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

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Written by Forex Automaton   
Monday, 06 October 2008 11:34

Not surprisingly, Euro/Pound Sterling and Pound Sterling/Japanese Yen are negatively correlated. The zero-time lag peak appears well localized in the hour scale analyzis, however there are marginally significant wave-like features away from zero, of the kind seen in a number of other cases.

EUR/GBP and GBP/JPY volatility comparison

Fig.1: comparing volatilities of hour-by-hour logarithmic returns in EUR/GBP (top panel) and GBP/JPY (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/JPY 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/JPY hour 1.2×10-3 1.4×10-3 1.2×10-3

Fig.1 and Table 1 show that the volatilities of EUR/GBP and GBP/JPY are quite 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/JPY 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 -0.43 -0.44 -0.38

EUR/GBP and GBP/JPY form a negatively correlated combination -- not surprising given that GBP is present as a base currency in one and quote currency in the other rate, therefore all the rest being equal, any factors affecting GBP make the two rates move in the opposite directions.

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

Fig.2: Cross-correlation of EUR/GBP and GBP/JPY, 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/JPY over the time lag (hours), for the various trading session (time zones). In the vicinity of the zero time-lag bin where the predictive tails of the correlation peak are usually located, the correlation appears tightly localized (or in other words, response happens quickly). The symmetric hegative signals at or around 14-20 hours, either sign of the time lag, European session, look intriguing. A comparison with the same analysis performed repeatedly on the random data designed to mimic volatilities of EUR/GBP and GBP/JPY lets one estimate the accuracy of the correlation measurements, see Fig.3 below.

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

Fig.3: Cross-correlation of EUR/GBP and GBP/JPY 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/JPY 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 negative signals located roughly symmetrically around zero and away from zero, again make one think of a wave-like pattern which is pronounced fairly weekly and can be easily dismissed in each individual pair of exchange rates but begins to look credible after a number of similar cases cases are inspected:

It is possible that historically, there have been periods when these signals have been more or less pronounced than they are in the history-integrated data shown here. This may become a subject of a separate study.


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

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