A fractional cointegration test of purchasing power parity: the case of selected members of OPEC

In recent years, analysts have used cointegration tests in determining whether the residuals of the purchasing power parity (PPP) model are mean-reverting. Cointegration methods, however, rest on the binary selection of the series as either stationary or integrated of degree one. This approach excludes a class of long-memory stochastic processes with a fractional differencing parameter which also have mean-reverting characteristics. Fractional cointegration method tests the mean-reverting property of a series which is based on this class of stochastic processes. This paper uses cointegration and fractional cointegration methods in determining the mean-reverting properties of the parallel market exchange rates for several members of the Organization of Petroleum Producing Countries. The Geweke and Porter-Hudak (GPH) test results suggest that the PPP models for Algeria, Ecuador, Saudi Arabia and Venezuela are fractionally cointegrated. Moreover, according to the Augmented Dickey-Fuller (ADF) test, the PPP models for all countries under study, appear not to have a cointegrating vector.