The following table presents data on three leading indicator

The following table presents data on three leading indicators for a three-month period. Construct the composite index (with each indicator assigned equal weight) and the diffusion index.

Month      Leading Indicator A     Leading Indicator B     Leading Indicator C

1                         100                           200                              30

2                         110                           230                              27

3                         120                           240                              33

P7: The composite index is obtained by calculating the percentage change for each series relative to the base month and then averaging these percentage changes. The percentage change from the first to the second month is 10 for indicator A, 15 for indicator B, and 10 for indicator C. Their simple average (since each indicator is given equal weight) is 5 percent. Taking the first month as the base period with a composite index of 100, we obtain the composite index of 105 for the second month. The diffusion index from month 1 to 2 is 66.7 (=2/3) because two indicators move up and move down

Solution

The composite index for the month from 2 to 3

We have the total percentage change of each series relative to the first month=40

Their average is 40/3=13.33

Now the composite index for the month of 3 is 13.33+100=113.33

Also the diffusionindex for the month 3

Procedure

The first step in computing the diffusion indexes is to calculate if a component increased, decreased, or had no change. Components that rise more than 0.05 percent are given a value of 1, components that change less than 0.05 percent are given a value of 0.5, and components that fall more than 0.05 percent are given a value of 0. Next, sum the values of the components. Third, divide by the number of components. Finally, multiply by 100.

In the month 3 all the changes are greater than 05 therefore their sum=1+1+1=3

Their average is 3/3 =1 In terms of percentage it is 1*100=100%

Therefore the diffusion index table and composite index table is