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 74.7 Q2 88.2 Q3 107.7 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 2,579 Time 52.5 What is the trend projection of the series for period 107? (please round your answer to 1 decimal place) MUST SHOW ALL WORK AND CALCULATIONS

Explanation / Answer

We got the seasonal indices for three quarters

q1 = 74.7

q2 = 88.2

q3 = 107.7

Let the fourth quarter index be q4

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

This means:

(74.7 + 88.2 + 107.7 + q4) / 4 = 100

270.6 + q4 = 400

q4 = 400 - 270.6

q4 = 129.4

.

Thus the seasonal index of fourth month is 129.4

.

Given the coeffcients of the deseasonaliszed model are: 2,579 and 52.5

Thus the equation of the model is:

Y = 2579 + 52.5 *Time

.

For Time = 107 , we get

Y = 2579 + 52.5 * 107

Y = 2579 + 5617.5

Y = 8196.5

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