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I derive a dynamic version of the Dornbusch "overshooting" model in which real yields and inflation vary stochastically, and the exchange rate (FX) delivers UIRP in expectations. Tests using the model provide support for the UIRP proposition. Simulations show that the "disconnect" of FX rates from fundamentals as well as their very high volatility is a necessary consequence of UIRP when real yields are autocorrelated. I also show that FX rates display some predictability as required by thedoi:10.2139/ssrn.2401873 fatcat:js6jijqebrf7dogcbbysmcaemu