\begin{definition}[Definition:Autocovariance Matrix]
Let $S$ be a strictly stationary stochastic process giving rise to a time series $T$.
Let $\sequence {s_n}$ be a sequence of $n$ successive values of $T$:
:$\sequence {s_n} = \tuple {z_1, z_2, \dotsb, z_n}$
The '''autocovariance matrix''' associated with $S$ for $\sequence {s_n}$ is:
:$\boldsymbol \Gamma_n = \begin {pmatrix}
\gamma_0 & \gamma_1 & \gamma_2 & \cdots & \gamma_{n - 1} \\
\gamma_1 & \gamma_0 & \gamma_1 & \cdots & \gamma_{n - 2} \\
\gamma_2 & \gamma_1 & \gamma_0 & \cdots & \gamma_{n - 3} \\
\vdots   & \vdots   & \vdots   & \ddots & \vdots \\
\gamma_{n - 1} & \gamma_{n - 2} & \gamma_{n - 3} & \cdots & \gamma_0
\end {pmatrix}$
where $\gamma_k$ is the autocovariance of $S$ at lag $k$.
That is, such that:
:$\sqbrk {\Gamma_n}_{i j} = \gamma_{\size {i - j} }$
\end{definition}