Non-Linear Structures and Exchange Rate Dynamics Identification

Federico Ravenna - New York University

In the past twenty years one of the major unsolved challenges to empirical and theoretical research in economics has been explaining the post-Bretton Woods behavior of the main foreign exchange rates (FX).

More recently the empirical evidence about international financial markets' behavior has provided a new wealth of findings. The new FX market Microstructure research established itself as a macroeconomic approach to institutional issues which macroeconomics cannot ignore when trying to explain FX rates movements. Much of the recent breakthrough was possible thanks to the availability of high frequency data.

The outburst of empirical results coincided with a very rich development of FX models, and with a renewed interest in both the existence of non-linearities from the statistical point of view, and the devising of theoretical stochastic and deterministic non-linear models.

The availability of a very high frequency data set made possible the reliable use of computationally heavy statistical techniques employed in the physical sciences. Such techniques require a minimum of some thousands of data points to provide reliable results, and a computing power which was available to the general public only in late seventies.

The first article introduces Rescaling analysis and provides original statistical results designed to establish the presence of long memory in FX rate daily time series. There has been lately much empirical and theoretical work on long memory processes, and our results show that the main currencies floating exchange rates time series display a remarkable degree of positive long term dependence. Rescaled Range behavior variability at different frequencies (from twenty minutes to eight hours) is evidence that fractional Gaussian noise processes are not appropriate to describe FX returns, as proposed in the literature. Long term dependence is higher as the sampling frequency gets lower. On the contrary, fractionally integrated processes appear suitable to model FX volatility. In the second part of the paper an original approach, Diffusion analysis, is used to identify exchange rate dynamics over the intra-day horizon. We take into account seasonal heteroscedasticity through a time scale transformation. The analysis is of great interest for several reasons. It supplies empirical evidence of structure not only in the volatility, but in the mean of the process, in contrast with previous studies. The fundamental result is that FX rate returns dynamics is partly explained by a deterministic process, and for a larger part by random noise. Moreover, the random noise has a higher frequency, so that the deterministic bias can be identified more clearly when FX rates are observed at larger time-intervals.

Scheduled for Session 3.2 Time Series - II