Each country's exposure to disaster risk varies over time according to a mean-reverting process
Thus, one way of testing the PPP is to test for the mean-reverting property of the nominal exchange rate that incorporates changes in relative prices into its mean-reverting process, that is, testing for stationarity of the real exchange rate.
Application of this new test by most recent studies reveals that the new test supports the PPP more often than the standard ADF test implying that the mean-reverting process of real exchange rates follows a non-linear path.
These results support the two-regime TAR specification for all five countries--a stationary mean-reverting process for interest rate differentials outside the bands and a unit root process inside the bands.
For four of the five economies, the interest rate differential follows a mean-reverting process only about 15% of the time, while for Japan 30% of the monthly observations mean revert.
The first model is a one-factor model in which the log of the spot price of the commodity is assumed to follow a mean-reverting process.
In the two-factor model, the convenience yield, denoted by [Delta] to distinguish it from the constant convenience yield in the basic model, is assumed to be stochastic and to follow a mean-reverting process.