Question

The following are quarterly data for the past two years: Quarter Actual 1 300 2 540 3 885 4 580 5 416 6 760 7 1191 8 760 REQUIRED: From these data, prepare a forecast for the upcoming year using decomposition.

Answer 1

To forecast sales using decomposition, break down the data into trend, seasonal, and random components. Calculate the average seasonal index for each quarter. Use the average seasonal index to adjust the trend component and estimate sales for the upcoming year.

Step-by-step explanation:

To forecast sales using decomposition, we can break down the data into its trend, seasonal, and random components. Based on the given quarterly data for the past two years, we can calculate the average seasonal index for each quarter. Then, we can use this average seasonal index to adjust the trend component and estimate the sales for the upcoming year. Here's how you can do it:

1. Calculate the average of each quarter's data to determine the trend component: (300+540+885+580)/4 = 576.25.
2. Calculate the average of all the quarterly data to get the average for the entire year: (300+540+885+580+416+760+1191+760)/8 = 720.75.
3. Calculate the average seasonal index for each quarter by dividing the quarterly data by the average for the year:
   • Q1: 300/720.75 = 0.416
   • Q2: 540/720.75 = 0.749
   • Q3: 885/720.75 = 1.226
   • Q4: 580/720.75 = 0.804
4. Calculate the adjusted trend component by multiplying the trend component for each quarter by its average seasonal index:
   • Q1: 576.25 * 0.416 = 239.75
   • Q2: 576.25 * 0.749 = 431.20
   • Q3: 576.25 * 1.226 = 706.46
   • Q4: 576.25 * 0.804 = 463.64
5. Estimate the sales for the upcoming year by adding up the adjusted trend component for each quarter:
   • Q1: 239.75
   • Q2: 431.20
   • Q3: 706.46
   • Q4: 463.64