Regimes and Nonlinearity in Exchange Rate Data

Robert J. T. Hillman
University of Southampton and European University Institute
Hillman@datacomm.iue.it

Mark Salmon
European University Institute
Salmon@datacomm.iue.it

Abstract

Recent attempts to exploit and characterize nonlinear structure in financial data that is suggested by a wide range of tests against linearity, have not been particularly successful. Although often nonlinear structure is detected in the residuals of a linear model, the use of flexible estimation methods such as kernel estimators, nearest-neighbour methods or neural networks rarely gives good evidence of exploitable nonlinear structure, as displayed for example in the out-of-sample forecasting abilities of these methods. In this paper we entertain the idea that nonlinearities can be time varying and the ability to outperform simple benchmarks such as a random walk, is as a result time varying. We first show using a recently suggested test for neglected non-linearity based on neural network methods, that the inference one would make regarding the degree of nonlinearity in daily exchange rate data is highly sensitive to the sample examined. Next we introduce a neural network based modelling method called gated networks. This method which is based on mixture modelling allows us to divide the input space up nonlinearily and to estimate each division of the space (regime). Although simple neural networks can in principle estimate a global function that produces a number of regimes with different dynamic properties, in practise the estimation is liable to be difficult. The gated network method allows us to consider the presence of different regimes with different properties and allows us to divide the data probabalistically into these regimes. The Hamilton regime-switching model is shown to be a special case of this more general structure. We show that using this technique we can identify periods of more or less nonlinearity and that our ability to forecast is improved upon as compared to the estimation of a single (1-regime) global model.