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 $\mu$.

Sources

• 1994: George E.P. Box, Gwilym M. Jenkins and Gregory C. Reinsel: Time Series Analysis: Forecasting and Control (3rd ed.) ... (previous) ... (next):

Part $\text {I}$: Stochastic Models and their Forecasting:

$2$: Autocorrelation Function and Spectrum of Stationary Processes:

$2.1$ Autocorrelation Properties of Stationary Models:

$2.1.2$ Stationary Stochastic Processes: Mean and variance of a stationary process: $(2.1.2)$