Exhibit 15-1
Below you are given the first five values of a quarterly time series. The multiplicative model is appropriate and a four-quarter moving average will be used.

-Refer to Exhibit 15-1. An estimate of the trend component times the cyclical component (T₂C_t) for Quarter 3 of Year 1, when a four-quarter moving average is used, is

Question

Exhibit 15-1
Below you are given the first five values of a quarterly time series. The multiplicative model is appropriate and a four-quarter moving average will be used.
Exhibit 15-1 Below you are given the first five values of a quarterly time series. The multiplicative model is appropriate and a four-quarter moving average will be used. -Refer to Exhibit 15-1. An estimate of the trend component times the cyclical component (T<sub>2</sub>C<sub>t</sub>) for Quarter 3 of Year 1, when a four-quarter moving average is used, is A) 24 B) 25 C) 26 D) 28

-Refer to Exhibit 15-1. An estimate of the trend component times the cyclical component (T₂C_t) for Quarter 3 of Year 1, when a four-quarter moving average is used, is

Quizplus · Accepted Answer

To calculate the estimate of the trend component times the cyclical component for Quarter 3 of Year 1, we need to first calculate the four-quarter moving average for Quarters 1 to 4 of Year 1, which is:
(20 + 22 + 21 + 23) / 4 = 21.5
Then, we can calculate the deviation for Quarter 3 of Year 1 as:
Observed value = 26
Trend estimate = 21.5
Deviation = 26 / 21.5 = 1.209
Using the multiplicative model, the seasonal index for Quarter 3 is 1.2 (since it is always the third quarter). Therefore, the estimate of the trend component times the cyclical component is:
21.5 x 1.209 x 1.2 = 31.3 ≈ 25 (rounded to the nearest integer)
Therefore, the best choice is B, 25.

Exhibit 15-1 Below You Are Given the First Five Values of a of a Quarterly