Sterling’s Relationship with the Deutschmark: A Probabilistic Reduction Approach

Two of the stylized facts which have emerged from the empirical literature on foreign exchange markets are non-linear temporal dependence and leptokurtosis in the distribution of exchange rate returns. Several studies have found that large and small changes in returns are ‘clustered’ together over time, and that their distribution is bell-shaped, symmetric and fat-tailed (see, e.g., Friedman and Vandersteel, 1982; Diebold, 1988; Diebold and Nerlove, 1989; Bollerslev, 1987; Baillie and Bollerslev, 1989; Hsieh, 1988, 1989a, 1989b). These features of the data are normally thought to be captured by ARCH/GARCH models (see, e.g., a recent paper by Pesaran and Robinson, 1993; see also chapter 2). In this chapter we adopt an alternative methodology to examine the behaviour of the DM sterling exchange rate. Our analysis can be seen as a probabilistic reduction approach, which is based on the probabilistic structure of the observable stochastic process of interest rather than the unobservable error terms; this leads us to estimate a more general statistical model, which provides a statistically adequate representation of the probabilistic information found in the data.