Mean reversion models of financial markets

Mean reversion, volatility persistence, long memory, time scales, stochastic volatility, GARCH, spurious long memory. - I discuss mean reversion in the first and the second moment of the return distribution. After a discussion of the concepts and a summary of the findings in the literature, I show that investorś perceptions of mean reversion play a role in stock market crashes. Turning to the second moment of the return distribution, expected volatility, I consider mean reversion using GARCH. The main finding is that in order to properly measure mean reversion, it is crucial to take parameter regime shifts into account. This can but need not necessarily be done by solving the change point detection problem.