Adjustments

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 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.

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