Question

QUESTION 27 Suppose the following are the seasonal indices for the first three quarters of the year for a quarterly series: Quarter Seasonal Index Q1 71.6 Q2 83.2 Q3 106 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 2,942 Time 67.1 What is the trend projection of the series for period 79? (please round your answer to 1 decimal place)

Answer 1

We got the seasonal indices for three quarters

q1 = 71.6

q2 = 83.2

q3 = 106

Let the fourth quarter index be q4

Now as stated all the four indices must average out to 100

This means:

(71.6 + 83.2 + 106 + q4) / 4 = 100

260.8 + q4 = 400

q4 = 400 - 260.8

q4 = 139.2

.

Thus the seasonal index of fourth month is 139.2

.

Given the coeffcients of the deseasonalized model are: 2,942 and 67.1

Thus the equation of the model is:

Y = 2942 + 67.1 *Time

For Time = 79 , we get

Y = 2942 + 67.1 *79

Y = 2942 + 5300.9

Y =8,242.9