Using the Kalman ®lter, we obtain maximum likelihood estimates of a permanent±transitory components model for log spot and forward dollar prices of the pound, the franc, and the yen. This simple parametric model is useful in understanding why the forward rate may be an unbiased predictor of the future spot rate even though an increase in the forward premium predicts a dollar appreciation. Our estimates of the expected excess return on short-term dollar-denominated assets are persistent and reasonable in magnitude. They also exhibit sign¯uctuations and negative covariance with the estimated expected depreciation.unbiased predictor of the future spot rate while at the same time, the forward premium predicts the future depreciation with the wrong negative sign.The`levels' regressions were originally ®tted by researchers such as Bilson (1981), Cornell (1977), and Frankel (1981, who were interested in testing the ecient market hypothesis Ð that the forward rate is the optimal predictor of the future spot rate under risk neutrality. 3 Although these early studies employed standard least-squares procedures, we demonstrate below that the hypothesis that the slope coecient is 1 cannot be rejected when appropriate cointegrating regression estimation is employed. But when the cointegrating regressions are transformed by subtracting the current log spot rate from both the regressor and the regressand, the resulting slope coecient in regressions of the future depreciation on the forward premium are typically negative. This anomalous result was ®rst reported in the literature by Cumby and Obstfeld (1984) and Fama (1984). Fama attributes these ®ndings to the presence of a time-varying expected excess currency return that is negatively correlated with and is more volatile than the expected depreciation. 4 We show that these two features of the data can be accounted for by a simple parametric permanent±transitory components model for spot and forward exchange rates. The twocomponent speci®cation draws its motivation from Mussa's (1982) sticky-price model in which the exchange rate is represented by a fundamental value and a transient disequilibrium term. We model the fundamental value by a stochastic trend that evolves as a driftless random walk that is common to both spot and forward rates. The temporary part, which measures the short-run disequilibrium of the economy, is represented by a vector ARMA process. The model is estimated by maximum-likelihood using the Kalman ®lter for monthly observations on bilateral exchange rates between the US dollar and the pound, the French franc, and the yen from 1976:1 to 1992:8. In addition to commonly employed diagnostic tests on residuals, we also gauge the adequacy of the model by its ability to account for various functions of the data that are not explicitly imposed in estimation. The accepted model is then used to generate estimates of the unobserved expected currency return and the expected depreciation. 5 The resulting estimates of the excess return are reasonable in magnitude, pe...
Using the Kalman filter, we obtain maximum likelihood estimates of a permanent–transitory components model for log spot and forward dollar prices of the pound, the franc, and the yen. This simple parametric model is useful in understanding why the forward rate may be an unbiased predictor of the future spot rate even though an increase in the forward premium predicts a dollar appreciation. Our estimates of the expected excess return on short‐term dollar‐denominated assets are persistent and reasonable in magnitude. They also exhibit sign fluctuations and negative covariance with the estimated expected depreciation. © 1997 John Wiley & Sons, Ltd.
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