Stationary time-series and N-order stationarity

Question

Suppose I have a stationary time series, does this imply that the series is also N-order stationary?

score 2 · Answer 1 · answered Feb 18 '13 at 18:32

2

It depends on the context. Stationary is not a term that is used very rigorously in every text book. Especially in the context of time series usually people are referring to wide sense stationarity. When people say strictly stationary then they mean stationarity of all orders.

answered Feb 18 '13 at 18:32

Cagdas Ozgenc

4,486

All orders only in the sense of those for which moments of the distribution exist. My answer contains an example where all orders are limited below unity. – Richard Hardy May 26 '20 at 11:07
A belated +1. You are perfectly correct in what you say and @RichardHardy's claim is wrong. – Dilip Sarwate Jun 14 '20 at 21:51

Stationary time-series and N-order stationarity

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