Stationary time series

From Glossary of Meteorology



stationary time series

A time series having stable statistical properties in the following sense.

Let x(t) denote the value of the variable at time t. Hold t fixed and imagine an indefinite series of repetitions of essentially the same generating process, giving rise to a population (ensemble) of values of x(t). For a stationary time series, the ensemble probability distribution of x(t) is independent of t. When the probability distribution changes very gradually with t, the time series is called quasi-stationary.


Copyright 2024 American Meteorological Society (AMS). For permission to reuse any portion of this work, please contact permissions@ametsoc.org. Any use of material in this work that is determined to be “fair use” under Section 107 of the U.S. Copyright Act (17 U.S. Code § 107) or that satisfies the conditions specified in Section 108 of the U.S.Copyright Act (17 USC § 108) does not require AMS’s permission. Republication, systematic reproduction, posting in electronic form, such as on a website or in a searchable database, or other uses of this material, except as exempted by the above statement, require written permission or a license from AMS. Additional details are provided in the AMS Copyright Policy statement.