QUESTION 29 Suppose the following are the seasonal indices for the first three q

Question

QUESTION 29

Suppose the following are the seasonal indices for the first three quarters of the year for a quarterly series:

Quarter

Seasonal Index

Q1

72

Q2

81.5

Q3

109

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

2,089

Time

66.8

What is the forecast for period 44, if period 44 is a Q3? (please round your answer to 1 decimal place)

Quarter

Seasonal Index

Q1

72

Q2

81.5

Q3

109

Explanation / Answer

Given Quarter Seasonal Indexes Q1= 72 Q2= 81.5 Q3= 109

Let 4th Quarter seasonal index =Q4

Given 4 seasonal average indexes is 100

(72 + 81.5 + 109 +Q4) /4 =100

Hence Q4 =400-262.5 =137.5

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

here for period 44 , deseasonalized forecast = 2089 + 66.8*44 = 5028.2

hence seasonalized forecast = deseasonalized forecast *seasonal index = 5028.2 * 137.5/100 = 6913.8

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