Nonstationarity in the levels of spot exchange rates and domestic and foreign price indices makes the use of conventional tests of the absolute version of purchasing power parity (PPP) inappropriate. If PPP is true, inter-country commodity arbitrage ensures that deviations from a linear combination of spot exchange rates and domestic and foreign price levels should be stationary. Under these conditions, exchange rates and price levels should form a cointegrated system. We find the null hypothesis of no cointegration cannot be rejected for all five countries, thus violating the long-run absolute version of PPP.

Band spectral regression with both deterministic and stochastic trends is considered. It is shown that trend removal by regression in the time domain prior to band spectral regression can lead to biased and inconsistent estimates in models with frequency dependent coefficients. Both semiparametric and nonparametric regression formulations are considered, the latter including general systems of two-sided distributed lags such as those arising in lead and lag regressions. The bias problem arises through omitted variables and is avoided by careful specification of the regression equation. Trend removal in the frequency domain is shown to be a convenient option in practice. An asymptotic theory is developed and the two cases of stationary data and cointegrated nonstationary data are compared. In the latter case, a levels and differences regression formulation is shown to be useful in estimating the frequency response function at nonzero as well as zero frequencies.