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...