CHF/JPY and EUR/USD 2002-2008: leader-follower correlation

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Written by Forex Automaton   
Friday, 25 July 2008 12:47

Swiss Franc/Japanese Yen and Euro/US Dollar show a complex picture of cross-correlations. The correlation peak is wider than one hour, is positive and asymmetric indicating a tendency for CHF/JPY to lead and for EUR/USD to follow in the same direction with the lag of up to a couple of hours. However, for larger time lags (12 to 24 hours), the data is in favor of negative correlation, although on the time scale considered (hourly), the noise competes with the signal at each individual time-lag bin in that range of lags.

CHF/JPY and EUR/USD volatility comparison

Fig.1: comparing volatilities of hour-by-hour logarithmic returns in CHF/JPY (top panel) and and EUR/USD (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 EUR/USD 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 1.2×10-3
EUR/USD hour 0.93×10-3 1.3×10-3 1.2×10-3

Fig.1 and Table 1 show that the volatilities of CHF/JPY and EUR/USD do not differ much but CHF/JPY has been slightly more volatile. Volatility of EUR/USD is seen to vary with trading time zone (session), being at the minimum during the Asia-Pacific session whose paritcipants presumably have less interest in this western hemisphere forex pair. If extreme movements happen to the EUR/USD, they happen during the European and American sessions. 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 EUR/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 0.43 0.52 0.49

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

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

Fig.2: Cross-correlation of CHF/JPY and EUR/USD, 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, correlations with non-zero time lags would be of particular importance. The correlation pattern of the European session look somewhat different from the rest in Fig.2: the central peak has a tail extending several bins to the left (meaning that the first currency of the pair, CHF/JPY, predicts the second, EUR/USD), whereas in the American session it's just a somewhat higher signal in the left bin next to the center.

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

Fig.3: Cross-correlation of CHF/JPY and EUR/USD 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 EUR/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.

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.

We inspect significance of the predictive correlation in the CHF/JPY and EUR/USD exchange rates by comparing it with the expected statistical fluctuaitons (noise) in Fig.3, as explained in the figure caption. The positive correlation amplitudes in the -3 through -1 -hour lag bins are well above the noise level and appear to be forming a solid tail of predictive positive correlation. Since the time lag is defined as


where "1" denotes CHF/JPY and "2" denotes EUR/USD, the negativeness of the time lags means that the trend is for the CHF/JPY to lead and for the EUR/USD to follow. To interpret this, recall that for the period in question (2002-08-20 to 2008-02-01), the interest rate differential (I am speaking of LIBORs) between EUR and USD changed sign and thus overall stayed below that of CHF and JPY, Switzerland having steadily higher interest rates than Japan. This reinforces the conclusion which seems to emerge from this series of notes -- if there is a leader-follower relationship between two currency pairs, it is the currency pair with the larger interest rate differential that becomes the leader.

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

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