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,
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then the time series x(t) is stationary in respect to any statistical characteristic.