We estimate a multivariate ARFIMA model to illustrate a cointegration testing methodology based on joint estimates of the fractional orders of integration of a cointegrating vector and its parent series. Previous cointegration tests relied on a two-step testing procedure and maintained the assumption in the second step that the parent series were known to have a unit root. In our empirical example of fractional cointegration, we illustrate how uncertainty regarding the order of integration of the parent series can be even more important than uncertainty regarding the order of integration of the cointegrating vector when testing for cointegration.

This paper merges the literature on technical trading rules with the literature on Markov switching to develop economically useful trading rules. The Markov models’ out-of-sample, excess returns modestly exceed those of standard technical rules and are profitable over the most recent subsample. A portfolio of Markov and standard technical rules outperforms either set individually, on a risk-adjusted basis. The Markov rules’ high excess returns contrast with mixed performance on statistical tests of forecast accuracy. There is no clear source for the trends, but permitting the mean to depend on higher moments of the exchange rate distribution modestly increases returns.