# Stationary time series

From AMS Glossary

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## 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.