Chari, Kehoe and McGrattan (2002)[2] showed how a model with two countries and where prices were only allowed to change once-a-year had the potential to simultaneously account for the volatility of U.S. output and real exchange rates.
These two anomalies are related to, but should not be confused with, the Backus-Smith consumption-real exchange rate anomaly, which is the observation that in most economic models the correlation between the real exchange rate and relative consumption is high and positive, whereas in the data it ranges from small and positive to negative.
[3] In this paper Mussa documented that industrial countries which moved from fixed to floating exchange rate regimes experienced dramatic rises in nominal-exchange-rate volatility.
The sixth puzzle is described as "why exchange rates are so volatile and apparently disconnected from fundamentals".
Here Obstfeld and Rogoff (2000) quotes the Meese and Rogoff (1983) exchange rate forecasting puzzle and the Baxter and Stockman (1989) neutrality of exchange rate regime puzzle.