Essentially Stationary <Back to Last Page>     <Full Glossary>

Definition of Essentially Stationary: A time series process {x_t} is essentially stationary iff E[x_t²] is uniformly bounded.

This definition may not be standard or widely used.

This means that even if the variance wanders around and is different for different t, there is a finite bound to those variances. The variance of the distribution of x_t is never infinite for any t and indeed never exceeds that finite bound. Thus an ARCH-type process might be essentially stationary even though its variance is not constant for all t.

Note that there are strictly stationary processes that have infinite second moments; such processes are not essentially stationary. (Econterms)

Terms related to Essentially Stationary:

• Strictly stationary

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