Forecasting Process Details

Adjustments

Adjustment predictors are subtracted from the response time series prior to model parameter estimation, evaluation, and forecasting. After the predictions of the adjusted response time series are obtained from the forecasting model, the adjustments are added back to produce the forecasts.

If ${y_{t}}$ is the response time series and ${X_{i,t}}$, ${1 \le i \le m}$ are m adjustment predictor series, then the adjusted response series ${w_{t}}$ is

\[ w_{t} = y_{t} - \sum _{i = 1}^{m}{X_{i,t} } \]

Parameter estimation for the model is performed by using the adjusted response time series ${w_{t}}$. The forecasts ${\hat{w}_{t}}$ of ${w_{t}}$ are adjusted to obtain the forecasts ${\hat{y}_{t}}$ of ${y_{t}}$.

\[ \hat{y}_{t} = \hat{w}_{t} + \sum _{i = 1}^{m}{X_{i,t}} \]

Missing values in an adjustment series are ignored in these computations.