My Real CPI (I avoid the term "shadow" to avoid confusion with ShadowStats) has basically copied the official CPI index until the late 1990's. It has, however, diverged since then.
The following chart shows another version of the Real CPI, which includes property prices as measured by the Case-Shiller index.
Now what? I believe my Real CPI is a more realistic measure of inflation than the officially published CPI. Of course, I can't influence the U.S. economic policy, but perhaps I'll be able to detect another bubble burst ahead of time. (If so, my efforts will pay generously.)