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69

Hourly Index (2 days in GMT)

FIGURE 6.4 The model activity decomposed into the three different continental markets over a period of 48 hr during normal business days for the same rates as in Figure 6.3. The top curve is the sum of oq ard the three market activities.

ers, Reuters and Knight Ridder,4 for the same period. The two resulting statistical functions differ substantially. Knight Ridder data are about half as frequent as Reuters data and cover the East Asian markets quite poorly. We measure the difference of the two curves in terms of the root mean squared error (RMSE) of all hourly differences.

We then apply the same approach for a comparison of absolute returns between the two suppliers. We analogously measure the difference between the two resulting curves in terms of the RMSE of the hourly differences.

4 Since this study was done, Knight Ridder has been integrated with Telerate to Bridge.



The RMSE ratio Rrmse is defined as follows:

-sh/sn2 (616)

TUMff - f?r)/ffe]2

where /) are the mean hourly number of ticks and V( arc the mean hourly absolute returns. The RMSE value here is consistently lower than that for the tick frequency; the ratio is 0.32 for DEM-USD, 0.17 for JPY-USD, 0.20 for USD-GBP, 0.42 for CHF-USD, and 0.52 for XAU-USD. This shows that the volatility is less dependent than the number of price revisions on the data supplier.

Another illustration of this is given in Figure 6.5. We show in these graphs the result of an intraday study of both the tick frequency and the average hourly returns for USD-JPY computed during the same time period on a sample coming from the traditional FXFX page of Reuters (left graphs) and another sample coming from the new method Reuters chose to publish its data, the Reuters Instrument Codes (RICs). This new method, being much more suited for computer manipulations, allows the data vendor to transmit much more information and this is very apparent when examining the two upper graphs on the hourly number of ticks. On the other hand, the two lower graphs show little differences because they are computed directly from the prices, which are not governed by the data vendor policy but rather by the market. We use a similar RMSE ratio as in Equation 6.16 and find values around 0.12. This example indicates clearly the problem one is faced with the activity definition. During the same period and for the same market, the activity should be independent of the data source. This is only the case for the hourly absolute returns.

2. Returns are less sensitive than the tick frequency to data holes. The frequency goes to zero if the communication line is broken (there is no good interpolation method for this variable) whereas, with the proper price interpolation, only the variation around the interpolated line for the returns is lost.

The transaction volume, a potential candidate to describe market activity, is not available in hourly frequency. Transaction volume data are available for particular dates through two surveys published by the Federal Reserve Bank of New York (1986 and 1989). Although these surveys are useful to quantify the amount of capital involved, they do not give any indication about intradaily, daily, and weekly changes. We do not propose our activity model as a direct model for the seasonal patterns of transaction volume, but suggest its usefulness in future research.



FXFX

W H

100.0 ; I

g> 50.0

<

J.....

<

FXFX

«

<

6 12 18 24 0

Intraday Interval Index

6 12 18 2

Intraday Interval Index

FIGURE 6.5 The comparison of the tick activity (upper graphs) and the hourly absolute return (lower graphs) for two data sources. The old Reuters FXFX page and the nev Reuters Instrument Code (RIC) data. The comparison is conducted for the USD-JP" from October 25, 1993 to March 18, 1995.

6.3 A NEW BUSINESS TIME SCALE (#-SCALE) 6.3.1 Definition of the #-Scale

In Section 6.2.2, the time scale & was introduced to model the seasonal, intradair and intraweekly aspect of heteroskedasticity. In Equation 6.1, the activity variabit has been defined as the "speed" of & against the physical time t. The continuom activity function a{t) of Equation 6.7, developed in the previous sections, allow; us to define ? as its time integral,



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