There is a book "Nerds on Wall Street: Math, Machines and Wired Markets" by David J. Leinweber, who also mentioned our 2007 paper on S&P 500. Select parts of the book are available on-line now.
We agree that the period between 2003 and 2008 is still not well modeled, even with real GDP. Still waiting for the 2010 census estimates. See what happens to the involved population estimates.
The model regains some predictive power, however, when the signal is very high. As observed since 2008.
The answer to the criticism is as always - quantitative. Follow our predictions in this blog.