Strictly Stationary Stochastic Process/Examples/Joint Probability Mass Function

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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:

The joint probability mass function of any set of $m$ successive values $\set {z_1, z_2, \dotsb, z_m}$

is the same as:

the joint probability mass function of any other set of $m$ successive values $\set {z_{1 + k}, z_{2 + k}, \dotsb, z_{m + k} }$

for an arbitrary lag $k$.


Sources

Part $\text {I}$: Stochastic Models and their Forecasting:
$2$: Autocorrelation Function and Spectrum of Stationary Processes:
$2.1$ Autocorrelation Properties of Stationary Models:
$2.1.2$ Stationary Stochastic Processes