Category:Autocovariance Matrices
Jump to navigation
Jump to search
This category contains results about Autocovariance Matrices.
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:
- $\sqbrk {\Gamma_n}_{i j} = \gamma_{\size {i - j} }$
Pages in category "Autocovariance Matrices"
The following 2 pages are in this category, out of 2 total.