Holt’s Linear Trend Model (Double Exponential Smoothing)

Double Exponential Smoothing extends Simple Exponential Smoothing (SES) by introducing a trend component (Trends in Time Series), allowing it to capture both the level and the trend of a time series.

It is governed by two smoothing parameters:

• $\alpha$ : level smoothing
• $\beta$ : trend smoothing

Update equations:

• Level: $L_t=\alpha X_t+(1-\alpha )(L_{t-1}+T_{t-1})$
• Trend: $T_t=\beta (L_t-L_{t-1})+(1-\beta )T_{t-1}$
• Forecast: ${\hat{X}}_{t+h}=L_t+h{T}_t$

This method is especially useful for datasets exhibiting consistent upward or downward trends.