CHF/JPY and EUR/AUD 2002-2008: leader-follower correlations

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Written by Forex Automaton   
Thursday, 10 July 2008 12:37

Swiss Franc/Japanese Yen and Euro/Australian Dollar are weakly positively correlated currency pairs. This pair of exchange rates shows a leader-follower relationship with CHF/JPY, a cross-rate of two carry-trade funding currencies being, surprisingly, the leader and EUR/AUD -- the follower.

CHF/JPY and EUR/AUD volatility comparison

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

Fig.1 and Table 1 show that the volatilities of CHF/JPY and EUR/AUD do not differ much. Volatilities of both exchange rates vary little with trading time zone (session). As always in forex, the distributions of logarithmic returns are not "bell-shaped", 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 scales 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/AUD 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 0.12 0.19 0.15

CHF/JPY and EUR/AUD are weakly correlated on average for the period. This is a pair of exchange rates whose correlation depends strongly on the session and is the strongest during the European session. The fact that CHF/JPY and EUR/AUD are positively correlated at all is a bit strange, comparing the interest rate differentials of the base and quote currencies in both cases.

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

Fig.2: Cross-correlation of CHF/JPY and EUR/AUD, 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 lag would be of particular importance. It is these correlations that allow us to make forecasts, and they are visible in the figure: the peak around the 0 time lag bin is asymmetric and extends to the left. This statement is quantified and supported by comparison with statistical noise in Fig.3.

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

Fig.3: Cross-correlation of CHF/JPY and EUR/AUD 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/AUD 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/AUD exchange rates by comparing it with the expected statistical fluctuations (noise) in Fig.3, as explained in the figure caption. The signal in the -1 and -2 hour time lag bin looks quote comfortably significant. In our convention, the time lag is

t1-t2

where "1" denotes CHF/JPY and "2" denotes EUR/AUD.

Therefore, the interpretation of the peak's tail extending to the left into the area of negative lags is as follows: CHF/JPY leads and EUR/AUD follows in the same direction within 0 to 2. hours.

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

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