In fact, the forecasts converge to \(\ell_T \phi b_T/(1-\phi)\) as \(h\rightarrow\infty\) for any value \(0<\phi<1\). For values between \(0\) and \(1\), \(\phi\) dampens the trend so that it approaches a constant some time in the future. If \(\phi=1\), the method is identical to Holt’s linear method. This method involves a forecast equation and two smoothing equations (one for the level and one for the trend): Holt ( 1957) extended simple exponential smoothing to allow the forecasting of data with a trend. 12.9 Dealing with missing values and outliers.12.8 Forecasting on training and test sets.12.7 Very long and very short time series.12.5 Prediction intervals for aggregates.12.3 Ensuring forecasts stay within limits.10.7 The optimal reconciliation approach.10 Forecasting hierarchical or grouped time series.
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