## 9.4 A taxonomy of exponential smoothing methods

Exponential smoothing methods are not restricted to those we have presented so far. By considering variations in the combinations of the trend and seasonal components, nine exponential smoothing methods are possible, listed in Table 9.5. Each method is labelled by a pair of letters (T,S) defining the type of ‘Trend’ and ‘Seasonal’ components. For example, (A,M) is the method with an additive trend and multiplicative seasonality; (A$$_d$$,N) is the method with damped trend and no seasonality; and so on.

Table 9.5: A two-way classification of exponential smoothing methods.
Trend Component
Seasonal Component
N A M
N (None) (N,N) (N,A) (N,M)
A$$_d$$ (Additive damped) (A$$_d$$,N) (A$$_d$$,A) (A$$_d$$,M)

Some of these methods we have already seen using other names:

Short hand Method
(N,N) Simple exponential smoothing
(A,N) Holt’s linear method
(A$$_d$$,N) Additive damped trend method
(A$$_d$$,M) Holt-Winters’ damped method
Table 9.6 gives the recursive formulas for applying the nine exponential smoothing methods in Table 9.5. Each cell includes the forecast equation for generating $$h$$-step-ahead forecasts, and the smoothing equations for applying the method.