CHF/JPY and GBP/USD 2002-2008: asymmetric (leader-follower) correlation

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Written by Forex Automaton   
Monday, 28 July 2008 14:45

Swiss Franc/Japanese Yen and Pound Sterling/US Dollar show a non-trivial time-lag dependency 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 GBP/USD to follow (on average over the time of observation) in the same direction with the lag of up to 2-3 hours. Overall, this correlation pattern is similar to the case of CHF/JPY and EUR/USD.

CHF/JPY and GBP/USD volatility comparison

Fig.1: comparing volatilities of hour-by-hour logarithmic returns in CHF/JPY (top panel) and and GBP/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 GBP/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
GBP/USD hour 0.94×10-3 1.2×10-3 1.1×10-3

Fig.1 and Table 1 show that the volatilities of CHF/JPY and GBP/USD do not differ much but CHF/JPY has been slightly more volatile. Volatility of GBP/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 Transatlantic forex pair. If extreme movements happen to the GBP/USD, they happen during the European and American but not Pacific 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 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 0.43 0.52 0.49

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

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

Fig.2: Cross-correlation of CHF/JPY and GBP/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 correlations measured in the European and American session show a tail extending several bins to the left (meaning that the first currency of the pair, CHF/JPY, predicts the second, GBP/USD -- more on this below).

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

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

Fig.3 demonstrates the non-flat (although quite predictable) behavior 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 GBP/USD exchange rates by comparing it with the expected statistical fluctuations (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

t1-t2

where "1" denotes CHF/JPY and "2" denotes GBP/USD, the negativeness of the time lags means that the trend on average is for the CHF/JPY to lead and for the GBP/USD to follow. The interpretation of this may be complicated: recall that for the period in question (2002-08-20 to 2008-02-01), the interest rate differential (I am speaking of LIBORs) between GBP and USD crossed zero more than once while Switzerland had steadily higher interest rates than Japan, while the exact magnitude of the difference varied in both cases. One has to bear in mind that the correlations in Fig.2. and 3 are time averages. While CHF/JPY seems to emerge as a cross-rate capable of foretelling GBP/USD on average for 2002-2008, this may not be true at any particular time period within this time frame. And the fact that there is also a very significant positive peak to the right of the central peak indicates that one needs to be cautious with conclusions. This may become a subject of a follow-up study.

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

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