Updating the Composite Indexes
The procedure for updating the composite indexes has four distinct steps.
In the notation below, the "t" and "t1" subscripts refer to the current and prior month, respectively, and the "x" and "m" subscripts refer to a particular
component of the index
Step 1  Monthtomonth changes are computed for each component.
If the component X is in percent change form or an interest rate, simple arithmetic differences are calculated: x_{t}=X_{t}X_{t1}. If the component is not in
percent change form, a symmetric alternative to the conventional percent
change formula is used: x_{t}=200*(X_{t}X_{t1})/(X_{t}+X_{t1}).
Details on symmetric percent change formula.

March 98 
April 98 
Average Weekly Hours, Mfg. 
41.8 
41.4 
Symmetric percent change 

0.96 
Step 2  The monthtomonth changes are adjusted using standardization factors that equalize the volatility of each component.

March 98 
April 98 
Average Weekly Hours, Mfg. 
41.8 
41.4 
Symmetric percent change 

0.96 
Standardized (0.96*.189) 

0.18 
Details on symmetric percent change formula.
TABLE with symmetric percent changes and standardized changes of all ten components of the
U.S. Leading Index for the period January 1998 to July 1998.
Step 3  With the previous month's index level, use the sum of the individual contributions as a symmetric percent change to compute the updated level of the
index.
March's level of 105.2 *(200+(0.06))/(200(0.06)) = April's level of 105.30
The above formula is consistent with (i.e., inverts) the symmetric percent change formula in Step 1.
All index levels are rounded to one decimal. Thus, March = 105.2, and April = 105.3
2001 Revisions
Prior to 2001, an additional adjustment was made to equalize the volatility of
the composite indexes. For the U.S. leading and lagging indexes, each monthly
sum (i_{t}) was multiplied by an index standardization factor (f) that
equalizes the volatility these indexes relative to the coincident index.
This factor is the ratio of the standard deviation of the percent changes for
the coincident index (vcoin) to the standard deviation of the unadjusted
percent changes for the particular composite index (flead = vcoin/vlead, flag =
vcoin/vlag). The Conference Board decided to remove this step as it was
proven not have any meaningful difference to the composite indexes' analytical
value.
The leading, coincident and lagging indicators that are not available at the
time of publication are estimated using statistical imputation. An
autoregressive model is used to estimate each component. The resulting
indexes are constructed using real and estimated data, and will be revised as
the data unavailable at the time of publication become available. Such
revisions are part of the monthly data revisions, now a regular part of the U.S.
and global business cycle indicators program. The main advantage of this
procedure is to utilize available data sooner. Empirical research by The
Conference Board suggests there are real gains in adopting this procedure to
make all the indicator series as uptodate as possible.
