# Double Exponential Smoothing: Approaches to Forecasting : A Tutorial

## Double Exponential Smoothing

…like regular exponential smoothing, except includes a component to pick up trends.

## Time Series with Trend: Double Exponential Smoothing

Formula

• Ft = Unadjusted forecast (before trend)
• Tt = Estimated trend

Ft = a* At-1 + (1- a) * (Ft-1 + Tt-1)

Tt = b* (At-1-Ft-1) + (1- b) * Tt-1

AFt = Ft + Tt

To start, we assume no trend and set our “initial” forecast to Period 1 demand.

… We then calculate our forecast for Period 2.

… But Period 2 demand turns out to be 20.

What is the trend estimate for Period 3?

By Period 4, the model is starting to pick up on the trend …

…And after a few periods the model “locks on” to the correct trend value.

(Of course, this example is simplified to make the numbers clearer.)