  An expanding literature articulates the view that Taylor rules are helpful in
predicting exchange rates. In a changing world however, Taylor rule parameters
may be subject to structural instabilities, for example during the Global
Financial Crisis. This paper forecasts exchange rates using such Taylor rules
with Time Varying Parameters (TVP) estimated by Bayesian methods. In core
out-of-sample results, we improve upon a random walk benchmark for at least
half, and for as many as eight out of ten, of the currencies considered. This
contrasts with a constant parameter Taylor rule model that yields a more
limited improvement upon the benchmark. In further results, Purchasing Power
Parity and Uncovered Interest Rate Parity TVP models beat a random walk
benchmark, implying our methods have some generality in exchange rate
prediction.
