9.2.3. Winter’s Additive Seasonal

This adds an additive seasonal component to Holt’s Linear method. For a data series forecasts are given by:

    

where:

·       is the level at time t.

·       is the trend at time t.

·       is the seasonal component at time t.

·       is the level smoothing constant.

·       is the trend smoothing constant.

·       is the seasonal smoothing constant.

·      s is the season period.

The initial values are based on the complete data series. level values are given by:

    

    

where  is the average level in season i.

The initial seasonal components  are given by the average value of , the observed value minus the expected value if no seasonal component is used. That is:

    

where:

·      i is the year in which t falls.

·      j is season with in t falls.

Example

Open TIMESER and select Statistics 2 → Forecasting → Winter’s Additive Seasonal and select Cola Sales (C2) as [Variable].

Winter's Additive Seasonal

Level Smoothing Constant =	0.2000
Trend Smoothing Constant =	0.1000
Seasonal Smoothing Constant =	0.0500
Seasonal Period =	12
Sum of Squares =	92856.6862

 

Summary Table

Row	Cola Sales	Forecast	Lower 95%	Upper 95%	Level	Trend	Seasonal
1	189.0000	132.8698	*	*	411.1948	10.6955	-264.8537
2	229.0000	202.5518	65.0353	340.0683	427.1800	11.2245	-218.2806
3	249.0000	222.1597	121.0029	323.3164	443.7725	11.7613	-215.1712
…	…	…	…	…	…	…	…
34	904.0000	906.4846	814.8228	998.1464	744.1618	13.7218	161.7265
35	715.0000	755.1910	666.0461	844.3359	749.8454	12.9180	-4.3002
36	441.0000	512.3320	422.9208	601.7432	748.4969	11.4913	-253.2846
37		493.3129	401.5309	585.0949
38		552.6437	458.9494	646.3381
39		567.1610	471.4072	662.9148
40		622.7754	524.8243	720.7266
41		572.9176	472.6404	673.1948
42		808.3282	705.6048	911.0516
43		1092.9881	987.7069	1198.2693
44		1226.4534	1118.5106	1334.3961
45		1416.6969	1305.9963	1527.3975
46		1025.1368	911.5891	1138.6844
47		870.6014	754.1240	987.0787
48		633.1083	513.6246	752.5920