AUD/USD and EUR/USD 2002-2008: intermarket correlations (oscillating pattern)

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Written by Forex Automaton   
Friday, 06 June 2008 15:58

Australian Dollar / US Dollar and Euro/US Dollar exchange rate are correlated, with an interesting symmetric wave-like pattern extending for up to 100 hours time lag.

Table: Pearson correlation coefficient for the time series of logarithmic returns   in AUD/USD and EUR/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 0.50 0.59 0.58

AUD/JPY and EUR/USD are weakly correlated on average for the period. The correlation is the least pronounced in the American session, most pronounced in the Asia-Pacific session.

AUD/USD and EUR/USD ntermarket correlation

Fig.1: Cross-correlation of AUD/USD and EUR/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.

The fact that most of the correlation is concentrated at the 0 lag means that the correlation (reported in the table) works out mostly on the time scale of up to 1 hour. However the reaction of AUD/USD to a change in EUR/USD and vice versa is not instantaneous, as seen from the finite width of the correlation peak centered at 0. The tails of positive correlation, symmetric around 0, indicate that there there is no clear leader between the two exchange rates: while sometimes AUD/USD leads and EUR/USD follows, exactly the opposite happens about just as frequently. Correlations with non-zero time lag, such as seen in the figures, are potentially useful for forecasting.

To judge how reliable the correlation signals at the non-zero lags are, one has to compare the signal with the noise level obtained from the martingale simulations.

AUD/USD and EUR/USD intermarket correlation European session 1 hour bin

Fig.2: Cross-correlation of AUD/USD and EUR/USD, derived from the hour-by-hour logarithmic returns, for the European (Eurasian) trading session shown against the backdrop of statistical noise (red). The noise is obtained from martingale simulations based on the historical volatilities of AUD/JPY and EUR/USD in this trading session.

Fig.2 demonstrates the non-flat (although quite predictable) behaviour of the noise level with time lag. 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 times 24 hours. Based on the level of the noise, the tails in the first bins to the left and to the right of the 0 peak look like a real effect. Not less curious are the negative deeps surrounding the central peak. Although every individual channel in this area (lags -30 to -10 and 10 to 30 hours) does not look convincing given the level of the noise, they look promising as a group.

AUD/USD and EUR/USD intermarket correlation European session 4 hour bin

Fig.3: Cross-correlation of AUD/USD and EUR/USD, derived from the hour-by-hour logarithmic returns, for the European (Eurasian) trading session shown against the backdrop of statistical noise (mean plus/minus 1 RMS band is shown in red). The noise is obtained from martingale simulations based on the historical volatilities of AUD/JPY and EUR/USD in this trading session. Time axis and binning expanded compared to Fig.2.

The time lag bins and the time lag axis are extended compared to Fig.2. As always, the time lag between first and second exchange rates is calculated as t1-t2. Therefore significant positive correlations at the negative lags should be understood as an indication of a leader-follower relationship with rate 1 (AUD/USD) leading and rate 2 (EUR/USD) following. Significant positive correlations at the positive lags should be understood as an indication of a leader-follower relationship with rate 2 (EUR/USD) leading and rate 1 (AUD/USD) following. For negative correlations, the interpretation is similar but instead of a leader/follower relationship we have something which can be called action/reaction, with AUD/USD and EUR/USD making opposite moves separated by a certain time lag. The Fig.2 contains examples of both types of patterns, not without a peculiar symmetry. Both are potentially valuable for forecasting.

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

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