# Shadowing ECRI’s Weekly Leading Index (WLI)

#### The Shadow Weekly Leading Index (Shadow WLI)

The Shadow WLI stems from an international collaborative effort by Franz Lischka, Georg Vrba, Dwaine van Vuuren, and Doug Short. We publish the final shadow levels one day ahead of the official ECRI WLI for underlying component data to Friday of the prior week.

According to ECRI, the Weekly Leading Index (WLI) is designed to anticipate the turns in the business cycle, while the growth rate of the index (WLIg) anticipates turns in the growth rate cycle.  It is supposed to provide leads to cycle peaks and troughs of about 10 months and 3 months, respectively.  This widely followed index is published every Friday morning by ECRI.

ECRI has not disclosed the current components of the WLI or how the index is calculated. In 1999 the underlying seasonally adjusted, where applicable economic indicator components of it were:

1. Initial claims for unemployment insurance,
2. Money supply (M2 plus),
3. Industrial materials price index,
4. Mortgage loan applications,
5. 10 year treasury bond yield / BAA corporate bond yield
6.  BAA corporate bond yield; and
7. Stock price index.

The Shadow WLI mimics the ECRI WLI with great accuracy.  For the published shadow levels the Pearson correlation coefficients are 0.992 and 0.997 for the WLI and the WLIg, respectively, for historic data since June 2012 .

#### Calculating the annualized growth rate of a time series

A superior measure for cyclical analysis, introduced by Geoffrey H. Moore, is the six-month smoothed compound annualized growth rate of a time series or index, such as the WLI.  The growth rate of the index (WLIg) is the compound annualized growth rate of the WLI for a 26.5 week period.

MA1 is the 4 week moving average of the WLI and MA2 is the moving average of MA1 over the preceding 52 weeks. Because the 52-week average in the denominator is centered 26.5 weeks before the current middle of the week, the ratio MA1/MA2 yields the change over a 26.5-week period, i.e. over six months.

WLIg =  [100*(MA1/MA2)^( 52/26.5)] – 100

One can also calculate the WLIg using the Excel function XIRR.

=XIRR((-MA1/MA2)six-months-ago : (MA1/MA2)now, (date)six-months-ago : (date)now)

MA1 is not limited to 4 weeks, however this number is used for the WLI.

#### Historic data

The shadow WLI has been generated since June 2012, the table below lists the historic data for the period 6-1-12 to 2-15-13 and the chart depicts the percent error of the shadow WLI compared to ECRI’s WLI over the same period. Note that the date in the table refers to the end of the week level of the WLI based on economic data for that week; the ECRI WLI publication date is one week later.

 for the week ending on Thur’s Shadow Friday’s ECRI WLI WLIg WLI WLIg
 02/22/13 02/15/13 129.2 7.50 129.1 7.55 02/08/13 129.9 8.47 129.7 8.39 02/01/13 130.0 8.83 130.3 8.88 01/25/13 129.8 8.30 129.7 8.18 01/18/13 131.0 7.31 130.6 7.07 01/11/13 130.6 6.30 130.3 6.02 01/04/13 127.5 4.74 128.0 4.93 12/28/12 126.4 5.17 126.4 4.92 12/21/12 127.3 5.00 127.5 5.15 12/14/12 127.2 4.99 127.1 4.75 12/07/12 127.6 4.33 127.5 4.14 11/30/12 127.1 3.69 126.5 3.36 11/23/12 126.1 3.42 126.1 3.35 11/16/12 125.6 3.81 125.3 3.74 11/09/12 125.3 4.43 125.2 4.49 11/02/12 126.2 5.11 126.2 5.26 10/26/12 126.5 5.87 126.8 6.09 10/19/12 126.3 5.81 126.8 6.19 10/12/12 126.7 6.10 126.7 6.35 10/05/12 127.2 5.53 127.8 5.95 09/28/12 126.9 4.94 126.5 4.89 09/21/12 126.3 3.70 126.6 4.02 09/14/12 125.3 2.75 125.3 2.95 09/07/12 124.6 1.67 124.8 2.24 08/31/12 123.5 0.95 124.1 1.54 08/24/12 123.5 0.55 123.8 0.92 08/17/12 122.8 -0.44 123.5 0.15 08/10/12 122.5 -0.79 123.1 -0.31 08/03/12 122.3 -1.33 122.7 -1.02 07/27/12 122.3 -1.13 122.2 -1.17 07/20/12 122.2 -1.8 122.7 -1.66 07/13/12 122.3 -1.8 121.8 -2.38 07/06/12 123.0 -2.4 122.8 -2.85 06/29/12 121.5 -3.3 121.4 -3.43 06/22/12 121.3 -3.6 121.3 -3.67 06/15/12 121.1 -3.5 121.1 -3.57 06/08/12 122.4 -2.6 121.8 -3.09 06/01/12 121.9 -1.9 121.3 -2.32

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