The following ratio-to-moving averages for the seasonally adjusted series were found by the decomposition method applied on a time series representing quarterly sales for the last three years: If the trend is described by the trend line = 1,000 + 30t, what is the forecast for the fourth quarter of this year?
A) 2,049.22
B) 1,519.95
C) 1,600.00
D) 2,171.36

Question

The following ratio-to-moving averages for the seasonally adjusted series were found by the decomposition method applied on a time series representing quarterly sales for the last three years:  If the trend is described by the trend line  = 1,000 + 30t, what is the forecast for the fourth quarter of this year?
A) 2,049.22 
B) 1,519.95 
C) 1,600.00 
D) 2,171.36

Quizplus · Accepted Answer

We need to use the ratio-to-moving averages and trend line to forecast the sales for the fourth quarter of this year. Here are the steps to follow:

1. Find the seasonal index for the fourth quarter using the ratio-to-moving averages:

Seasonal index for Q4 = (Actual sales for Q4) / (Average sales for all Q4)

From the ratio-to-moving averages table, we can see that the average for Q4 is 1.20, and the actual value for Q4 in the last three years is 2.00. Therefore, the seasonal index for Q4 is:

Seasonal index for Q4 = 2.00 / 1.20 = 1.67

2. Find the trend value for the fourth quarter using the trend line:

Trend value for Q4 = 1,000 + 30(4) = 1,120

3. Multiply the seasonal index and trend value to get the forecast for the fourth quarter:

Forecast for Q4 = Seasonal index for Q4 x Trend value for Q4

Forecast for Q4 = 1.67 x 1,120 = 2,171.36

Therefore, the best choice is D, with a forecast of 2,171.36.

The Following Ratio-To-Moving Averages for the Seasonally Adjusted Series Were