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

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Written by Forex Automaton   
Monday, 25 August 2008 15:03

The story of Euro/Swiss Franc and US Dollar/Japanese Yen exchange rates is similar to that of EUR/CHF and EUR/USD and EUR/CHF and GBP/USD: weak "instantaneous" correlations, robust predictive ones. We now have evidence for three different exchange rates that "trigger" EUR/CHF -- too bad EUR/CHF is one of the least volatile forex rates!

EUR/CHF and USD/JPY volatility comparison

Fig.1: comparing volatilities of hour-by-hour logarithmic returns in EUR/CHF (top panel) and USD/JPY (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/JPY 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/JPY hour 1.1×10-3 1.3×10-3 1.2×10-3

Fig.1 and Table 1 show that the volatilities of EUR/CHF and USD/JPY are grossly different, EUR/CHF being one of the least volatile among the freely floating exchange rates. USD/JPY is seen to be least volatile, suprisingly, in the Asia-Pacific time zone. 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/JPY 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 0.15 0.23 0.24

EUR/CHF and USD/JPY are weakly positively correlated on average for the period, throughout the three trading sessions studied. These exchange rates are minimally correlated in the Asia-Pacific trading session even though one might expect that USD/JPY is actively traded there (but EUR/CHF probably isn't).

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

Fig.2: Cross-correlation of EUR/CHF and USD/JPY, 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. In Fig.2, such correlations are seen in this pair of exchange rates for all three trading time zones, in the +1 and +2 hour time bins. Curiously, even though the zero-lag bin is much lower for the Asia-Pacific time zone compared to the two other ones, this means little for the non-zero lag signals at +1 and +2 -- these are almost as high in the Asia-Pacific as they are in Europe and America. Fig.3 quantifies uncertainty of the correlation measurements by using random time series (martingales) to evaluate precision of these measurements.

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

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

t1-t2

where "1" denotes EUR/CHF and "2" denotes USD/JPY, the positiveness of the time lags associated with the positive correlation signals means that similar things happen to rate 1 (EUR/CHF) at a later time after they have already happened to rate 2 (USD/JPY) at an earlier time. In other words, USD/JPY leads, EUR/CHF follows. Dependense of these correlations on time and LIBOR rates 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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