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

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Written by Forex Automaton   
Tuesday, 07 October 2008 10:59

Euro/Pound Sterling and Pound Sterling/US Dollar form another pair with the negative correlation feature at the positive time lag. Unlike many other forex pairs, this is not an extention of the zero-time lag correlation (negative and well localized in this case) but an isolated feature of the correlation function at larger time lags.

EUR/GBP and GBP/USD volatility comparison

Fig.1: comparing volatilities of hour-by-hour logarithmic returns in EUR/GBP (top panel) and GBP/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 GBP/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
GBP/USD hour 0.94×10-3 1.2×10-3 1.1×10-3

Fig.1 and Table 1 show that the volatilities of EUR/GBP and GBP/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 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 GBP/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 -0.41 -0.30 -0.18

EUR/GBP and GBP/USD form a negatively correlated combination. The session dependence of the correlation coefficient is quite unusual, the strongest being the Asia-Pacific session.

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

Fig.2: Cross-correlation of EUR/GBP and GBP/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 GBP/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). The difference in patterns between European trading session and the rest of the data looks remarkable, the European pattern being definitely the strongest. A comparison with the same analysis performed repeatedly on the random data designed to mimic volatilities of EUR/GBP and GBP/USD lets one estimate the accuracy of the correlation measurements, see Fig.3 below. That comparison can tell whether the pattern seen in the European session is strong enough to be more than a lucky coincidence of random walk effects.

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

Fig.3: Cross-correlation of EUR/GBP and GBP/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 GBP/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. For the noise, both the position of center of the red hatched band and its vertical extent are informative -- the position systematically above zero is possible if the random time series (based on the historical returns) have a common "bias" towards positive returns, or in other words, both exchange rates have a long-term positive trend, which is indeed the case as can be seen even from the visual inspection of the peak asymmetries in Fig.1.

The group of 2-3 standard deviation negative correlation signals in the range of time lags 15-18 hours looks significant, given the noise level and its positive bias. The pattern of negative correlation belongs into the class of patterns seen previously:

These patterns vary in the degree of symmetry -- some of them have the wave at the negative lags more and some them less pronounced, but they all have the feature at the positive lags qualitatively similar to the one seen here. Given the definition of the time lag,


td = t1-t2,

where index "1" denotes EUR/GBP and index "2" denotes GBP/USD, this feature indicates that opposite movements tend to happen in EUR/GBP 15 to 18 hours after the movements in GBP/USD.

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

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