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Double Exponential Smoothing

Double Exponential Smoothing is also sometimes referred to as Second Order Exponential Smoothing

This method is useful, improving on Simple (Single) Exponential Smoothing, when the data has a trend.

One Parameter Double Exponential Smoothing

Uses the same smoothing constant (parameter) for both the permanent and trend components.

Also known as Brown double exponential smoothing. 

Two Parameter Double Exponential Smoothing

Uses two separate smoothing constants, one for the permanent component, and the other for the trend component.

Also known as Holt-Winter's two-parameter double exponential smoothing.

For exponential smoothing that is capable of incorporating seasonal components, see the Holt-Winters' method.


Note from Bowerman section 8.3:
"There is no theoretical statistical basis for Holt-Winter's two-parameter double exponential smoothing.  The prediction interval formula [...] is an intuitive modification of the one-parameter double exponential smoothing prediction interval (which is based on statistical theory)."