Set out how an order-p autoregressive (AR) model is built and, from its fitted coefficients, work out forecasts one and two periods ahead
The idea
An autoregressive model of order p explains a series by its own previous p values: x(t) = b0 + b1x(t − 1) + … + bpx(t − p) + ε. The one-period forecast plugs in the latest actual values. For two periods ahead, apply the chain rule of forecasting: use the one-period forecast in place of the unknown next value, keep actual values wherever they are known, and add the intercept again at each step. In an AR(2), the two-step forecast uses the one-step forecast for the first lag and the latest actual value for the second. Multi-period forecasts are less certain than one-period ones, because each step builds on an estimate.
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