This note provides a proof of Granger's (1986) error correction model for fractionally cointegrated variables and points out a necessary assumption that has not been noted before. Moreover, a simpler, alternative error correction model is proposed which can be employed to estimate fractionally...

Voting and non-voting shares of ten German companies are analyzed for fractional cointegration. It turns out that seven pairs of price series are fractionally cointegrated, which means that for each pair there is a linear combination of the two series that is a long-memory process. If two stocks...

This paper shows that the properties of nonlinear transformations of a fractionally integrated process depend strongly on whether the initial series is stationary or not. Transforming a stationary Gaussian I(d) process with d 0 leads to a long-memory process with the same or a smaller...

This paper reports on an extensive Monte Carlo study of seven residual-based tests of the hypothesis of no cointegration. Critical values and the power of the tests under the alternative of fractional cointegration are simulated and compared. It turns out that the Phillips-Perron t-test when...