QUESTION 5, suppose the following are the seasonal indices for the first three q

Question

QUESTION 5, suppose the following are the seasonal indices for the first three quarters of the year for a quarterly series:

Quarter                        Seasonal Index

Q1                                        72.6

q2                                         80.9

Q3                                        108.6

Remember that the seasonal indices should average 100 so you should e able to infer the seasonal index for Q4.

Furthermore suppose that the estimated coefficients from a regerssion of the deseasonalized series on Time are given below

Intercept                                   2209

time                                            61.2

If the original value of the series in a Q4 was 2451, then what is the seasonally adjusted value?

ANSWER IS 1777.4. just unsure how to get the answer

Explanation / Answer

here for average value of all seasonal index=100

hence (72.6+80.9+108.6+x)/4=100

hence seasonal index of Q4 x=400-72.6-80.9-108.6=137.9

for seasonalized value 2451 ; deseasonalized value =seasonaized value/seasonal index =2451*100/(137.9)=1777.375

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