The Ft values in the table are obtained using triple exponential smoothing, also known as the Holt-Winters method. This method is used for forecasting time series data that exhibit trend and seasonality.
The formula for triple exponential smoothing is:
Ft = St-1 + Tt-1 + It-m
where Ft is the forecast for period t, St-1 is the smoothed value for period t-1, Tt-1 is the trend value for period t-1, and It-m is the seasonal component for period t-m, where m is the number of periods in a season.
The smoothed value for period t is calculated using the following formula:
St = α(Yt - It-m) + (1 - α)(St-1 + Tt-1)
where α is the smoothing parameter for the level component, and Yt is the actual demand for period t.
The trend value for period t is calculated using the following formula:
Tt = β(St - St-1) + (1 - β)Tt-1
where β is the smoothing parameter for the trend component.
The seasonal component for period t-m is calculated using the following formula:
It-m = γ(Yt - St) + (1 - γ)It-m
where γ is the smoothing parameter for the seasonal component.
The values of α, β, and γ are determined through a process of trial and error, where the goal is to minimize the sum of squared errors between the actual demand and the forecasted demand.
In summary, the Ft values in the table are obtained by adding the smoothed value, trend value, and seasonal component for each period, which are calculated using the formulas and smoothing parameters described above.
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