A Fractional Cointegration Analysis of Purchasing Power Parity

A generalized notion of cointegration, called fractional cointegration, is introduced to examine the long-run purchasing power parity (PPP) hypothesis. By allowing deviations from equilibrium to follow a fractionally integrated process, the fractional cointegration analysis can capture a wider range of mean-reversion behavior than standard cointegration analyses. This gain is flexibility in modeling subtle mean-reverting dynamics is found to be important for a proper evaluation of long-run PPP. Empirical results based on historical data for the 1914–1989 period show that PPP reversion exists and can be characterized by a fractionally integrated process in three out of five countries studied. The results support PPP as a long-run phenomenon, though significant short-run deviations from PPP can exist.