The Chaotic Behavior of Foreign Exchange Rates

By Aczel, Amir D.; Josephy, Norman. | American Economist, Fall 1991 | Go to article overview

The Chaotic Behavior of Foreign Exchange Rates


Aczel, Amir D., Josephy, Norman., American Economist


1. Introduction

In the early 1970s, many economists believed that the floating currency exchange rates that were to characterize the post-Bretton Woods period could be well explained by the purchasing power parity theory [see Bilson and Marston, 1984]. As empirical data soon demonstrated, however, the theory was not sufficient to explain the large fluctuations in exchange rates, and the latter

part of the decade saw the development of several new economic theories of exchange rate determination. Among these are the theories of Dornbusch (1976), Mussa (1976), and Frenkel (1976). The exchange rate was no longer viewed merely as an equalizer of relative inflation rates as suggested by the PPP theory. Rather, the new theories suggested that a country's exchange rate was the market price of local money in the world market. Among the determinants of this price a key element was deemed to be the supply of and the demand for the local currency. The theories also accounted for the effects of other economic variables, and rational expectations. An example of an economic model based on this approach to exchange rate determination is Woo (1985). Similar paper used vector autoregression (VAR), a time series technique that analyzes the evolution of exchange rates in conjunction with other economic variables [see, for example, Branson, 1984]. The technique, which is equivalent to simultaneous equations [Zellner and Palm, 1974], requires the specification of a particular model for exchange rates. Consistent with the view of the exchange rate as the market price of an asset traded in an efficient market, the VAR approach has not met with much success in explaining and predicting exchange rate movements [see Diebold, 1988].

In this paper, we follow a new approach to exchange rates. We believe that one explanation for the persistency of large unpredictable fluctuations in exchange rates is that the mechanism determining the exchange rates may be chaotic. We use a technique developed by Grassberger and Proaccai (1983) for measuring the amount of chaos inherent in a time series. To do so, we compute an estimate of the correlation dimension of a series, and use the bootstrap [Efron (1979) to determine the estimator standard error. The estimated correlation dimension of various exchange rates then provides us with information about the behavior of exchange rates, without having to assume an econometric model.

We use the correlation dimension for two purposes. First, we estimate this parameter for series of daily (U.S. Dollar) exchange rates of five currencies: Sterling, the French franc, the Italian lira, the German mark, and the Singapore dollar. We show how the correlation dimension reflects the degree to which chaotic behavior characterizes the fluctuations in the exchange rate, and how this conforms with ideas about exchange rate management. Second, we use the correlation dimension and its estimated standard error in carrying out an intervention analysis. The analysis is aimed at determining whether the exchange rates of the five currencies were affected by the stock market crash of October 19, 1987. Generally, an intervention analysis would have required building separate time series models for each currency [Box and Tiao (1975)], or a single VAR model for all the currencies [Abraham (1980)]. In our case, neither is necessary and the correlation dimension leads to clear results.

2. The Correlation Dimension

Since Lorenz (1963) first showed that relatively simple mathematical systems can lead to unpredictable behavior, much work has gone into trying to understand the complex behavior characterizing chaos. The developed theory is linked to fractals in the sense of Mandelbrot (1983) because truly chaotic motion often possesses the intricate geometry of the fractal. Pure chaos is deterministic in nature, yet impossible to predict. Physicists studying turbulence observe chaotic systems, and so do workers in biology, ecology, and other areas. …

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