Question

The table below shows semi-annual demand (in thousands) for Shidgets (they're like Widgets, only quieter). A linear trend has been estimated using this data set with t = 1 for 1990.1 and t = 8 for 1993.2. It has an intercept of 0.76 and a slope of 0.20:

Y= 0.76+0.20T

Use the ratio-to-trend method to calculate seasonal adjustment factors for the first and second half of the year and then forecast the level of demand for 1995.1. Note: Round all intermediate calculations to two decimal places.

		Year		Demand
	1990.1			1.0
	1990.2			1.1
	1991.1			1.4
	1991.2			1.5
	1992.1			1.8
	1992.2			1.9
	1993.1			2.3
	1993.2			2.3

Answer 1

Solution

Year	Demand(A)	Forecast(F)	A/F
1990.1	1.0	0.96	1.04
1990.2	1.1	1.16	0.95
1991.1	1.4	1.36	1.03
1991.2	1.5	1.56	0.96
1992.1	1.8	1.76	1.02
1992.2	1.9	1.96	0.97
1993.1	2.3	2.16	1.06
1993.2	2.3	2.36	0.97

Finding Forecast(F)

Year	t	Forecast (F)
1990.1	1	Y=0.76+0.20(t) =0.76+0.20(1) =0.96
1990.2	2	=0.76+0.20(2) =1.16
1991.1	3	=0.76+0.20(3) =1.36
1991.2	4	=0.76+0.20(4) =1.56
1992.1	5	1.76
1992.2	6	1.96
1993.1	7	2.16
1993.2	8	2.36

Seasonal factor for year.1

have to add all the A/F of .1 years

=(1.04+1.03+1.02+1.06)/4=1.04

Seasonal factor for year.2

=(0.95+0.96+0.97+0.97)/4=0.96

Forecast for 1995.1= (t=11) :(1.04) ( 0.76+0.20(11)) = (1.04)(2.96) =3.08

Forecast for 1995.2= (t=12) : (0.96) (0.76 +0.20(12)) = (0.96) (3.16)= 3.03