Panel unit root testing and the martingale difference hypothesis for German stocks

Several panel unit root tests based on different ways to account for cross-unit dependence are reviewed. The note then illustrates the tests by checking whether the martingale difference hypothesis is appropriate for stock prices on the German stock market: according to the martingale difference hypothesis, logarithmized stock prices follow an integrated process without short-run dynamics. Compared with usual tests for no autocorrelation, unit root tests do not require strong moment conditions and can cope with stock returns series exhibiting infinite kurtosis. Evidence against the martingale difference hypothesis is found in a panel of 30 DAX stocks observed daily between 2004 and 2007.