2.1. The Deutschemark- U.S. dollar foreign exchange data

The sample mean of the 5-minute Deutschemark appreciation of 0.000175% is

indistinguishable from zero at standard significance levels given the sample

standard deviation of 0.047% 8. However, the returns are clearly not normally

distributed. For example, the sample skewness of 0.367 and the sample kurtosis of

21.5 are both highly statistically significant 9. At the same time, the maximum and

minimum 5-minute returns of 1.24% and -0.637% do not suggest the presence of

sharp discontinuities in the series. A small negative first order autocorrelation

coefficient of -0.04 provides some support for the hypothesis that foreign

exchange dealers position their quotes asymmetrically relative to the perceived

'true market price' as a way to manage their inventory positions, thus causing the

midpoint of the quoted prices to move around in a fashion similar to the bid-ask

bounce often observed on organized exchanges 10. A more detailed set of summary

statistics are available in Andersen and Bollerslev (1994).

In order to evaluate the intraday periodicity of the returns, Fig. l a plots the

average sample mean for each 5-minute interval. The average returns are centered

around zero but numerous violations of the constant 5% confidence band for the

null of an i.i.d, series occur between 09.00 GMT and 18.00 GMT (interval range

produces a more realistic time-varying confidence band that is violated at seemingly

random points in time and at a frequency consistent with the 5% band (13

violations over 288 intervals). Thus, there appears to be little evidence for any

systematic DM-$ appreciation or depreciation through the regular trading day

J l This is counter to Ito and Roley (1987) who found evidence for systematic dollar appreciation

during the U.S. segment of the market but dollar depreciation during the European trading hours.

lunch hour in the Tokyo and Hong Kong markets. Activity then picks up during

the afternoon session in the Far Eastern markets and is further fueled by the

opening of the European markets around 07.00 GMT (interval 84). The market

volatility then declines slowly until the European lunch hour at 11.30 GMT

(interval 138), before it increases sharply during the overlap of afternoon trading

in Europe and the opening of the U.S. markets around 13.00 GMT, or 7.00 a.m.

New York (interval 156). After the European markets close volatility declines

monotonically until trading associated with the Far Eastern markets starts to pick

up again around 21.00 GMT (interval 252). The robustness of this intraday

volatility pattern is confirmed by the sub-sample analysis and the sorting of days

according to volatility levels reported in the more detailed analysis in Andersen

and Bollerslev (1994), which is also consistent with earlier findings in Wasser122

fallen (1989), Miiller et al. (1990), Baillie and Bollerslev (1991) and Dacorogna et

al. (1993) ~3. Standard summary statistics further verify the overwhelming significance

of this intraday volatility pattern. In particular, the first order autocorrelation

coefficient for the absolute 5-minute returns of pA = 0.309 exceeds the 1/x/T

asymptotic standard error by almost a factor of one hundred, while the Ljung-Box

statistic for up to tenth order serial correlation in ]Rt,,,] equals QA(10) = 36,680 J4

The sample mean of the 5-minute Deutschemark appreciation of 0.000175% is

indistinguishable from zero at standard significance levels given the sample

standard deviation of 0.047% 8. However, the returns are clearly not normally

distributed. For example, the sample skewness of 0.367 and the sample kurtosis of

21.5 are both highly statistically significant 9. At the same time, the maximum and

minimum 5-minute returns of 1.24% and -0.637% do not suggest the presence of

sharp discontinuities in the series. A small negative first order autocorrelation

coefficient of -0.04 provides some support for the hypothesis that foreign

exchange dealers position their quotes asymmetrically relative to the perceived

'true market price' as a way to manage their inventory positions, thus causing the

midpoint of the quoted prices to move around in a fashion similar to the bid-ask

bounce often observed on organized exchanges 10. A more detailed set of summary

statistics are available in Andersen and Bollerslev (1994).

In order to evaluate the intraday periodicity of the returns, Fig. l a plots the

average sample mean for each 5-minute interval. The average returns are centered

around zero but numerous violations of the constant 5% confidence band for the

null of an i.i.d, series occur between 09.00 GMT and 18.00 GMT (interval range

produces a more realistic time-varying confidence band that is violated at seemingly

random points in time and at a frequency consistent with the 5% band (13

violations over 288 intervals). Thus, there appears to be little evidence for any

systematic DM-$ appreciation or depreciation through the regular trading day

J l This is counter to Ito and Roley (1987) who found evidence for systematic dollar appreciation

during the U.S. segment of the market but dollar depreciation during the European trading hours.

lunch hour in the Tokyo and Hong Kong markets. Activity then picks up during

the afternoon session in the Far Eastern markets and is further fueled by the

opening of the European markets around 07.00 GMT (interval 84). The market

volatility then declines slowly until the European lunch hour at 11.30 GMT

(interval 138), before it increases sharply during the overlap of afternoon trading

in Europe and the opening of the U.S. markets around 13.00 GMT, or 7.00 a.m.

New York (interval 156). After the European markets close volatility declines

monotonically until trading associated with the Far Eastern markets starts to pick

up again around 21.00 GMT (interval 252). The robustness of this intraday

volatility pattern is confirmed by the sub-sample analysis and the sorting of days

according to volatility levels reported in the more detailed analysis in Andersen

and Bollerslev (1994), which is also consistent with earlier findings in Wasser122

fallen (1989), Miiller et al. (1990), Baillie and Bollerslev (1991) and Dacorogna et

al. (1993) ~3. Standard summary statistics further verify the overwhelming significance

of this intraday volatility pattern. In particular, the first order autocorrelation

coefficient for the absolute 5-minute returns of pA = 0.309 exceeds the 1/x/T

asymptotic standard error by almost a factor of one hundred, while the Ljung-Box

statistic for up to tenth order serial correlation in ]Rt,,,] equals QA(10) = 36,680 J4