Autori
Guarda, Paolo
Salmon, Mark

Titolo
On the detection of nonlinearity in foreign exchange data
Periodico
European University Institute of Badia Fiesolana (Fi). Department of Economics - Working papers
Anno: 1995 - Fascicolo: 36 - Pagina iniziale: 1 - Pagina finale: 38

The analysis in this paper is based on the common observation that many nonlinear dynamic processes may in fact be approximately linear over wide ranges of the economically relevant state space and hence over long periods of time. Only when state variables move into particular regions of the phase space may nonlinear reactions become apparent and perhaps only then, statistically detectable. Standard unconditional methods of testing linearity do not seem to have recognised the potential importance of this observation, that a given sample may not be particularly informative regarding nonlinearity since it may be only occasionally important and not uniformly represented throughout a given observation period. This, we believe, could be one reason why evidence for nonlinearity in the conditional mean has been difficult to find in economic time series. We argue that an explicitly conditional approach to testing linearity in which the metric used in inference incorporates any potential ancillary information reflecting the statistical curvature of the underlying data generation process may provide a more suitable framework for the detection of nonlinearity in economic time series. We first put forward theoretical arguments for adopting a conditional approach to testing linearity and discuss the difficulties in following this suggestion through in applied work. Then, in an attempt to explicitly investigate the periodic importance of nonlinearity, we apply a set of linearity tests recursively to both monthly and weekly observations on the US Dollar/UK Pound Sterling spot exchange rate over the period 1973-1990. Our main interest lies in the detection of nonlinearity in the first moment of the data but we are also concerned that misspecification of the first moment may lead to error specifications that imply ARCH type processes and so also consider tests for conditional heteroskedasticity. The different tests we employ provide different indications of nonlinearity over different levels of temporal aggregation and under different transformations of the data but the overwhelming conclusion is clearly in favour of the periodic but not the continuous importance of nonlinear effects in the first moment of the data. The weekly series display considerably more evidence of nonlinearity than the monthly data and GARCH(1,1) residuals show the least evidence of nonlinearity both in first moment and naturally in the second moment, with random walk residuals clearly indicating model misspecification. Those periods in which the recursive tests indicate nonlinearity are briefly compared with an historical event analysis in an attempt to identify potential behavioural causes for the deviations from linearity. Some of these episodes appear to be associated with public reversals of government policy and intervention in the market for foreign exchange but others would seem to have no obvious economic cause. We also find little association between periods of first moment nonlinearity and periods of high volatility. Exploring such evidence for periodic nonlinear effects in the first moment of financial data further might aid the development of improved models of behaviour in financial markets.



Testo completo: http://hdl.handle.net/1814/561

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