An AR model of order $p$ aims to capture the linear dependence between time series values at different lags and can be written as follows:

This closely resembles a multiple linear regression on lagged values of y_t. This model has the following characteristic equation:

The inverses of the solution to this equation in x are the characteristic roots, and the AR(p) process is stationary if these roots are all less than 1 in absolute terms, and unstable otherwise. For a stationary series, multi-step forecasts will converge to the mean of the series.

We can estimate the model parameters with the familiar least squares method using the p+1, ..., T observations to ensure there is data for each lagged term and the outcome.