EUR/CHF and USD/CHF 2004-2008: "trivial" intermarket correlation

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Written by Forex Automaton   
Tuesday, 25 November 2008 18:03

The intermarket correlation between Euro/ Swiss Franc and US Dollar/Swiss Franc has a narrow positive peak at the zero time lag whose internal structure can not be resolved on the hour time scale -- simply put, these currencies are correlated positively with fast enough response to one another, and their combination offers no visible benefit for forecasting.

EUR/CHF and USD/CHF volatility comparison

Fig.1: comparing volatilities of hour-by-hour logarithmic returns in EUR/CHF (top panel) and USD/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/CHF and USD/CHF in various trading sessions in 2004-2008.

currency pair time scale Asia-Pacific session European session American session
EUR/CHF hour 0.50×10-3 0.62×10-3 0.56×10-3
USD/CHF hour 1.1×10-3 1.5×10-3 1.4×10-3

Fig.1 and Table 1 show that the volatilities of EUR/CHF and USD/CHF are fairly different, EUR/CHF being one of the least volatile floating exchange rates. The volatility of USD/CHF depends on the trading session, and is at the minimum during the Asia-Pacific session, and goes up strongly (about 40%) during the hours of European and American trading. Along the same lines, some decrease in the volatility of EUR/CHF is seen during the Asia-Pacific session as well. 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 tails of the distributions look roughly linear 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.

Table 2: Pearson correlation coefficient for the time series of logarithmic returns in EUR/CHF and USD/CHF in various trading sessions in 2004-2008. Time frames of the sessions are shown in New York time.

time scale Asia-Pacific session European session American session
hour 0.50 0.54 0.52

On average for the pediod covered, EUR/CHF and USD/CHF form a positively correlated combination.

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

Fig.2: Cross-correlation of EUR/CHF and USD/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.

Fig.2 presents the cross-correlation of EUR/CHF and USD/CHF over the time lag (hours), for the various trading session (time zones). There is no interesting features to talk about in the vicinity of the zero time-lag bin where the predictive tails of the correlation peak are usually located, meaning that the correlation is tightly localized (or in other words, response happens quickly). A comparison with the same analysis performed repeatedly on the random data designed to mimic volatilities of EUR/CHF and USD/CHF lets one estimate the accuracy of the correlation measurements, see Fig.3 below.

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

Fig.3: Cross-correlation of EUR/CHF and USD/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 EUR/CHF and USD/CHF 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. What looks like a slight peak asymmetry to the right, into the area of positive lags (wherby EUR/CHF would be lagging begind USD/CHF) is so weakly significant given the noise level that it's hard to defend. The word of caution is in place: this is a time-averaged picture and an in-depth study of a time evolution of this picture may turn out to be more informative.

The data used are from the period 2004-04-01 00:00:00 to 2008-10-01 00:00:00.

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