Holt's Trend-Corrected Exponential Smoothing
Holt's Trend-Corrected Exponential Smoothing expands simple exponential smoothing to create a forecast from data that has a linear trend. It's often called double exponential smoothing, because unlike SES, which has one smoothing parameter alpha and one non-error component, double exponential smoothing has two.
If the time series has a linear trend, you can write it as:
- Demand at time t = level + t*trend + random error around the level at time t
The most current estimates of the level and trend (times the number of periods out) serve as a forecast for future time periods. If you're at month 36, what's a good estimate of demand at time period 38? The most recent level estimate plus two months of the trend. And time 40? The level plus four months of the trend. Not as simple as SES but pretty close.
Now, just as in simple exponential smoothing, you need to get some initial estimates of the level and trend values, called...