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

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Written by Forex Automaton   
Monday, 29 September 2008 09:34

The intermarket correlation between Euro/Pound Sterling and Euro/Japanese Yen, analyzed on an hour time scale, shows a correlation peak narrow enough to be localized inside the zero-hour time-lag bin. Longer range picture may be more complex with hints of a correlation going negative as the time lag extends into the neighborhood of 20 hours.

EUR/GBP and EUR/JPY volatility comparison

Fig.1: comparing volatilities of hour-by-hour logarithmic returns in EUR/GBP (top panel) and EUR/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 EUR/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
EUR/JPY hour 1.1×10-3 1.3×10-3 1.2×10-3

Fig.1 and Table 1 show that the volatilities of EUR/GBP and EUR/JPY 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 (lognormal distributions of returns 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.

Table 2: Pearson correlation coefficient for the time series of logarithmic returns in EUR/GBP and EUR/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 0.22 0.26 0.27

EUR/GBP and EUR/JPY form a weakly positively correlated combination -- not surprising given that EUR is present as a base currency in both rates. The correlation is visibly lower in the Asia-Pacific session.

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

Fig.2: Cross-correlation of EUR/GBP and EUR/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 EUR/JPY 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). A comparison with the same analysis performed repeatedly on the random data designed to mimic volatilities of EUR/GBP and EUR/JPY lets one estimate the accuracy of the correlation measurements, see Fig.3 below.

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

Fig.3: Cross-correlation of EUR/GBP and EUR/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 EUR/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. Maxima in the red background at +12 and -12 hours are clearly seen, and such maxima repeat themselves regularly. This can not be ignored otherwise one risks over-interpreting the picture. However, 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. When looking at correlations for the range of lags 13-21 hours (with either sign), it looks like another weakly pronounced oscillation pattern. After looking at many of those, EUR/GBP and CHF/JPY, AUD/USD and EUR/USD, CHF/JPY and EUR/JPY, CHF/JPY and EUR/USD, EUR/AUD and EUR/JPY one can not help the feeling that there is a certain propensity in these pairs to form a wave-like pattern or oscillating pattern, even though in many individual cases it is hard to say so with certainty. Most but not all of these crosses involve yen.

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

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