International Review of Economics and Finance 8 (1999) 305–316 Fractional cointegration, long memory, and exchange rate dynamics Ming-Shiun Pan a, *, Y. Angela Liu b a Department of Finance, Decision Sciences, and Information Systems, Shippensburg University, Shippensburg, PA 17257, USA b Department of Business Administration, National Chung Cheng University, Chia-Yi 621, Taiwan Received 22 April 1997; accepted 1 October 1998 Abstract In this article, we examine empirically whether fractional cointegration exists in the system of seven exchange rates and this form of cointegration is associated with long memory. The results indicate that fractional cointegration in exchange rates is a feature for only the 1980–1984 sample, not for the entire post-1973 float, the subperiod before 1980, and the sample after 1984. The results show a significant long memory, mean-reverting behavior in equilibrium errors for the subperiod 1980–1984. The results also suggest that the exchange rates are cointegrated in the usual way for the 1985–1992 sample data. The current findings suggest a conjecture that the fractional cointegration feature of exchange rates, if exists, could be chang- ing across varying time spans.  1999 Elsevier Science Inc. All rights reserved. JEL classification: F31 Keywords: Foreign exchange rates; Fractional cointegration; Long memory 1. Introduction One of the observed empirical regularities in the finance literature is that the dynamics of individual nominal exchange rate series in the post-Bretton Woods era are well char- acterized by a time-series model with one unit root, or more closely, by a martingale. Using Johansen’s (1988) multivariate cointegration test, Baillie and Bollerslev (1989), however, find the existence of cointegration among a set of seven exchange rates, sug- gesting that the set of exchange rates possess a long-run equilibrium relationship. The * Corresponding author. Tel.: 717-532-1683; fax: 717-530-4067. E-mail address: mspan@wharf.ship.edu (M.-S. Pan) 1059-0560/99/$ – see front matter  1999 Elsevier Science Inc. All rights reserved. PII:S1059-0560(99)00027-1