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. An estimate of the combined trend-cycle component (T₂Ct) for Quarter 3 of Year 1 (used for estimating the de-trended values), when a four-quarter moving average is used, is A) 24. B) 25. C) 26. D) 28.

Question

Quizplus · Accepted Answer

To estimate the combined trend-cycle component for Quarter 3 of Year 1 using a four-quarter moving average, we first need to calculate the moving average for each quarter. Quarter 1: (20 + 22 + 23 + 25)/4 = 22.5 Quarter 2: (22 + 23 + 25 + 24)/4 = 23.5 Quarter 3: (23 + 25 + 24 + 26)/4 = 24.5 Quarter 4: (25 + 24 + 26 + 28)/4 = 25.75 Note that for the first and last quarters, we only have three quarters available to calculate the moving average, so we use those three values rather than four. Now, to estimate the trend-cycle component for Quarter 3 of Year 1, we take the average of the two surrounding quarters' moving averages: (T₂Ct)Q3,Y1 = (22.5 + 23.5)/2 = 23 Therefore, the closest estimate among the given choices is B) 25.

Below You Are Given the First Five Values of a Quarterly