Question

Describe the differences between Holt-Winters additive seasonal models and multiplicative seasonal models. Under what circumstances would you employ each? How is the modeling different if trend and seasonality are both multiplicative

Answer 1

Holt-Winters additive seasonal models :

Holt-Winters additive seasonality algorithm evaluates a trend equation with a seasonal adjustment which is additive.Amount of adjustment is constant for all level of series.It makes use of the following formula ;

at=(Xt-Ft-s)+(1-)(at-1+bt-1)

bt=(at-at-1)+(1-)(bt-1)

Ft=(Xt-at)+(1-)Ft-s

Here ,, are smoothing constants with values between 0 & 1. at the y intercept and bt gives the slope at time t. s is the number of periods per year.

Holt-Winters multiplicative seasonal models:

Holt-Winters multiplicative seasonality algorithm evaluates a trend equation with a seasonal adjustment which is multiplicative.Amount of adjustment varies for various level of series.The equations for multiplicative model are:

at=(Xt /Ft-s)+(1-)(at-1+bt-1)

bt=(at-at-1)+(1-)(bt-1)

Ft=(Xt/at)+(1-)Ft-s

Here ,, are smoothing constants with values between 0 & 1.at the y intercept and bt gives the slope at time t. s is the number of periods per year.

If trend and seasonality both are multiplicative it will become a purely multiplicative model.

y=Trend * Seasonality