Integer and fractional cointegration of exchange rates : the Portuguese case

Abstract

The purchasing power parity (PPP) hypothesis is examined by means of residual-based cointegration tests. A generalized concept of cointegration is used. that is, fractional cointegration. This method aims to be a complement of the Engle-Granger procedure, whose test for cointegration assumes that the equilibrium error is strictly I(1) (nonstationary) or I(0) (stationary). It is known and it will be shown in this work through Monte Carlo simulation, that the unit root tests turn out to perform poorly against long memory alternatives. To perform a test for fractional cointegration, empirical distributions are obtained through a Monte Carlo experiment. This means that the PPP hypothesis is not con…ned to the value of the fractional estimate. By allowing equilibrium errors to follow a fractional integrated process, the fractional cointegration analysis capture a wider range of stationary and level reversion behaviour. This ‡exibility is important to a proper evaluation of the exchange rate dynamics. Two bilateral relations are studied, between Portugal as the home country and the United Kingdom and the United States of America. We also consider the use of structural change tests, since a long range of time is covered by the data, with periods that were a¤ected by di¤erent policy regimes in these countries. For this century, the empirical results provide some support for the PPP between Portugal and the two other countries. Deviations from equilibrium can be modelled by a level-reverting fractionally integrated process. Although short run deviations can occur, the results support the PPP as a long run phenomenon.