EUR/AUD and USD/JPY 2002-2008: asymmetric "contrarian" correlations

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Written by Forex Automaton   
Monday, 11 August 2008 14:50

On average for the period, Euro/Australian Dollar and US Dollar/Japanese Yen are negatively correlated. Time-lag dependence of the correlations has a complex asymmetric shape and the nature of the correlation seems to depend on the time-lag: even though at the zero time-lag bin (hour scale) the correlation is negative, a positive correlation with USD/JPY as a leader and EUR/AUD the follower is seen at 1-2 hour time-lag bins.

EUR/AUD and USD/JPY volatility comparison

Fig.1: comparing volatilities of hour-by-hour logarithmic returns in EUR/AUD (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/AUD and USD/JPY in various trading sessions in 2002-2008.

currency pair time scale Asia-Pacific session European session American session
EUR/AUD hour 1.1×10-3 1.3×10-3 1.3×10-3
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/AUD and USD/JPY are similar and they do not differ much from session to session. 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 -0.13 -0.18 -0.19

EUR/AUD and USD/JPY are negatively correlated on average for the period, throughout the three trading sessions studied. Strangely, the correlation is minimal during the Asia-Pacific session even though both JPY and AUD belong to the region.

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

Fig.2: Cross-correlation of EUR/AUD 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. The correlation amplitudes have to be discriminated against the respective values expected to emerge from the same analysis done on completely random data, as will be shown in Fig.3. Already in Fig.2 and even before looking at Fig.3, the couple of bins to the right of the central deep look (+1 and +2 hour lags) look provocative and attract attention: it hardly can be an accident that two adjacent correlation amplitudes shoot up in unison significantly and do so for both European and American trading sessions.

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

Fig.3: Cross-correlation of EUR/AUD 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/AUD 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.

We inspect significance of the predictive correlation between the EUR/AUD and USD/JPY exchange rates by comparing it in Fig.3 with the random fluctuations expected on the basis of efficient market assumption, as explained in the figure caption. The positive correlation amplitudes in the +1 and +2 -hour lag bins are well above the noise level.

Since the time lag is defined as


where "1" denotes EUR/AUD and "2" denotes USD/JPY, the positiveness of the time lags means that the trend on average is for the USD/JPY to lead and for the EUR/AUD to follow.

What makes the interpretation hard is the fact that the correlation signals surrounding the zero time-lag bin have a polarity opposite to that of the zero time-lag correlation. I call these features "contrarian" because a contrarian investor benefits from going against the trend, against the positive auto-correlation if you will. If indeed there is a stable pattern whereby USD/JPY leads and EUR/AUD follows, as the data suggests, then under conditions of the overall negative correlation between the two exchange rates, that implies a kind of a break-up in the behaviour of either exchange rate, of the kind that could reward a contrarian investor. Similar patterns have been seen in the correlations between AUD/USD and EUR/AUD, and AUD/JPY and EUR/AUD, but in those cases more symmetry was noticed. In particular, smaller correlation peaks of the same polarity as the zero-time lag correlation could be seen symmetrically at the lags between 14 and 22 hours or -22 and -14 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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