Forex Automaton

Euro/Pound Sterling and Australian Dollar/US Dollar are weakly positively correlated but the correlation, as seen on average for the 6 year period of hour-by-hour data, is too tight to offer forecasting potential on this time scale. Such simple one-peak structures centered at the zero time-lag are called "trivial" in this series of analysis notes.

Fig.1 and Table 1 show that the volatilities of EUR/GBP and AUD/USD are quite different, EUR/GBP being, along with EUR/CHF, among the least volatile of the floating exchange rates. Some decrease in the volatility of EUR/GBP is seen 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. The distributions look roughly triangular on the log scale. Therefore a lot more appropriate model for the tails would be an exponent, meaning the returns themselves (not the logarithms) follow a power law.

EUR/GBP and AUD/USD form a weakly positively correlated combination. The volatility decrease seen in the case of EUR/GBP in the Asia-Pacific trading is accompanied by the corresponding decrease in the normalized correlation between EUR/GBP and AUD/USD -- not a trivial observation, see Table 2.

Fig.2 presents the cross-correlation of EUR/GBP and AUD/USD over the time lag (hours), for the various trading session (time zones). There is no features to talk about in the vicinity of the zero time-lag bin where the predictive tails of the correlation peak are usually located, meaning that the correlation is tightly localized (or in other words, response happens quickly). A comparison with the same analysis performed repeatedly on the random data designed to mimic volatilities of EUR/GBP and AUD/USD 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 peak at the zero time lag.

The data used are from the period 2002-08-20 00:00:00 to 2008-02-01 00:00:00.

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