This paper provides a robust statistical approach to testing the unbiasedness hypothesis in forward exchange market efficiency studies. The methods we use allow us to work explicitly with levels rather than differenced data. They are statistically robust to data distributions with heavy tails, and they can be applied to data sets where the frequency of observation and the futures maturity do not coincide. In addition, our methods allow for stochastic trend nonstationarity and general forms of serial dependence. The methods are applied to daily data of spot exchange rates and forward exchange rates during the 1920’s, which marked the first episode of a broadly general floating exchange rate system. The tail behavior of the data is analyzed using an adaptive data-based method for estimating the tail slope of the density. The results confirm the need for the use of robust regression methods. We find cointegration between the forward rate and spot rate for the four currencies we consider (the Belgian and French francs, the Italian lira and the US dollar, all measured against the British pound), we find support for a stationary risk premium in the case of the Belgian franc, the Italian lira and the US dollar, and we find support for the simple market efficiency hypothesis (where the forward rate is an unbiased predictor of the future spot rate and there is a zero mean risk premium) in the case of the US dollar.
This paper implements a new statistical approach to robust regression with nonstationary time series. The methods are presently under theoretical development in other work, and are briefly exposited here. They allow us to perform regressions in levels with nonstationary time series data, they accommodate data distributions with heavy tails and they permit serial dependence and temporal heterogeneity of unknown form in the equation errors. With these features the methods are well suited to applications with frequently sampled exchange rate data, which generally display all of these empirical characteristics. Our application is to daily data on spot and forward exchange rates between the Australian and US dollars over the period 1984-1991 following the deregulation of the Australian foreign exchange market. We find big differences between the robust and the non-robust regression outcomes and in the associated statistical tests of the hypothesis that the forward rate is an unbiased predictor of the future spot rate. The robust regression tests reject the unbiasedness hypothesis but still give the forward rate an important role as a predictor of the future spot rate.