EUR/JPY and GBP/USD 2002-2008: asymmetric leader-follower correlations

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Written by Forex Automaton   
Wednesday, 27 August 2008 15:05

Euro/Japanese Yen and Pound Stering/US Dollar are moderately positively correlated exchange rates. The significant correlation, while dying with the time lag, extends in time for as long as two hours, and on average for the period is asymmetric with EUR/JPY leading the trend and GBP/USD following.

EUR/JPY and GBP/USD volatility comparison

Fig.1: comparing volatilities of hour-by-hour logarithmic returns in EUR/JPY (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/JPY and GBP/USD in various trading sessions in 2002-2008.

currency pair time scale Asia-Pacific session European session American session
EUR/JPY hour 1.1×10-3 1.3×10-3 1.2×10-3
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/JPY and GBP/USD are similar and are little dependent on the time zone. 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. An option buyer armed with the right pricing formula could capitalize on the fat tails (provided that the tails persist on the time scale of interest to such a trader) but one would not be able to make forecasts based on Fig.1.

Table 2: Pearson correlation coefficient for the time series of logarithmic returns in EUR/JPY 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 0.26 0.32 0.32

EUR/JPY and GBP/USD are weakly positively correlated on average for the period, throughout the three trading sessions studied.

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

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

The fact that most of the correlation is concentrated at the 0 lag means that the correlation (reported in the table) works out mostly on the time scale of up to 1 hour. For the purpose of forex trading system development, correlation amplitudes at non-zero time lags are of particular importance. As you see in Fig.2, the correlation amplitudes in the time lag bins at -1 and -2 hours are coincidentally strong for both European and American trading sessions. Comparison with martingale simulations (Fig.3) is needed to quantify uncertainty of the correlation measurements and decide whether we are dealing with significant predictive signals here, suitable for trading system implementation.

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

Fig.3: Cross-correlation of EUR/JPY 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/JPY 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. The predictive negative correlations at -1 and -2 hour time lags are seen to stand out of the noise by significant factors. As usual, the tail decays rapidly as the time lag increases and the markets discount whatever moved them. Old news do not move the markets. Since the time lag is defined as

t1-t2

where "1" denotes EUR/JPY and "2" denotes GBP/USD, the negativeness of the time lags associated with the positive correlation signals means that similar things happen to rate 1 (EUR/JPY) at an earlier time before they happen to rate 2 (GBP/USD) at a later time. In other words, EUR/JPY leads, GBP/USD follows. Dependense of these correlations on time and LIBOR rates deservers a special 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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