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Data Analysis with R - Second Edition by Tony Fischetti

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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 ...

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