ARIMA Forecasting

Procedure

ARIMA forecasting models depend on the parameters and lead times:

• AR(1): ${\hat{Y}}_t(l)=\mu +{\varphi }^l(Y_t-\mu )$
• MA(1): $Y_t=\mu +e_t-\theta e_{t-1}$ gives ${\hat{Y}}_t(1)=\mu -\theta e_t$
• Random Walk with Drift: $Y_t=Y_{t-1}+{\theta }_0+e_t$ gives ${\hat{Y}}_t(1)=Y_t+{\theta }_0$
• ARMA(p,q): Forecasts for long lead times depend on autoregressive parameters and the mean.
• Nonstationary Models: The error variance grows without bound as the lead time $l$ increases.