EUR/GBP and USD/CAD 2002-2008: intermarket correlations

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Written by Forex Automaton   
Monday, 13 October 2008 11:22

The intermarket correlation between Euro/Pound Sterling and US Dollar/Canadian Dollar has a narrow, relatively week negative peak at the zero time lag whose internal structure can not be resolved on the hour time scale -- simply put, these currencies are weakly negatively correlated with fast enough response to one another. Another feature is common to many cross-correlations involving EUR/GBP: this European pair seems to "listen" to what happened with various other pairs -- USD/CAD in this case -- in the American trading late the previous day, and "take a note". The evidence of this behaviour is fairly weak in every individual case, but becomes significant for forex collectively. Of course the direction of response EUR/GBP shows varies for each individual intermarket combination.

EUR/GBP and USD/CAD volatility comparison

Fig.1: comparing volatilities of hour-by-hour logarithmic returns in EUR/GBP (top panel) and USD/CAD (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 USD/CAD 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
USD/CAD hour 0.88×10-3 1.4×10-3 1.3×10-3

Fig.1 and Table 1 show that the volatilities of EUR/GBP and USD/CAD are fairly different, EUR/GBP being, along with EUR/CHF, among the least volatile floating exchange rates. The volatility of USD/CAD depends on the trading session: it is at the minimum during the Asia-Pacific session, and goes up strongly (50% and more) during the hours of European and American trading. Obviously the North-American traders have more interest in the USD/CAD pair than do their Asian colleagues -- therefore USD/CAD does not support the traders' wisdom that low volume generally leads to high volatility. Along the same lines, some decrease in the volatility of EUR/GBP is seen during the Asia-Pacific session as well. 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 USD/CAD 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 -0.079 -0.12 -0.14

On average for the pediod covered, EUR/GBP and USD/CAD form a weakly negatively correlated combination.

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

Fig.2: Cross-correlation of EUR/GBP and USD/CAD, 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 USD/CAD over the time lag (hours), for the various trading session (time zones). There is no interesting 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). An outstanding feature is a bump on positive time lags in the range 16-21 hours. This feature is only seen in the European trading time zone. Similar features have been seen in many other intermarket correlation functions involving EUR/GBP. A comparison with the same analysis performed repeatedly on the random data designed to mimic volatilities of EUR/GBP and USD/CAD lets one estimate the accuracy of the correlation measurements, see Fig.3 below.

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

Fig.3: Cross-correlation of EUR/GBP and USD/CAD 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 USD/CAD 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 group of bins at 16-21 hour time lag looks tantalizing in its marginal significance. Similar features have been seen in the intermarket correlations involving other pairs of forex exchange rates:

These patterns differ in "polarity" with respect to the zero-lag correlation peak and in degree of symmetry with respect to lag zero. Given the definition of the time lag,

 

td = t1-t2,

where "1" denotes EUR/GBP and "2" denotes "USD/CAD", the interpretation is that EUR/GBP follows (in a weak "statistical" sense) the 16-21 hour old movements in USD/CAD (apparently, previous day's movements). Because this happens only in the European session and not seen in the American session (see Fig.2), I conclude that this happens before the overlap between European and American trading, that is in the European morning. Thus, the response is to the events with USD/CAD early in the American session the previous day. 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.

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

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