The high persistence of both PPP deviations and the proxy variables for the equilibrium real rate might create a problem of spurious coefficient significance within recently applied nonlinear models. To illustrate we consider the real Dollar-Sterling exchange rate over the period 1871â1994. A nonlinear ESTAR process with a time-varying equilibrium seems to parsimoniously fit the data. Appropriate significance levels are obtained using the wild bootstrap method to adequately capture the conditional heteroskedasticity in the data. Our results provide further evidence for the nonlinear model and the implied speed of adjustment is found to be substantially faster than previously reported in the literature.