Definition:Variance of Stochastic Process

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

The variance of $S$ is calculated as:


 * $\sigma_z^2 = \expect {\paren {z_t - \mu}^2} = \ds \int_{-\infty}^\infty \paren {z - \mu}^2 \map p z \rd z$

where $\map p z$ is the (constant) probability mass function of $S$.

It is a measure of the spread about the constant mean level $\mu$.