Definition:Autocovariance Function

Definition

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

Let $\gamma_k$ denote the autocovariance coefficient of $S$ at $k$.

The function that maps $k$ to its corresponding $\gamma_k$ is referred to as the autocovariance function.

Also see

• Definition:Autocorrelation Function

• Definition:Autocovariance

• Results about autocovariance can be found here.

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:

$2.1.4$ Autocovariance and Autocorrelation Functions