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ON A CLASS OF NONSTATIONARY PROCESSES
Author(s) -
Gray H. L.,
Zhang Nien Fan
Publication year - 1988
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/j.1467-9892.1988.tb00460.x
Subject(s) - multiplicative function , mathematics , autocorrelation , stationary process , stationary ergodic process , ergodic theory , class (philosophy) , autoregressive model , euler's formula , spectral density , binary number , statistical physics , mathematical analysis , econometrics , computer science , statistics , physics , arithmetic , invariant measure , artificial intelligence
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.