EUR/AUD and GBP/JPY 2002-2008: "trivial" intermarket correlations only
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Written by Mikhail Kopytine   
Wednesday, 06 August 2008 08:40

On average for the period, Euro/Australian Dollar and Pound Sterling/Japanese Yen are weakly negatively correlated. The correlation appears to be "trivially" limited to the 0-time-lag bin leaving little room for predicting one exchange rate on the basis of the other.

EUR/AUD and GBP/JPY volatility comparison

Fig.1: comparing volatilities of hour-by-hour logarithmic returns in EUR/AUD (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 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
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/AUD and GBP/JPY are similar, GBP/JPY being a bit more volatile on average. As usual, the volatility peaks during the European trading session. The distributions of logarithmic returns, at least on the 1-hour time scale considered, 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/AUD 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 -0.086 -0.055 -0.087

EUR/AUD and GBP/JPY are weakly negatively correlated on average for the period, throughout the three trading sessions studied. One can hardly think of any investment themes connecting the two exchange rates, other than the interest-rate differentials.

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

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

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. Such correlations are not present in this pair of exchange rates with the 1 hour time scale chosen for the analysis.

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

Fig.3:Cross-correlation of EUR/AUD 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/AUD 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. However even that area does not contain anything more than a couple of marginally significant bins to the right of the central deep. I call such correlations "trivial" in a sense that despite being useful for risk management, they offer little predictive power.

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

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