EUR/GBP and AUD/USD 2002-2008: "trivial" intermarket correlations

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Written by Forex Automaton   
Wednesday, 17 September 2008 12:59

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.

EUR/GBP and AUD/USD volatility comparison

Fig.1: comparing volatilities of hour-by-hour logarithmic returns in EUR/GBP (top panel) and AUD/USD (bottom panel) for the three trading sessions: Asia-Pacific session, European session, and the American session. The sessions are defined in New York time to be at least 12 hour long each. The histograms are normalized distributions of logarithmic returns.

Table 1: Hour-by-hour volatilities (RMS) for the time series of logarithmic returns in EUR/GBP and AUD/USD in various trading sessions in 2002-2008.

currency pair time scale Asia-Pacific session European session American session
EUR/GBP hour 0.76×10-3 0.93×10-3 0.79×10-3
AUD/USD hour 1.3×10-3 1.5×10-3 1.5×10-3

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.

Table 2: Pearson correlation coefficient for the time series of logarithmic returns in EUR/GBP and AUD/USD in various trading sessions in 2002-2008. Time frames of the sessions are shown in New York time.

time scale Asia-Pacific session European session American session
hour 0.077 0.14 0.17

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.

EUR/GBP and AUD/USD intermarket correlation 1 hour time-lag bin

Fig.2: Cross-correlation of EUR/GBP and AUD/USD, derived from the hour-by-hour logarithmic returns, for the three trading sessions. Time frames of the sessions are shown in New York time.

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.

EUR/GBP and AUD/USD intermarket correlation 1 hour time-lag bin with uncertainty estimate

Fig.3: Cross-correlation of EUR/GBP and AUD/USD for the European (Eurasian) trading session shown against the backdrop of statistical noise (red). The noise is obtained from martingale simulations based on the recorded volatilities of EUR/GBP and AUD/USD in this trading session for the period under study. The noise is presented as mean plus-minus 1 RMS, where RMS characterizes the distribution of the correlation value obtained for each particular bin by analyzing 20 independent simulated pairs of uncorrelated time series.

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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