Strictly Stationary Stochastic Process/Examples/Autocovariance

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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 autocovariance between every two observations $z_t, z_{t + k}$ separated by a given lag $k$

is the same as:

the autocovariance between every other two observations $z_{t + m}, z_{t + m + k}$separated by a given 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: Autocovariance and autocorrelation coefficients