Figure 1.

Equations for Holt-Winters exponential smoothing, where y_x and ŷ_x denote the initial series and the forecasts, respectively. The l_x, b_x, and s_x denote the level, the trend, and seasonal estimates for month x, respectively, with m denoting the period of the seasonality (ie, 12 in this case), and h⁺_m=⌊(h–1)mod m⌋+1. The level, trend, and seasonal change smoothing factors are denoted by constants α, β*, and γ, respectively. The estimated values for the coefficients for the level and trend are denoted by a and b, respectively, while the seasonal coefficients are denoted by s₁,...,s₁₂, for month 1,...,12, respectively.