EUR/CHF and USD/CAD 2002-2008: weak and "trivial" correlations

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Written by Forex Automaton   
Wednesday, 20 August 2008 13:18

Euro/Swiss Franc and US Dollar/ Canadian Dollar are weakly positively correlated in the European trading session and very weakly positively correlated the rest of the time (the session dependence is considerable for some reason). Little predictability potential in either rate with respect to the other is revealed by this hour time scale study.

EUR/CHF and USD/CAD volatility comparison

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

currency pair time scale Asia-Pacific session European session American session
EUR/CHF hour 0.45×10-3 0.55×10-3 0.49×10-3
USD/CAD hour 0.88×10-3 1.4×10-3 1.3×10-3

Fig.1 and Table 1 show that the volatilities of EUR/CHF and USD/CAD are grossly different, EUR/CHF being one of the least volatile among the freely floating exchange rates. Volatility of USD/CAD depends strongly on the trading session, being at the minimum during 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) 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/CHF 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 0.016 0.031 0.015

EUR/CHF and USD/CAD are weakly positively correlated on average for the period. The correlation coefficient is twice as strong for the European session as it is for the rest. Not seen from the data in the table alone, the Pearson coefficients are significantly non-zero for all trading sessions.

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

Fig.2: Cross-correlation of EUR/CHF 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. Such correlations are not seen in this pair of exchange rates on the hourly time scale considered. This statement is supported by comparison with martingale simulations (Fig.3) which quantify uncertainty of the correlation measurements.

EUR/CHF and USD/CAD intermarket correlation 1 hour time-lag bin with uncertainty estimate

Fig.3: Cross-correlation of EUR/CHF 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/CHF 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.

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. As the comparison with noise indicates, there is no significant predictive signal in this pair of exchange rates seen on the hour time scale. It is the lack of predictive power which we refer to by calling these correlations "trivial".

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

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