Nonlinear Mean Reversion in Stock Prices

We investigate evidence for nonlinear mean reversion in yearly S\&P500 data from 1871 until 2001. We find that up to 1990 there is significant evidence of nonlinear mean reversion. In particular, stock prices are characterized by a persistent process close to the fundamental value. However, when prices deviate significantly a mean reverting regime is activated and prices adjust to fundamental values. Instead, the stock price run-up of the late 90s exacerbated the persistence of the deviations and there is no evidence for a mean reverting regime that drives prices back to fundamentals.