A number of tests for non-linear dependence in time series are presented and implemented on a set of 10 daily sterling exchange rates covering the entire postBrettonÐ Woods era until the present day. Irrefutable evidence of non-linearity is shown in many of the series, but most of this dependence can apparently be explained by reference to the GARCH family of models. It is suggested that the literature in this area has reached an impasse, with the presence of ARCH e ects clearly demonstrated in a large number of papers, but with the tests for non-linearity which are currently available being unable to classify any additional non-linear structure.
I . I N T R O D U C T I O NTesting for non-linear dependence has become an important area of research in ® nancial econometrics because of its profound implications for model adequacy, market e ciency, and predictability. If we ® nd evidence of non-linearity in ® nancial time series, this suggests that, at least in the short term, forecasts may be improved by switching from a linear to a non-linear modelling strategy, and furthermore, the tests may be viewed as general tests of model adequacy for linear models in the sense that if there is still dependence in the residuals of a linear model (of an albeit more complex form), the original linear models can no longer be viewed as an accurate representation of the data (Hinich and Patterson, 1989). Evidence of non-linear dependence in market returns may also cast doubts on the informational e ciency of ® nancial markets, since in theory (at least) it may be possible to devise a trading strategy which systematically generates positive returns with a probability considerably in excess of one half. It is also of interest to consider whether there is any di erence in general between the extent of non-linearity in widely traded currencies, such as the US dollar and Deutschmark relative to those which are infrequently traded or traded in considerably smaller volumes, such as the Austrian schilling or Danish krone. We may expect that, a priori those currencies which are frequently traded should more closely follow the random walk model of weakly e cient markets (Fama, 1970), since their closer and more detailed inspection by traders and analysts should ensure that autoregressive dependencies of any form (i.e. linear or non-linear) are quickly arbitraged away.The structure of the remainder of the paper is as follows. Section II gives a brief survey of the ® ndings of other studies which have investigated the use of the tests discussed here. Section III introduces and explores the data to be used, and Section IV gives a theoretical treatment of a number of tests for non-linear dependence in time series. The results generated thereof are described in Section V. Section VI o ers an analysis of the results and concludes.
I I . A S U M MA R Y O F P R EV I O U S R E S EA R C H I N T H E A R E ASince the techniques explored in this paper were popularized by Brock (1986), Hsieh (1989b and co-workers, there has been an explosion of interest...