# Definition:Autocorrelation Function

## Definition

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

Let $\rho_k$ denote the autocorrelation coefficient of $S$ at $k$.

The function that maps $k$ to its corresponding $\rho_k$ is referred to as the autocorrelation function.

## Also see

• Results about autocorrelation can be found here.

## Sources

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