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Forecasting Process Details |
Depending on the smoothing model, the smoothing weights consist of the following:
Larger smoothing weights (less damping) permit the more recent data to have a greater influence on the predictions. Smaller smoothing weights (more damping) give less weight to recent data.
The optimization process can result in weights to be chosen outside both the zero-to-one range and the ARIMA additive-invertible region. By restricting weight optimization to additive-invertible region, you can obtain a local minimum with stable predictions. Likewise, weight optimization can be restricted to the zero-to-one range or other ranges. It is also possible to fix certain weights to a specific value and optimize the remaining weights.
The standard errors associated with the smoothing weights are calculated from the Hessian matrix of the sum of squared one-step-ahead prediction errors with respect to the smoothing weights used in the optimization process.
For Simple or Double (Brown) Exponential Smoothing, a level weight near zero implies that simple differencing of the time series may be appropriate.
For Linear (Holt) Exponential Smoothing, a level weight near zero implies that the smoothed trend is constant and that an ARIMA model with deterministic trend may be a more appropriate model.
For Damped-Trend Linear Exponential Smoothing, a damping weight near one implies that Linear (Holt) Exponential Smoothing may be a more appropriate model.
For Winters Method and Seasonal Exponential Smoothing, a seasonal weight near one implies that a nonseasonal model may be more appropriate and a seasonal weight near zero implies that deterministic seasonal factors may be present.
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