ETS and the state space model

We've seen three methods so far: simple exponential smoothing for trend-less data, double exponential smoothing (also known as Holt's linear method) for a linear or damped trend component, and triple exponential smoothing (or Holt–Winters) for additive or multiplicative seasonality.

In a taxonomy of these methods first proposed in 1969 and expanded/refined in an important 2001 paper by Rob Hyndman (the author of the forecast package) et al., these methods can be nicely summarized in a table such as this:

Seasonal component

Trend component	None	Additive	Multiplicative
None	NN	NA	NM
Additive	AN	AA	AM
Additive Damped	DN	DA	DM
Multiplicative	MN	MA	MM

 

This taxonomy encompasses all popular exponential smoothing methods including all the ones we've used so far (and many that we haven't). For example, the simple exponential smoothing method we used on the white noise series is NN, the models we tried on the climate change data (linear, and damped trend) were AN, and DN,...