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