Structural exchange rate models explain only a small part of the movements in dollar exchange rate. Recent empirical work has focused on the failure to account for nonlinearities in the data generating mechanism, as an explanation of this bad performance. Here two bivariate threshold autoregressive models for the spot and forward exchange rates are considered. In the first model the regimes are determined by the log difference of the two rates; in the second one the regimes are driven by the forward spot no-arbitrage condition. These processes are able to capture the ‘swing’ behaviour observed in the exchange rate market. Finally the forecasting ability of the models for the dollar/DM exchange rate is evaluated by stochastic simulation.

Abstract This paper examines,the use of proxies (or reference variables) for the true factors in the ,Arbitrage Pricing Theory ,(APT). It generalises ,the work ,of Reisman(1992) and Shanken(1992) and shows that, when there are more reference variables than the true factors, the APT still holds. The possibility of fewer reference variables than the true factors is also considered, but the APT is not shown to hold, in the same sense, for this case. This work builds on an earlier paper by Ingersoll(1984), and our propositions can be thought of as specialisations of his Theorems 1 and 6. Our work,does not use the mathematics,of Hilbert and,Banach spaces,(as used by Reisman(1992)) and, thus, is open to a much wider audience. Deriving the APT when the Number of Factors is Unknown

Most non-linear techniques give good in-sample fits to exchange rate data but are usually outperformed by random walks or random walks with drift when used for out-of-sample forecasting. In the case of regime-switching models it is possible to understand why forecasts based on the true model can have higher mean squared error than those of a random walk or random walk with drift. In this paper we provide some analytical results for the case of a simple switching model, the segmented trend model. It requires only a small misclassification, when forecasting which regime the world will be in, to lose any advantage from knowing the correct model specification. To illustrate this we discuss some results for the DM/dollar exchange rate. We conjecture that the forecasting result is more general and describes limitations to the use of switching models for forecasting. This result has two implications. First, it questions the leading role of the random walk hypothesis for the spot exchange rate. Second, it suggests that the mean square error is not an appropriate way to evaluate forecast performance for non-linear models. Copyright (C) 1999 John Wiley & Sons, Ltd.