Econometric modelling of nonlinearity and nonstationarity in the foreign exchange market

Hillman, Robert John Timothy (1998) Econometric modelling of nonlinearity and nonstationarity in the foreign exchange market. University of Southampton, Doctoral Thesis.

Abstract

This thesis comprises of four major papers concerning the econometric modelling of the foreign exchange market. Taken together the papers strongly suggest that a new paradigm for the study of financial markets is emerging, based on transient statistical properties and computational agent based models. I propose that consideration of the latter are critical if we are to meaningfully exploit the new territory offered by the current glut of nonlinearity and nonstationarity tests and models. I demonstrate how statistical properties are variably detectable through time, and discuss what this means for testing and modelling techniques.

In response to the existing and rather negative nonlinear forecastability literature, I explore the idea that as nonlinearity is only occasionally detectable, it follows that nonlinear forecastability ought to be transient as well. I show that whilst over large samples we might not detect any forecast improvements, there are indeed sub-periods in which both significant point and direction forecastability can be uncovered. By applying concepts developed for the stability analysis of nonlinear dynamical systems I provide evidence that the occurrence of such periods of predictability may itself be predictable.

Building on this idea I introduce a novel statistical modelling framework which combines aspects of mixture modelling and computational learning. I thoroughly present the model in context with other more familiar econometric models, and add to the literature on this model by providing evidence on the ability of the model to recover conditional statistical properties. In common with many nonlinear models the model I propose presents difficult inference problems. In fact the central problem of determining the number of mixture components is as yet unsolved. I add to the mixture inference literature by thoroughly surveying the existing proposals, and making a number of novel suggestions for improved inference methods. I explore the practical performance of such inference methods via a number of simulation studies. A number of applications of the model demonstrate it is able to replicate many of the stylized facts of exchange rate data, and provide good forecasts out-of-sample.

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