Final answer:
An ARMA(p, q) model can be used to derive autocovariances by considering the correlation between the values of a time series at different lags and the coefficients of the AR and MA components. The Yule-Walker equations for the AR component and the moving average representation of the MA component are used to calculate the autocovariances.
Step-by-step explanation:
An ARMA(p, q) model consists of an autoregressive (AR) component of order p and a moving average (MA) component of order q.
Autocovariances are used to measure the relationship between the values of a time series at different lags. Autocovariances can be derived for an ARMA(p, q) model by considering the correlation between the values of the time series at different lags and the coefficients of the AR and MA components.
To derive the autocovariances, you can use the Yule-Walker equations for the AR component and the moving average representation of the MA component.
The Yule-Walker equations allow you to express the autocovariances in terms of the AR coefficients, while the moving average representation provides the necessary information about the MA coefficients.
By combining these two components, you can calculate the autocovariances for an ARMA(p, q) model.