Holt-Winters’ Multiplicative Seasonal Smoothing

To find the initial values:

Calculate: P = Value for P

Set: Lt = P, bt = 0, St = Yt/P, for t = 1 to s

For the remaining periods, use the following formulas:

Formula for Holt-Winters' multiplicative seasonal smoothing

where the parameters are:

α—Alpha

β—Beta

γ—Gamma

m—Number of periods ahead to forecast

s—Length of the seasonality

Lt—Level of the series at time t

bt—Trend of the series at time t

St—Seasonal component at time t

Note:

First fit is available from period (s + 1)