Joint Tests for Non-linearity and Long Memory: The Case of Purchasing Power Parity

Abstract

A pervasive finding of unit roots in macroeconomic data often runs counter to intuition regarding the stochastic nature of the process under consideration. Two econometric techniques have been utilized in an attempt to resolve the finding of unit roots, namely long memory and models that depart from linearity. While the use of long memory and stochastic regime switching models have developed almost independently of each other, it is now clear that the two modeling techniques can be intimately linked. In particular, both modeling techniques have been used in isolation to study the dynamics of the real exchange rate. To determine the importance of each technique in this context, I employ a testing and estimation procedure that allows one to jointly test for long memory and non-linearity (regime switching behavior) of the STAR variety. I find that there is substantial evidence of non-linear behavior for the real exchange rate for many developing and European countries, with little evidence for ESTAR non-linearity for countries outside the European continent including Japan and Canada. In cases where non-linearity is found, I also find significant evidence of long memory for the majority of the countries in my sample. Thus, long memory and non-linearity can also be viewed as compliments rather than substitutes. The linear model in isolation appears to be inadequate for breaking down the paradox known as the PPP puzzle. On the other hand, a combination of long memory and non-linearity may be a promising research avenue for pursuing an answer to the paradox.