How to Compute Diffusion Indexes

Please refer to January 26, 2012 technical notes for details on the comprehensive revisions.

 

Diffusion indexes measure the proportion of the components that contribute positively to the index. 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.

NOTE: For series that are already in percent form, such as BCI-129 - interest rate spread of the U.S. Leading Index, arithmetic differences are used instead of percent changes. BCI-5: The average weekly initial claims for unemployment insurance series, contributes positively to the index when the number of claims declines and negatively to the index when the number of claims increases. For this reason, a value of “1” is assigned to this series in the diffusion index computation in the example below because the number of unemployment insurance claims was greater in June than it was in July.

One-month diffusion indexes measure the percent of components rising over a one-month span, i.e., June 1997 to July 1997. Six-month diffusion indexes measure the percent of components rising over a six-month span, i.e., June 1997 to Dec. 1997.

Using data as of October 1998, the following example uses the components of the U.S. leading index to compute a one-month diffusion index.

Date BCI-1 BCI-5 BCI-8 BCI-32 BCI-27 BCI-29 BCI-19 BCI-106 BCI-129 BCI-83 Index Level
Jun-97 41.9 337.2 150,729 54.9 44,749 1,398 876.29 3,501.3 0.93 98.9
Jul-97 41.9 305.2 151,764 54.8 44,873 1,441 925.29 3,509.0 0.70 102.6
Values for Jul-97 0.5 1 1 0 1 1 1 1 0 1 75

Sum the values to obtain 7.5. Divide by 10 (the number of components), multiply by 100 to get 75

Using this procedure, the following table shows the value for July 1997 to Dec. 1997

Date BCI-1 BCI-5 BCI-8 BCI-32 BCI-27 BCI-29 BCI-19 BCI-106 BCI-129 BCI-83 Index Level
Jul-97 0.5 1 1 0 1 1 1 1 0 1 75
Aug-97 0.5 0 1 1 1 1 1 1 1 0 75
Sep-97 0.5 1 0 0 1 1 1 1 0 1 65
Oct-97 1 0 0 0 1 1 1 1 0 1 60
Nov-97 1 0 0 1 1 0 0 1 0 0 40
Dec-97 1 1 1 0 0 0 0 1 0 0 40

Six-month Diffusion Index

The six-month diffusion index follows the same steps as the one-month index with the exception that diffusion index levels are centered within the six-month span. Index levels are placed in the fourth month of the span. If we are calculating index levels for the June 1997 to Dec. 1997 span, the diffusion index level would be place in Sept. 1997.

Using this procedure, the following table shows the values for components for the six-month diffusion index from June 1997 to December 1997.

Date A0M001 A0M005 A0M008 A0M032 A0M027 A0M029 U0M019 A0M106 U0M129 U0M083 Index Level
Jun-97 41.9 337.2 150,729 54.9 44,749 1,398 876.29 3,501.3 0.93 98.9
Jul-97 41.9 305.2 151,764 54.8 44,873 1,441 925.29 3,509.0 0.7 102.6
Aug-97 41.9 326.2 155,386 55.6 45,031 1,445 927.74 3,534.1 0.76 100.3
Sep-97 41.9 310.2 154,784 55.5 46,336 1,475 937.02 3,548.4 0.67 100.7
Oct-97 42.0 311.1 154,233 55.0 47,387 1,502 951.16 3,563.5 0.53 102.8
Nov-97 42.1 318.6 152,877 55.2 55,182 1,475 938.92 3,583.0 0.36 102.3
Dec-97 42.2 313.4 155,490 54.0 44,180 1,467 962.37 3,601.7 0.31 96.1
Values for Sep-97 1 1 1 0 0 1 1 1 0 0 60
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