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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.
Phillips, Peter C.B. and McFarland, James W., "Forward Exchange Market Unbiasedness: The Case of the Australian Dollar Since 1984" (1993). Cowles Foundation Discussion Papers. 1298.