**Further Improving the Use of the ECRI WLI**

January 17, 2012

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Last week, we described how best to use the growth figure of the Economic Cycle Research Institute’s Weekly Leading Index (WLI) to predict recessions, but we also highlighted an impediment to our research –an inability of outsiders to replicate the index (and thus know its components) and its “growth figure” which ECRI publishes weekly. Last week, however, the formula to calculate the WLI growth figure (which we will refer to simply as “WLIg”) was found. Armed with that data, we have made further progress to improving the recession-dating performance of the WLI.

Doug Short’s last commentary on this same topic prompted an exchange of e-mails among him, Franz Lischka – he’s the person who cracked the formula for the WLIg – Georg Vrba, and Dwaine van Vuuren on how this – fairly arcane and counterintuitive – formula worked and why. Franz’s formula has four components, namely a first moving average MA1, a second moving average MA2, a power coefficient n and a constant m. We do not understand why ECRI has kept this formula a secret for so long.

“MA1” = 4 week moving average of the WLI

“MA2” = 53 week moving average of MA1

“n”= 2

“m”= 1

WLIg = [(MA1/MA2)^n – m] *100

This produces a virtually identical replicate of the WLIg, with a correlation of 1.0 and an average deviation of 0.0026 from the published WLIg number. As a result of these discussions, we decided it would be useful to perform an optimization on Franz’s formula to see if we could obtain better recession-dating performance from a new WLIg derived from the WLI using the same performance measurement methods we described in our previous article. The results were surprising – and quite pleasing.

Those who read last week’s article may recall that even our best recession-predicting method with WLIg yielded four false positives. This time around, we found a WLI growth metric (we decided to call it “WLIg+” which uses MA1=16, MA2=50, n=2.2258 and m=0.9838) that raised the area-under-the-curve (AUC) metric from 0.904 to 0.923 and National Bureau of Economic Research (NBER) capture rate from 86.1% to 93.3%. That last change is deceiving – it is actually a *massive improvement*, given that there are only 360 weeks of NBER recessions in the last 2,290 weeks of the sample period. The WLIg+ correctly categorized an additional 26 weeks as recession. The resulting “improved” WLIg+ is shown below, together with the original WLIg:

The WLIg+ makes recession calls when it drops below zero, and it calls the end of recessions when it rises above zero. This is another improvement, since one need not remember any ostensibly arbitrary thresholds for triggers (like the -2.638 for the original WLIg). We ignored the last recession signal to the right of the chart when counting false positives, as we cannot yet judge any system until the NBER determines definitively whether we are currently at the beginning of a recession (this takes up to 8-12 months!)

You will notice that this is a much smoother and “lazier” interpretation of WLI growth.

In our prior article, we showed how taking a three-week moving average of the 52-week percent change of the WLIg produced a recession forecasting/dating system with only one false positive. We will call this WLIg+1 as shown below:

While we could not replicate a suitable “one-false positive” version of the WLIg+, we did manage to build one with only two false positives (call it “WLIg+2”) :

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