Equality of Real Returns on Canadian and US Treasury Bills: A Fractional Cointegration Analysis

This paper empirically analyzes the long memory relationship between the real returns on Canadian and US Treasury bills. A fractional cointegration approach, instead of conventional integer integration (unit root) and cointegration approaches, is used in analyzing the relationship. The advantage of fractionally integrated models is that they allow a smooth transition from a stationary process to a unit-root process. Furthermore, such models embody unit-root models as a special case. The models are therefore more general and appropriate for empirical analysis. By using fractionally integrated models, one also resolves the problems of an inconsistency in test results associated with using unit root and cointegration approaches. Briefly, it is found that the real returns on Canadian and US Treasury bills are fractionally integrated and the order of integration is significantly less than unity. Furthermore, the difference between the real returns follows a stationary process. This indicates that the Canadian and the US capital markets as well as product markets are well integrated. Furthermore, the domestic monetary authorities will not be able to influence the domestic real interest rate independent of the other market in the long-run.