EUR/AUD and EUR/CHF 2002-2008: asymmetric predictive correlations

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Written by Forex Automaton   
Wednesday, 30 July 2008 14:43

Euro/Australian Dollar and Euro/Swiss Franc exchange rates are weakly negatively correlated on average for the time period in 2002-2008 considered in this report. On the hour-by-hour time scale considered, indications of predictive correlations are marginal at best for the European session, but appear significant for the American session, contrary to what is usually the case.

EUR/AUD and EUR/CHF volatility comparison

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

currency pair time scale Asia-Pacific session European session American session
CHF/JPY hour 1.1×10-3 1.3×10-3 1.3×10-3
GBP/USD hour 0.45×10-3 0.56×10-3 0.49×10-3

As seen from Fig.1 and Table 1, EUR/CHF is a lot less volatile than EUR/AUD. EUR/CHF shows considerable changes in volatility session-to-session, European session being the most volatile for this currency pair. 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 -0.11 -0.12 -0.15

EUR/AUD and EUR/CHF are weakly negatively correlated on average for the period, throughout the three trading sessions studied. This is despite the fact that these two cross-rates have the same base currency, EUR. However the interest rate differentials have the opposite signs for these pairs, and apparently that has the decisive effect.

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

Fig.2: Cross-correlation of EUR/AUD and EUR/CHF, derived from the hour-by-hour logarithmic returns, for the three trading sessions. Time frames of the sessions are shown in New York time.

As noted above the correlation is weak and negative. 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, correlations with non-zero time lags would be of particular importance. There may be indications that the central deep extends into adjacent bins.

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

EUR/AUD and EUR/CHF intermarket correlation 1 hour time-lag bin with uncertainty estimate, American trading session

Fig.3: Cross-correlation of EUR/AUD and EUR/CHF 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 CHF/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. Top: European trading hours, bottom: American trading hours.

Fig.3 (European session) and Fig.4 (American session) show 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.

We inspect significance of the correlation signals in the EUR/AUD and EUR/CHF exchange rates by comparing them with the expected statistical fluctuations (noise) in Fig.3, as explained in the figure caption. The deviations up to 2 RMS in a few channels, including the channel to the left of the 0 lag in Fig.3, can not be taken as a serious indication of non-randomness. It is possible however that the signal in the -1 hour bin is the remainder of a more significant correlation tail hidden inside the 0 lag bin. Speaking of Fig.4, the predicitive signals in the bins adjacent to the zero lag appear significant. They indicate that either of the rates could be used to predict the other. The usual caveats have to be made that this is an average of the correlation over the long period and the actual picture could have changed during the period.

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

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