Definition:Sample Variance of Stochastic Process

Definition
Let $S$ be a stochastic process giving rise to a time series $T$.

The sample variance of $S$ over a set of $N$ successive values $\set {z_1, z_2, \dotsb, z_N}$ is defined as:


 * $\ds \hat \sigma_z^2 := \frac 1 N \sum_{t \mathop = 1}^N \paren {z_t - \overline z}^2$

where $\overline z$ denotes the sample mean of $S$ over $\set {z_1, z_2, \dotsb, z_N}$.