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 $\set {z_1, z_2, \dotsb, z_N}$.

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: $(2.1.4)$