EUR/CHF and GBP/USD 2002-2008: leader-follower correlations

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Written by Forex Automaton   
Tuesday, 19 August 2008 13:48

Euro/Swiss Franc and Pound Stering/US Dollar are weakly negatively correlated. The weakness of the 0-hour time lag correlation does not prevent this pair of exchange rates from having one of the most convincing predictable patterns seen in this series of notes so far: it is the non-zero time lags that matter for forecasting and trading system development.

EUR/CHF and GBP/USD volatility comparison

Fig.1: comparing volatilities of hour-by-hour logarithmic returns in EUR/CHF (top panel) 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 EUR/CHF and GBP/USD 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
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 EUR/CHF and GBP/USD are grossly different, EUR/CHF being one of the least volatile among the freely floating exchange rates. 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 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 -0.033 -0.10 -0.11

EUR/CHF and GBP/USD are weakly negatively correlated on average for the period. It is remarkable that the correlation is extremely weak during the Asia-Pacific session. None of the four currencies composing the two pairs belongs to the Asia-Pacific region. This is consistent with the idea that it is the commercial traders who create the correlations, as the speculators from a particular time zone would not necessarily feel limited to trading currency pairs containing currencies of their geographic area.

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

Fig.2: Cross-correlation of EUR/CHF 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 zero 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 amplitudes are seen by bare eye with confidence in this combination of exchange rates, and one can say they are present even without our usual comparison with martingale simulations (Fig.3) which quantify uncertainty of the correlation measurements. Looking at the Asia-Pacific data again, it is noteworthy that despite the relatively low zero lag negative peak, the +1 hour lag signal is relatively and even absolutely strong.

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

Fig.3: Cross-correlation of EUR/CHF 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 EUR/CHF 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) 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. The predictive negative correlations at +1 and +2 hour time lags are seen to stand out of the noise by significant factors. As usual, the tail decays rapidly as the time lag increases and the markets discount whatever moved them. Old news do not move the markets. Since the time lag is defined as


where "1" denotes EUR/CHF and "2" denotes GBP/USD, the positiveness of the time lags means that the trend on average for the period of observation, 2002-2008, is for the GBP/USD to lead and for the CHF/EUR to follow (EUR/CHF "follows" in the opposite direction to GBP/USD as the negative correlation amplitudes indicate -- or you could say that USD/GBP leads EUR/CHF). Dependence of these correlations on time and the LIBOR deservers a special 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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