ON A CLASS OF NONSTATIONARY PROCESSES

H. L. Gray and Nien Fan Zhang

Journal of Time Series Analysis, 1988, vol. 9, issue 2, 133-154

Abstract: 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.

Date: 1988
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