Definition:Variance of Stochastic Process
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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: $(2.1.2)$
- $2.1$ Autocorrelation Properties of Stationary Models:
- $2$: Autocorrelation Function and Spectrum of Stationary Processes:
- Part $\text {I}$: Stochastic Models and their Forecasting: