Question

Quarter	Year 1	Year 2	Year 3
1	4	6	8
2	2	4	7
3	3	5	6
4	5	7	8

1. Show the four-quarter and centered moving average values for this time series (to 3 decimals if necessary).
   

   Year	Quarter	Time Series Value	Four-Quarter Moving Average	Centered Moving Average
   1	1	4
   	2	2
   	3	3
   	4	5
   2	1	6
   	2	4
   	3	5
   	4	7
   3	1	8
   	2	7
   	3	6
   	4	8

   
   

• 1. Compute seasonal indexes and adjusted seasonal indexes for the four quarters (to 3 decimals).

  Quarter	Seasonal Index	Adjusted Seasonal Index
  1
  2
  3
  4
  Total

Answer 1

Four quarter moving average is computed by taking four values at a time, computing the average and moving one step below. Repeat this process until we have a set of four values.

Eg. The first four quarter moving average is computed by

The second four quarter moving average is computed by

This process is repeated until we have set of 4 values to compute average.

The centered moving average is computed by calculating the average of 2 consecutive moving averages.

Eg. The first centered four quarter moving average is

This process is repeated until we have set of 2 moving average values to compute the centered average.

Steps to calculate seasonal index:

1. Compute seasonal average for every quarter:

Eg. Quarterly average of quarter 1 = 4+6+8/3 = 6

2. Compute the seasonal index for every year by the formula

3. Repeat step 2 for all years

4. Seasonal index is computed by averaging the seasonal index for every quarter

Steps to compute Adjusted Seasonal Index

1. Compute quarterly totals for all quarters

Eg Quarterly total 1 = 4+6+8 = 18

2. Compute overall total of values

3. Divide the quarterly total by overall total to get the adjusted seasonal index