Forex Automaton

Pound Sterling/Japanese Yen is weakly positively correlated with US Dollar/Swiss Franc and, what is an independent piece of information, predictive correlations seem absent in this pair of exchange rates with this (hour time scale) resolution. The necessary caveat is that this is a time-integrated picture.

Fig.1 and Table 1 show that volatilities of USD/CHF and GBP/JPY are comparable, with similar shapes of the logarithmic return distributions. Volatilities of both exchange rates depend on the trading session and are at the minimum during the Asia-Pacific session. As always in forex, at least on the 1-hour time scale considered, the distributions of logarithmic returns are not "bell-shaped", they are strongly non-Gaussian, with pronounced tails.

GBP/JPY and USD/CHF form a weakly correlated combination in Europe and the Americas and virtually no correlation in the Pacific.

Fig.2 presents the cross-correlation of GBP/JPY and USD/CHF over the time lag (hours), for the various trading session (time zones). The difference of the zero time lag peaks among the different time zones is striking. A comparison with the same analysis performed repeatedly on the random data designed to mimic volatilities of GBP/JPY and USD/CHF lets one estimate the accuracy of the correlation measurements, see Fig.3 below.

Fig.3 demonstrates the non-flat (although quite predictable) behaviour of the noise level with time lag, caused by the constraint on the time lags associated with the definition of the trading session time window. This can not be ignored otherwise one risks over-interpreting the picture. The area around zero is fairly safe since the noise is at the minimum when the lag is at an integer number of days. Naturally, as the random model responsible for the noise (red background in the figure) does not contain any correlation between the two exchange rates, it shows no correlation feature at the zero time lag. The magnitude of correlation almost everywhere except for the zero time-lag bin is too low to compete with noise; although perhaps the few bins to the left of the zero time lag might contain a remnant of a signal. The word of caution is in place: this is a time-averaged picture and an in-depth study of a time evolution of this picture may turn out to be more informative. That is the subject of a special section on the time evolution of forex inefficiencies. The data used are from the period 2004-04-01 00:00:00 to 2008-10-01 00:00:00.

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