Autocorrelation at Zero Lag for Strictly Stationary Stochastic Process is 1

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

Then the autocorrelation at zero lag is given by:


 * $\rho_0 = 1$

Proof
From Autocorrelation of Strictly Stationary Stochastic Process:
 * $\rho_k = \dfrac {\gamma_k} {\gamma_0}$

where $\gamma_k$ denotes the autocovariance of $S$.

For zero lag, $k = 0$.

Hence:
 * $\rho_0 = \dfrac {\gamma_0} {\gamma_0} = 1$