Testing Forward Exchange Rate Unbiasedness Efficiently: A Semiparametric Approach

We apply semiparametric efficient estimation procedures for a seemingly unrelated regression model where the multivariate error density is elliptically symmetric to study the efficiency of the foreign exchange market. We consider both cointegrating regressions and standard stationary regressions. The elliptical symmetry assumption allows us to avoid the curse of dimensionality problem that typically arises in multivariate semiparametric estimation procedures, because the multivariate elliptically symmetric density function can be written as a function of a scalar transformation of the observed multivariate data. We test the unbiasedness hypothesis on both weekly and daily exchange rate data and strongly reject unbiasedness at the weekly horizon, but fail to reject the unbiasedness hypothesis on the daily data. Estimates of the semiparametric procedure in some cases differ substantially from traditional OLS estimates.

[1]  Forward exchange market unbiasedness: the case of the Australian dollar since 1984 , 1997 .

[2]  Douglas J. Hodgson.  Adaptive Estimation of Cointegrated Models: Simulation Evidence and an Application to the Forward Exchange Market , 1999 .

[3]  Charles F. Manski,et al.  Monte Carlo evidence on adaptive maximum likelihood estimation of a regression , 1987 .

[4]  Craig S. Hakkio,et al.  Market efficiency and cointegration: an application to the sterling and deutschemark exchange markets , 1989 .

[5]  E. Fama,et al.  Forward and spot exchange rates , 1984 .

[6]  John F. O. Bilson,et al.  The "Speculative Efficiency" Hypothesis , 1980 .

[7]  Peter C. B. Phillips,et al.  Statistical Inference in Instrumental Variables Regression with I(1) Processes , 1990 .

[8]  Rudolf Beran,et al.  Testing for Ellipsoidal Symmetry of a Multivariate Density , 1979 .

[9]  W. Stute,et al.  Nonparametric Estimation of Elliptically Contoured Densities , 1991 .

[10]  Scott W. Barnhart,et al.  Testing the Unbiased Forward Rate Hypothesis: Evidence on Unit Roots, Co-Integration, and Stochastic Coefficients , 1991, Journal of Financial and Quantitative Analysis.

[11]  Yanqin Fan.  Testing the Goodness of Fit of a Parametric Density Function by Kernel Method , 1994, Econometric Theory.

[12]  P. J. Green,et al.  Density Estimation for Statistics and Data Analysis , 1987 .

[13]  P. Phillips.  Robust Nonstationary Regression , 1995, Econometric Theory.

[14]  Oliver Linton,et al.  Testing the capital asset pricing model efficiently under elliptical symmetry: a semiparametric approach , 2002 .

[15]  M. Steel,et al.  Modeling and Inference with υ-Spherical Distributions , 1995 .

[16]  Ross Levine.  An empirical inquiry into the nature of the forward exchange rate bias , 1991 .

[17]  B. Mccallum,et al.  A Reconsideration of the Uncovered Interest Parity Relationship , 1992 .

[18]  Anton Schick,et al.  A note on the construction of asymptotically linear estimators , 1987 .

[19]  P. Jeganathan.  Some Aspects of Asymptotic Theory with Applications to Time Series Models , 1995, Econometric Theory.

[20]  Craig S. Hakkio.  Expectations and the Forward Exchange Rate , 1981 .

[21]  Patrick Minford,et al.  The Foreign Exchange Market: Theory and Econometric Evidence , 1990 .

[22]  H. White.  Maximum Likelihood Estimation of Misspecified Models , 1982 .

[23]  R. Muirhead.  Aspects of Multivariate Statistical Theory , 1982, Wiley Series in Probability and Statistics.

[24]  Douglas J. Hodgson.  Adaptive Estimation of Cointegrating Regressions with ARMA Errors , 1998 .

[25]  Douglas J. Hodgson.  Unconditional pseudo-maximum likelihood and adaptive estimation in the presence of conditional heterogeneity of unknown form , 2000 .

[26]  Tim Bollerslev,et al.  The long memory of the forward premium , 1994 .

[27]  P. C. McMahon,et al.  Interpreting Econometric Evidence on Efficiency in the Foreign Exchange Market , 1984 .

[28]  R. Hogg,et al.  On adaptive estimation , 1984 .

[29]  C. J. Stone,et al.  Adaptive Maximum Likelihood Estimators of a Location Parameter , 1975 .

[30]  S. Johansen.  STATISTICAL ANALYSIS OF COINTEGRATION VECTORS , 1988 .

[31]  A. Zellner.  An Efficient Method of Estimating Seemingly Unrelated Regressions and Tests for Aggregation Bias , 1962 .

[32]  W. Härdle,et al.  APPLIED NONPARAMETRIC METHODS , 1992 .

[33]  Eugene F. Schuster,et al.  Incorporating support constraints into nonparametric estimators of densities , 1985 .

[34]  K. Mardia.  Measures of multivariate skewness and kurtosis with applications , 1970 .

[35]  Ross Levine.  The pricing of forward exchange rates , 1989 .

[36]  Douglas G. Steigerwald,et al.  Adaptive estimation in time series regression models , 1992 .

[37]  G. Chamberlain.  A characterization of the distributions that imply mean—Variance utility functions☆ , 1983 .

[38]  Douglas J. Hodgson.  ADAPTIVE ESTIMATION OF ERROR CORRECTION MODELS , 1998, Econometric Theory.

[39]  L. Hansen,et al.  Forward Exchange Rates as Optimal Predictors of Future Spot Rates: An Econometric Analysis , 1980, Journal of Political Economy.

[40]  P. C. McMahon,et al.  Robust tests of forward exchange market efficiency with empirical evidence from the 1920s , 1996 .

[41]  P. Phillips,et al.  Forward exchange market unbiasedness: the case of the Australian dollar since 1984 , 1997 .

[42]  O. Linton,et al.  Testing the Capital Asset Pricing Model Efficiently Under Elliptical Symmetry: A Semiparametric Approach , 2000 .

[43]  The impact of data errors on measurement of the foreign exchange risk premium , 1989 .

[44]  Jens-Peter Kreiss.  On Adaptive Estimation in Stationary ARMA Processes , 1987 .

[45]  Oliver Linton,et al.  SECOND ORDER APPROXIMATION IN THE PARTIALLY LINEAR REGRESSION MODEL , 1995 .

[46]  C. Engel,et al.  The Forward Discount Anomaly and the Risk Premium: A Survey of Recent Evidence , 1995 .

[47]  Richard T. Baillie,et al.  Testing rational expectations and efficiency in the foreign exchange market , 1983 .

[48]  Alex Maynard,et al.  Rethinking an old empirical puzzle: econometric evidence on the forward discount anomaly , 2001 .

[49]  R. Baillie,et al.  Common Stochastic Trends in a System of Exchange Rates , 1989 .

[50]  Martin D.D. Evans,et al.  Do Long-Term Swings in the Dollar Affect Estimates of the Risk Premia? , 1995 .