Threshold-autoregressive, median-unbiased, and cointegration tests of purchasing power parity

We use Dickey–Fuller tests, threshold autoregressive unit-root tests, median unbiased estimators, and cointegration tests for I(1) and I(2) variables to examine the validity of Purchasing Power Parity (PPP). The within-sample tests generally lead to the rejection of long-run PPP. Long-term out-of-sample forecasts assuming various forms of long-run PPP are not especially better than those assuming that real rates contain a unit-root. We show that no one method emerges as the ‘best’ in the sense that it provides the smallest out-of-sample forecast errors.