Cointegration Modeling of Expected Exchange Rates

An enduring problem in international finance is forward premium bias. Forward rates consistently provide biased estimates of future exchange rate movements. Some attack the rationality assumption for the foreign exchange market, claiming the forward premium may reflect irrational expectations of market participants. Our work re-addresses this evidence. In particular, our paper studies the process by which exchange rate expectations adjust. If foreign exchange market participants are rational, exchange rate forecasts of those agents should be matched to the subsequent realization of the exchange rate, i.e., rational forecasts of a time series and the observed series should be cointegrated. We apply this insight to multiple exchange rate series and a corresponding set of market expectations of future values of the exchange rate series. We build a cointegration (and associated error-correction) model of actual and expected exchange rates for seven exchange rates, using weekly expectations data from Money Market Services, International for the 1986Ü1997 period. We picture the connections between actual and expected exchange rates. And, the error-correction model estimates provide an interesting picture of the dynamic process by which exchange rate expectations adjust to movements in exchange rates and realized forecasting errors. We contrast our findings with other expectations-adjustment models. Our paper has several distinctive features. First, we do not assume symmetric adjustment of cointegration errors, but instead use threshold cointegration methods. We get strong evidence of cointegration between the exchange rate series and the expected rates series. Second, in pretesting individual series for I(1) properties, we apply the Enders-Granger (1998) momentum threshold autoregressive model. Here, the unit-root test admits the possibility of asymmetric adjustments to deviations from unit-root behavior. When the forecast error is positive, we may observe a different autoregressive coefficient than when negative. While unit-root tests cannot reject the null hypothesis of unit roots, we find clear evidence of asymmetric adjustments in about 25 per cent of the cases. Third, our sample period, 1986Ü1997, has witnessed significant shifts in institutional exchange rate arrangements, such as Great Britain's entry and exit from the Exchange Rate Mechanism. Structural shifts are important to the economics and econometrics of our investigation. Because structural shifts can compromise standard cointegration tests, we apply the test methods developed by Gregory and Hansen (1996). Despite evidence of structural shifts, the cointegration evidence remains very compelling. Fourth, in work still underway, we are investigating several issues raised by our results. We are probing the extent to which structural shifts may masquerade as threshold behavior.