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

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Written by Forex Automaton   
Tuesday, 30 September 2008 13:15

Euro/Pound Sterling and Euro/US Dollar form a positively correlated pair. The central correlaiton peak is narrow enough not to have visible tails when analyzed on the hour time scale. Hints of a negative correlation are seen at positive time lags, similar to the correlation of EUR/GBP with EUR/JPY and CHF/JPY.

EUR/GBP and EUR/USD volatility comparison

Fig.1: comparing volatilities of hour-by-hour logarithmic returns in EUR/GBP (top panel) and EUR/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 EUR/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
EUR/USD hour 0.93×10-3 1.3×10-3 1.2×10-3

Fig.1 and Table 1 show that the volatilities of EUR/GBP and EUR/USD are fairly different, EUR/GBP being, along with EUR/CHF, among the least volatile floating exchange rates. Some decrease in the volatility of EUR/GBP and a considerable decrease in the volatility of EUR/USD 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, while if the returns had been lognormal, the distribution would have looked parabolic. Therefore a lot more appropriate model for the tails would be an exponent, meaning the returns themselves (not the logarithms) follow a power law on this time scale.

Table 2: Pearson correlation coefficient for the time series of logarithmic returns in EUR/GBP 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 0.40 0.43 0.48

EUR/GBP and EUR/USD are positively correlated -- not surprising given that EUR is present as a base currency in both rates. The correlation coefficient is strongly dependent on the trading session, being at the minimum during the Asia-Pacific trading hours.

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

Fig.2: Cross-correlation of EUR/GBP 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.

Fig.2 presents the cross-correlation of EUR/GBP and EUR/USD 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). In the area of time lags 15 to 20 hours, the pattern resembles a wave of a negative "polarity" (an anticorrelation). This seems to be unique to the European trading session, which is usually the one with reachest correlations. A comparison with the same analysis performed repeatedly on the random data designed to mimic volatilities of EUR/GBP and EUR/USD lets one estimate the accuracy of the correlation measurements, and thus the significance of the conclusion, see Fig.3 below.

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

Fig.3: Cross-correlation of EUR/GBP and EUR/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 EUR/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 area with lags in the range 15-20 hours with several 2-3 standard deviation signals looks serious enough to say a few words about it. This pair, EUR/GBP and EUR/USD is not alone in having such a feature. Compare Fig.3 with similar figures for EUR/GBP and EUR/JPY, EUR/GBP and CHF/JPY. The time lag is defined as t1-t2 where "1" denotes EUR/GBP and "2" denotes EUR/USD. Therefore, the negative correlation at positive lags means that trends tend to be opposite for EUR/GBP and EUR/USD when the time lags are in the range 15-20 hours, that is an EUR/USD trend tends to be followed by an opposite trend in EUR/GBP with a 15-20 hour lag. The reason for that is not clear. Same can be said about those other examples with similar features just mentioned.

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

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