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Winters' Three-Parameter Exponential smoothing

Winters' Three-Parameter Exponential smoothing

Equations are:
S_t = α * (Y_t / I_t-L + (1 - α) * (S_t-1 + b_t-1)
b_t = γ (S_t - S_t-1) + (1 - γ) * b_t-1
I_t = β * (S_t - S_t-1)

Forecast
F_t+p = S_t + p * b_t

Where:
p = Number of periods forecasted (forecast horizon)

Initialisation
S₁ = Y₁
b₁ = ((Y₂ - Y₁) + (Y₄ - Y₃)) / 2

Demand of serie is in the Examples Data as Serie C (Strong Trend).

Advantages

Models trend and level
requires less data than double moving averages
adds more flexibility

Disadvantages

Needs two parameters, more complexity to find the best parameters
Does not model seasonality

For the example α = 0.4 and γ = 0.5

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