EUR/AUD and USD/CAD 2002-2008: leader-follower correlations

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Written by Forex Automaton   
Monday, 11 August 2008 08:06

Euro/Australian Dollar and US Dollar/Canadian Dollar show a leader-follower correlation which, on average for the period, is particularly pronounced in the Asia-Pacific trading session.

EUR/AUD and USD/CAD volatility comparison

Fig.1: comparing volatilities of hour-by-hour logarithmic returns in EUR/AUD (top panel) and USD/CAD (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 CHF/JPY and GBP/USD 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
USD/CAD hour 0.88×10-3 1.4×10-3 1.3×10-3

Fig.1 and Table 1 show the volatilities of EUR/AUD and USD/CAD. Not surprisingly, USD/CAD, not involving any Asian currency, is least volatile in 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. 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. However, one would not be able to make forecasts based on Fig.1 as that would require two-point statistics at the very least.

Table 2:Pearson correlation coefficient for the time series of logarithmic returns in EUR/AUD and USD/CAD 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 0.10 0.085 0.10

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

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

Fig.2:Cross-correlation of EUR/AUD and USD/CAD, 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. To assess their significance, these have to be discriminated against the random fluctuations in the measured correlation amplitudes, as expected based on the recorded volatilities of the two exchange rates for each trading session under study. Such a study is presented in Fig.3.

EUR/AUD and USD/CAD intermarket correlation 1 hour time-lag bin with uncertainty estimate, European session

EUR/AUD and USD/CAD intermarket correlation 1 hour time-lag bin with uncertainty estimate, Asia-Pacific session

Fig.3:Cross-correlation of EUR/AUD and USD/CAD 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 USD/CAD 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. Top: European trading session. Bottom: Asia-Pacific trading session.

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.

In the top panel, Eurasian trading session, the time lag bins to the left of the central peak, corresponding to the time lags from -5 to -1, look possibly significant as a group even though none of the them has a signal above 3 RMS from noise. In the bottom panel, Australasian or Asia-Pacific trading session, there is a very strong signal in the -1 hour time lag bin, but little to talk about for the rest of the time lags which had signals in the top plot.

Since the time lag is defined as

t1-t2

where "1" denotes EUR/AUD and "2" denotes USD/CAD, the negativeness of the time lags means that the trend on average is for the EUR/AUD to lead and for the USD/CAD to follow. This falls nicely into the framework: larger interest rate differential pair leads, smaller one follows.

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

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