The first-order autoregressive model AR(1) is appropriate when successive values of a time series are linearly related. An AR(1) model can be estimated by regressing the time series on a lag one variable. In some cases, more lags can be added to the model to improve the fit.
The partial autocorrelations function (PACF) shows adjusted autocorrelations that help in determining how many lags to add to the model.
Lag variables can be added to trend and seasonal models to capture autocorrelation effects that are not captured by trend and seasonal indicator variables.