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*11 Week Average Warning for the Past 7 Recessions with No False Positives*

Knowing when the U.S. Economy is heading for recession is paramount for successful investment decisions. We have designed the weekly iMarketSignals Business Cycle Index (BCI) so it would have provided early reliably warnings for the past seven recessions. We achieved recession leads averaging 11 weeks, all with similar lengths. The absence of false positives, for the analyzed time period of 1967 to 2013, enhances the quality and reliability of the recession warnings.

**Composition of BCI**

We developed BCI from the following basic economic data:

- 10-year treasury yield (daily)
- 3-month treasury bill yield (daily)
- S&P500 (daily)
- Continues Claims Seasonally Adjusted (weekly)
- All Employees: Total Private Industries (monthly)
- New houses for sale (monthly)
- New houses sold (monthly)

The data set is available from 1967 onwards, a timeframe that encompasses the last seven recessions. When combining the component for the index the "real time" aspect was considered, i.e. the data was only incorporated into the index at its publication date.

The BCI was not specifically designed to be a measure of the strength or weakness of the economy; it was designed to provide high probability recession forecasts (based on past performance). The various parameters of the BCI model, with which the input data are preconditioned and combined, were adjusted to provide the best recession capturing characteristics to the growth rate of BCI, with emphasis on getting the beginning of recessions right.

A superior measure for cyclical analysis is the 6-month smoothed annualized growth rate of an index. (See appendix A for the formula.) We used this method in our approach to obtain BCIg, the growth of BCI plus 6.0% to make zero the recession trigger. This provided recessions leads of 11 weeks on average with a standard deviation of 2.6, giving a Sharpe ratio of 4.2 (See Table 1). This high ratio indicates that all the leads are of similar length. Furthermore, using this method on the historical data we note that there are no false positives, which is also evident form Figure 1 that plots the BCI and BCIg from1967 onwards.

We note that the current configuration of BCI and BCIg (updated to April 18) are far removed from typical past recession configurations. The last five readings of BCI and BCIg are also shown in Figure 1.

The BCI will be maintained on a dedicated iMarketSignal.com page, updated every Thursday.

**Appendix A**

*Calculating the annualized growth rate of a time series*

The compound annualized growth rate (CAGR) of a time series is calculated for a 26.5 week period. MA1 is the 4 week moving average of the series 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 of MA1 over a 26.5-week period, i.e. over six months.

6-mo CAGR = [100*(MA1/MA2)^( 52/26.5)] – 100

One can also calculate the 6-mo CAGR using the Excel function XIRR.

=XIRR(cell 1: cell 2, (date)6-months-ago : (date)now)where: cell 1 contains: -1 and cell 2 contains: MA1/MA2now

MA1 is not limited to 4 weeks, however this number is generally used for a weekly time series.

Anton Vrba & Georg Vrba

*Anton Vrba is an electrical engineer. He pursued a career in R&D, manufacturing and construction project management. His interests are mathematics and physics. He is a lateral thinker and has ideas that challenge the established explanations to the workings of the universe, which he is in the process of publishing on his website.*

*Georg Vrba is a professional engineer who has been a consulting engineer for many years. In his opinion, mathematical models provide better guidance to market direction than financial "experts." He has developed financial models for the stock market, the bond market, yield curve, gold, silver and recession prediction, all published in Advisor Perspectives. The models are updated weekly at http://imarketsignals.com/.*