Purchasing power parity: Evidence of long memory processes and fractional integration

The Purchasing Power Parity (PPP) theory, which serves as a key to the determination of several models of exchange rates, suggests a long-term relationship between exchange rates and relative prices. It states that the price levels in all the countries are the same when measured in terms of a single currency. The purpose of this study is to model the behavior of the exchange rates of five partner countries of Tunisia, namely, (Germany, the United States, France, Italy, the UK, Morocco and Libya) relative to its fundamentals over the period 1990-1999. Beyond the traditional linear cointegration, we use the approaches based on fractional cointegration. We are trying to discriminate between the adjustment dynamics with long memory (but linear) and a dynamics of a short memory (nonlinear). Given the important role of the exchange rates in the successful experience of open economies, we are interested, in this work, in analyzing the dynamics of the exchange rates in the long run. The econometric results obtained through the GPH tests, make us consider the PPP as an event in the long run if significant short-term deviations from the PPP cannot exist. Therefore, the analysis of the fractional cointegration makes the deviations, regarding equilibrium, follow a slightly integrated process and therefore capture a much wider group of research parity or mean-reverting behavior.