AUD/USD and NZD/USD 2005-2008: intermarket correlations (oscillating pattern)

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Written by Forex Automaton   
Monday, 16 June 2008 12:17

Australian Dollar/ US Dollar and New Zealand Dollar /US Dollar are strongly correlated currency pairs. Plotted over time lag, the correlation between them has a peculiar symmetric pattern which is easier to plot than describe (although we dared to do both).

Table: Pearson correlation coefficient for the time series of logarithmic returns in AUD/USD and NZD/USD in various trading sessions in 2004-2008. Time frames of the sessions are shown in New York time.

time scale Asia-Pacific session European session American session
hour 0.68 0.72 0.70

AUD/USD and NZD/USD are strongly correlated on average for the period. Looking at the 0-hour time lag, which is what the table represents, the correlation is the least pronounced in the Asia-Pacific session, most pronounced in the European and American session.

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

Fig.1: Cross-correlation of AUD/USD and NZD/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 0 lag means that the correlation (reported in the table) works out mostlyon the time scale of up to 1 hour. For the purpose of trading system development, correlations with non-zero time lag are of particular importance. It is these correlations that allow us to make forecasts. Those are usually the least pronounced in the Asia-Pacific session and the most pronounced in the European and to a lesser extent in the American session. Fig.1 is not an exception. The central peak looks narrow, it appears to be localized within the 0-lag bin. Fig.1 looks like there might be interesting features at the time lags 6-20 hours either direction away from 0.

AUD/USD and NZD/USD intermarket correlation 4 hour time-lag bin

Fig.2: Cross-correlation of AUD/USD and NZD/USD, as in Fig.1, but with time lag binning increased to 4 hours.

In Fig.2, with coarser binning, the pattern begins to look like consisting of waves whose period grows while amplitude diminishes as the time lag goes away from zero in either direction. Trading such a pattern would require a lot of confidence, since the high amplitude correlations and anticorrelations with limited separation in time would prescribe frequent alternations in the buy/sell strategy.

To judge how reliable the correlation signals at the non-zero lags are, one has to compare the signal with the noise level obtained from the martingale simulations.

AUD/USD and NZD/USD intermarket correlation European session 4 hour bin + noise

Fig.3: Cross-correlation of AUD/USD and NZD/USD, derived from the hour-by-hour logarithmic returns, for the European (Eurasian) trading session shown against the backdrop of statistical noise (red). The noise is obtained from martingale simulations based on the historical volatilities of AUD/USD and NZD/USD in this trading session.

The non-flat behaviour of the noise level with time lag in Fig.3 is due to a time-lag limitation imposed by the constraint associated with the duration of the 12-hour long "trading session" (our working definition). The noise is at the minimum at 24 times an integer number, its adjacent maxima and minima are offset by 12 hours with respect to each other. This can not be ignored otherwise one risks over-interpreting the picture. The area around zero is relatively safe to interprete since the noise is at the minimum when the lag is at an integer number of days, however in this case the area around zero is featureless. Based on the level of the noise, the peculiar positive-negative alternation in the [-18;-14] and [-14;-10] bins, symmetrically repeated in the [10,14], [14;18] bins looks real.

The data used are from the period 2005-08-16 00:00:00 to 2008-02-01 00:00:00.

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