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

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Written by Forex Automaton   
Monday, 07 July 2008 16:49

Australian Dollar/Japanese Yen and Euro/ Australian Dollar are negatively correlated currency pairs. In all trading sessions, the correlation function has a peculiar symmetric "contrarian" shape, meaning that while AUD/JPY and EUR/AUD move in predictably opposite directions on the time scale of up to one hour, sometimes it pays to be a "contrarian" and bet on the relationship to be reversed with a time lag 0 to 2 hours. The reason for this is not clear. Same thing has been seen in the correlations between AUD/USD and EUR/AUD.

AUD/JPY and EUR/AUD volatility comparison

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

currency pair time scale Asia-Pacific session European session American session
AUD/JPY hour 1.5×10-3 1.7×10-3 1.6×10-3
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 AUD/JPY and EUR/AUD differ, although not by 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. A lot more appropriate model for the tails would be an exponent, as the tails look roughly linear on the logarithmic scale. This implies that a good model of returns themselves (not the logarithms) would be 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 AUD/JPY and EUR/AUD in various trading sessions in 2002-2008.

time scale Asia-Pacific session European session American session
hour -0.67 -0.66 -0.67

AUD/JPY and EUR/AUD are significantly correlated on average for the period.

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

Fig.2:Cross-correlation of AUD/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. The correlation signals in the bins adjacent to the 0-time-lag bin are quite strong and positive. This statement is quantified and supported by comparison with statistical noise in Fig.3.

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

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

The interpretation of the "contrarian" features at +1 hour and -1 hour time lag bins is as follows: AUD/JPY leads and EUR/AUD follows in the same direction within 0 to 2. hours, or EUR/AUD leads and AUD/JPY follows. I say within 0 to 2. hours despite the fact that we are looking at the 1 hour time lag because if the moves are such that one happens at the end of an hour, and the other -- at the very beginning of the next hour, they are separated by almost 0 time lag and yet they belong to the different time bins. They will contribute to a pattern with a one-hour time difference despite the actual separation being a lot smaller. 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 AUD/JPY leads and EUR/AUD follows, as the data suggests, that implies a kind of a break-up in the behaviour of AUD, of the kind that could reward a contrarian investor. This kind of pattern has been seen in the correlations between AUD/USD and EUR/AUD.

AUD/JPY and EUR/AUD intermarket correlation 4 hour time-lag bin

Fig.4:Cross-correlation of AUD/JPY and EUR/AUD, derived from the hour-by-hour logarithmic returns, for the three trading sessions. The time lag binning is increased to 4 hours an d the time axis is expanded. Time frames of the sessions are shown in New York time.

Fig.4 shows correlations on a larger scale. It seems that between 14 and 22 hour lags, the positive "contrarian" correlation gives way to a more natural negative correlation. You can also note the striking symmetry of these features with respect to the sign of time lag, meaning that either pair can in principle be used to predict the other.

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

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