This paper uses fractional integration and cointegration in order to model the DM/dollar and the yen/dollar real exchange rates in terms of both monetary and real factors, more specifically real interest rate and labour productivity differentials. We find that whilst the individual series may be integrated of order 1, their long-run relationship might have a fractionally cointegrated structure. This means that mean reversion occurs, consistently with the findings of other studies. However, it also indicates, in contrast to such studies, that the cointegrating relationship possesses long memory. In other words, the error correction term responds slowly to shocks, implying that deviations from equilibrium are long-lived. It appears that only a combination of real and monetary variables can accurately track down the movements of real exchange rates.
fractional integration fractional cointegration real exchange rates