\begin{definition}[Definition:Autocorrelation 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 '''autocorrelation matrix''' associated with $S$ for $\sequence {s_n}$ is:
:$\mathbf P_n = \begin {pmatrix}
1 & \rho_1 & \rho_2 & \cdots & \rho_{n - 1} \\
\rho_1 & 1 & \rho_1 & \cdots & \rho_{n - 2} \\
\rho_2 & \rho_1 & 1 & \cdots & \rho_{n - 3} \\
\vdots   & \vdots   & \vdots   & \ddots & \vdots \\
\rho_{n - 1} & \rho_{n - 2} & \rho_{n - 3} & \cdots & 1
\end {pmatrix}$
where $\rho_k$ is the autocorrelation of $S$ at lag $k$.
That is, such that:
:$\sqbrk {P_n}_{i j} = \rho_{\size {i - j} }$
\end{definition}