![22/ [21.75 -(5/2-4)(.875) ] =.9539 30/ [21.75 -(5/2-3)(.875) ] =1.352 23/ [21.75 -(5/2-2)(.875) ] =1.079 12/ [21.75 -(5/2-1)(.875) ] =.5872 17/ [ 18.25-(5/2-4)(.875) ] =.869 26/ [ 18.25-(5/2-3)(.875) ] =1.391 20/ [ 18.25-(5/2-2)(.875) ] =1.123 10/ [ 18.25-(5/2-1)(.875) ] =.5904 c 0 c -1 c -2 c -3 c -4 c -5 c -6 c -7 So=21.75+(.875)(1.5) =23.06 Go=(21.75-18.25)/4 =.875 .9115 22 8 1.3720 30 7 1.1010 23 6 (.5904+.5872)/2 =.5888 21.75 12 5 17 4 26 3 20 2 18.25 10 1 V i D t Period](https://image.slidesharecdn.com/wintersmethod-100210005500-phpapp01/85/Winters-Method-11-320.jpg)
Winters Method
- 1. Chapter 2: Forecasting Methods for Seasonal Series Methods for Stationary Series Seasonal factors Seasonal decomposition using MA Methods for seasonal series with trend Winter’s Method
- 2. A Seasonal Demand Series Fig. 2-8
- 3. Seasonal Series with Increasing Trend Fig. 2-10
- 4. Winter’s Method We assume a model of the form μ : base signal or intercept at time 0 G: trend or slope component c t : multiplicative seasonal component ε t : error term This model assumes that the underlying series has a form similar to that in Figure 2-10.
- 5. Assumptions: The season is exactly N periods Seasonal factors are the same each period and Σ c t = N Three exponential smoothing equations are used each period to update estimates of : Deseasonalized series Seasonal factors Trend These equations have different smoothing constants, α , β , and γ
- 6. The series: The trend The seasonal factors
- 7. Forecast made in period t for any future period t + τ
- 8. Initialization Procedure Suppose that current period is t=0 Past observations are labeled D -2N+1 , D -2N+1 , … , D 0 Calculate the sample means for the 2 seasons data: 2. Define the initial slope estimate
- 9. Initialization for Winters’s Method Fig. 2-11
- 10. 3. Set the estimate of the value of the series at t=0 4 (a). Initial SF are obtained by dividing each observation by the corresponding point on the line connecting V 1 and V 2 using the formula: i=1,2 for the 1st , 2 nd season j : period of the season (b). Average the seasonal factors: (c ). Normalize the SF:
- 11. 22/ [21.75 -(5/2-4)(.875) ] =.9539 30/ [21.75 -(5/2-3)(.875) ] =1.352 23/ [21.75 -(5/2-2)(.875) ] =1.079 12/ [21.75 -(5/2-1)(.875) ] =.5872 17/ [ 18.25-(5/2-4)(.875) ] =.869 26/ [ 18.25-(5/2-3)(.875) ] =1.391 20/ [ 18.25-(5/2-2)(.875) ] =1.123 10/ [ 18.25-(5/2-1)(.875) ] =.5904 c 0 c -1 c -2 c -3 c -4 c -5 c -6 c -7 So=21.75+(.875)(1.5) =23.06 Go=(21.75-18.25)/4 =.875 .9115 22 8 1.3720 30 7 1.1010 23 6 (.5904+.5872)/2 =.5888 21.75 12 5 17 4 26 3 20 2 18.25 10 1 V i D t Period