EUR/AUD and EUR/JPY 2002-2008: leader-follower correlations

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Written by Forex Automaton   
Thursday, 31 July 2008 14:33

On average for the period, Euro/Australian Dollar and Euro/Japanese Yen show a prominent predictive correlation with EUR/JPY being the leader and EUR/AUD the follower, despite the fact that the 0-hour lag correlation peak is fairly week for this pair of exchange rates. However what matters for prediction is not the amplitude of the 0-lag correlation (with respect to unit), but the amplitude of the non-zero lag signals with respect to martingale noise.

EUR/AUD and EUR/JPY volatility comparison

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

currency pair time scale Asia-Pacific session European session American session
EUR/AUD hour 1.1×10-3 1.3×10-3 1.3×10-3
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/AUD and EUR/JPY are similar and they do not differ much from session to 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. 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 CHF/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 0.085 0.14 0.096

EUR/AUD and EUR/JPY are correlated on average for the period, throughout the three trading sessions studied.

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

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

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 would be of particular importance. The correlations measured in the European and American session show a tail extending several bins to the right (meaning that the second rate of the pair, EUR/JPY, predicts the first, EUR/AUD -- more on this below).

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

Fig.3: Cross-correlation of EUR/AUD 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/AUD 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) behavior 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.

We inspect significance of the predictive correlation between the EUR/AUD and EUR/JPY exchange rates by comparing it in Fig.3 with the random fluctuations expected on the basis of efficient market assumption, as explained in the figure caption. The positive correlation amplitudes in the +1 and +2 -hour lag bins are well above the noise level and appear to be forming a tail of predictive positive correlation. The correlation is seen to decrease rapidly as the time lag increases. Since the time lag is defined as

t1-t2

where "1" denotes EUR/AUD and "2" denotes EUR/JPY, the positiveness of the time lags means that the trend on average is for the EUR/JPY to lead and for the EUR/AUD to follow. During the period in question (2002-08-20 to 2008-02-01), there were times when the interest rate differential (I am speaking of LIBORs) between AUD and EUR exceeded that between EUR and JPY, but there were also time when the opposite was the case.

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

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