Time and Foreign Exchange Markets

Abstract

The definition of time is still an open question when one deals with high frequency time series. If time is simply the calendar time, prices can be modeled as continuous random processes and values resulting from transactions or fixings are discrete samples of this underlying dynamics. On the contrary, if one takes the business time point of view, price dynamics is a discrete random process, and time is simply the ordering according which prices are quoted in the market. In this paper we suggest that the business time approach is perhaps a better way of modeling price dynamics than calendar time. This conclusion is mostly based on the study of some conditional variances. If this result is correct it would simply mean that a price has a slow evolution when the corresponding asset is low traded and a fast evolution when the asset is highly traded. The data set we use contains the DEM/USD exchange quotes provided to us by Olsen & Associates during a period of one year from January to December 1998. In this period 1,620,843 quotes entries in the EFX system were recorded. The reason for using FX data is that this market is not subject to any working time restriction; in fact, it is open 24 hours a day, seven days a week. This is in contrast to stock markets, where artificial time regulation would have made more difficult, if not impossible, to find out the results outlined in this paper.