11.4 Regression forecasting

Regression can model trend, seasonal indicators, interventions, and relevant external variables. A basic trend model is

\[ y_t=\beta_0+\beta_1t+\varepsilon_t. \]

Add seasonal indicators or transformations when justified. Regression forecasts require future values of all explanatory variables. If those future values are unknown, they must themselves be forecast or supplied as scenarios.

Residual autocorrelation indicates that time structure remains unexplained. Extrapolating a linear trend far beyond the observed period can produce implausible results.