006. "Time-frequency analysis--G([lambda])-stationary processes," Computational Statistics & Data Analysis, Elsevier, vol. 51(3), pages 1997-2028, December.

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