Explicit Equations for ACF in Autoregressive Processes In the Presence of Heteroscedasticity Disturbances

Abstract

The autocorrelation function, ACF, is an important guide to the properties of a time series. Explicit equations are derived for ACF in the presence of heteroscedasticity disturbances in pth order autoregressive, AR(p), processes. Two cases are presented: (1) when the disturbance term follows the general covariance matrix, Σ , and (2) when the diagonal elements of Σ are not all identical but σ_i,j = 0 ∀i ≠ j.