A strictly stationary process is a process with a random probability distribution, such that its joint probability distribution is independent of time.

Strong sense stationarity: A time series T is called strongly or strictly stationary if two or more random vectors have equal joint distribution for all indices and integers, for example:

Random vector 1 = { Xt1, Xt2, Xt3, ..., Xtn}

Random vector 2 = { Xt1 +s, Xt2 + s, Xt3+s, ..., Xtn +s}

• s is all integers
• t1..tn is all indices

Weak or wide sense stationarity: A time series T is called weakly stationary if it has a shift invariance for the first and second moments of the process.