Strictly Stationary Stochastic Process/Examples/Constant Mean Level

Example of Strictly Stationary Stochastic Process
Let $S$ be a strictly stationary stochastic process giving rise to a time series $T$.

It is necessary that $T$ has a constant mean level, so that:
 * The sample mean over a set of $N$ successive values $\set {z_1, z_2, \dotsb, z_N}$

is the same as:
 * the sample mean over any other set of $N$ successive values $\set {z_{1 + k}, z_{2 + k}, \dotsb, z_{N + k} }$

for an arbitrary lag $k$.