Stationary time series:

A time series x(t); t=1,... is called to be stationary if its statistical properties do not depend on time t . A time series may be stationary in respect to one characteristic, e.g. the mean, but not stationary in respect to another, e.g. the variance:

M(x(t)) = const - the mean does not depend on time t;

Var(x(t)) = v(t) - the variance depends on time t;

where M(·) is the mean, Var(·) is the variance.

If joint probability distributions does not depend on time itself but only on the difference of time moments,