SCENARIO 16-12
A local store developed a multiplicative time-series model to forecast its revenues in future quarters,using quarterly data on its revenues during the 5-year period from 2009 to 2013.The following is the resulting regression equation:
log₁₀Y^ˆ = 6.102 + 0.012 X - 0.129 Q₁ - 0.054 Q₂ + 0.098 Q₃
where
Y^ˆis the estimated number of contracts in a quarter.
X is the coded quarterly value with X = 0 in the first quarter of 2008.
Q₁ is a dummy variable equal to 1 in the first quarter of a year and 0 otherwise.
Q₂ is a dummy variable equal to 1 in the second quarter of a year and 0 otherwise.
Q₃ is a dummy variable equal to 1 in the third quarter of a year and 0 otherwise.
Time-Series Forecasting 16-31
-Referring to Scenario 16-12,to obtain the fitted value for the first quarter of 2013 using the model,which of the following sets of values should be used in the regression equation?

Question

Quizplus · Accepted Answer

Since X is coded with X = 0 in the first quarter of 2008, the first quarter of 2013 would be 5 years later, which is 20 quarters later. However, since the coding starts at 0, the 20th quarter is coded as 19 (subtracting 1 to align with the coding starting at 0). Therefore, the correct coding for the first quarter of 2013 is X = 19, not 16 or 17 as provided in the options. Given the mistake in the question's options, the closest correct option based on the provided scenario (assuming a typographical error in the options) would be to select the option that correctly identifies the first quarter of a year, which is option A, with the understanding that the correct value for X should be 19 for the first quarter of 2013.

SCENARIO 16-12 A Local Store Developed a Multiplicative Time-Series Model to Forecast