Several recent empirical studies have been forced to reject exact 1:1 cointegration between spot and forward exchange rates. Theoretically, this is shown to provide a possible explanation for the puzzling negative estimates reported from spot-return-forward-premium regressions. In particular, the coefficient in this regression has a unit root component in its limit distribution that imparts a bias and skewness to the estimator. Simulations are used to demonstrate how even very small deviations from 1:1 cointegration can result in substantial bias. The empirical evidence suggests that the implied Dickey-Fuller-type terms do exhibit a downward bias, yet are of insufficient magnitude to fully account for the puzzling regression coefficients mentioned above.

We assess the information content of order flow for the cross-section of cryptocurrency returns. Our analysis is based on a set of international order flows denominated in 11 major currencies that reflect world order flow. We find that world order flow has strong explanatory and predictive power for cryptocurrency returns. Order flow tends to dominate economic fundamentals for out-of-sample prediction, especially in the context of non-linear machine learning models, and its performance cannot be explained by limits to arbitrage. Overall, our findings indicate that order flow has a permanent effect on cryptocurrency returns.