This paper proposes simple Hausman-type tests to check for bias in the log-periodogram regression of a time series believed to be long memory. The statistics are asymptotically standard normal on the null hypothesis that no bias is present, and the tests are consistent.

This paper revisits the question whether volatilities of different markets and trading zones have a long-run equilibrium in the sense that they are fractionally cointegrated. We consider the U.S., Japanese and German stock, bond and foreign exchange markets to see whether there is fractional...