Suppose the following are the seasonal indices for the first three quarters of t

Question

Suppose the following are the seasonal indices for the first three quarters of the year for a quarterly series: Quarter Seasonal Index Q1 75 Q2 82.7 Q3 108.5 Remember that the seasonal indices should average 100 so you should be able to infer the seasonal index for Q4. Furthermore, suppose that the estimated coeffcients from a regression of the deseasonalized series on Time are given below: Coefficients Intercept 2,941 Time 56.3 In general, what quarter is the busiest time of the year? (please just answer 1, 2, 3, or 4) MUST SHOW CALCULATIONS FOR ANSWER

Explanation / Answer

Given Quarter Seasonal Indexes Q1= 75 Q2= 82.7 Q3= 108.5

Let 4th Quarter seasonal index =Q4

Given 4 seasonal average indexes is 100

(75 + 82.7 + 108.5 +Q4) /4 =100

Hence Q4 =400-266.2 =133.8

Deseasonal series of the time for 1,2,3,4

For the TIME1

Y1=2,941+56.3*1 = 2997.3

TIME 2

Y2=2,941+56.3*2 = 3053.6

TIME 3

Y2=2,941+56.3*3 =3109.9

TIME 4

Y2=2,941+56.3*4 =3166.2

Calculations for seasonal indexes

YS1 =(2997.3*75) /100 = 2247.975

YS2=(3053.6 *82.7) /100= 2525.3272

YS3=(3109.9*108.5)/100= 3374.2415

YS4=(3166.2*133.8)/100= 4236.3756

In general YS4 is the highest value

Quarter 4 is the busiest time of the year.

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.