AUD/USD and USD/CHF intermarket correlations, 2004-2008

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Written by Forex Automaton   
Tuesday, 09 December 2008 15:13

Even though both interest rate differentials, that of AUD with respect to USD and USD with respect to CHF, have been fairly large and positive, the Australian Dollar/US Dollar and US Dollar/Swiss Franc and negatively correlated, apparently due to the presense of USD in both exchange rates in the opposite capacities. When studied with one hour time lag bin, the correlation deep looks broader than one bin (except for the American trading hours). This means that either exchange rate could be in principle used to statistically foretell the other -- with the usual caveat that this is a time-integrated picture. As a function of the time lag, the correlation appears somewhat asymmetric giving AUD/USD a slight preference in terms of "leadership".

AUD/JPY and USD/CHF volatility comparison

Fig.1: comparing volatilities of hour-by-hour logarithmic returns in AUD/USD (top panel) and USD/CHF (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/USD and USD/CHF in various trading sessions in 2004-2008.

currency pair time scale Asia-Pacific session European session American session
AUD/USD hour 1.4×10-3 1.6×10-3 1.5×10-3
USD/CHF hour 1.1×10-3 1.5×10-3 1.4×10-3

Fig.1 and Table 1 show that AUD/USD is somewhat more volatile. The volatility of USD/CHF depends on the trading session, is at the minimum during the Asia-Pacific session, and goes up strongly (about 40%) during the hours of European and American trading. Some decrease in the volatility of AUD/USD is seen during the Asia-Pacific session as well. 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, with pronounced tails.

Table 2: Pearson correlation coefficient for the time series of logarithmic returns in AUD/USD and USD/CHF 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 -0.41 -0.50 -0.48

AUD/USD and USD/CHF form a negatively correlated combination. The trading session with lower volatility (and presumably lower volume), the Asia-Pacific trading session, is also the one with the lower correlation amplitude.

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

Fig.2: Cross-correlation of AUD/USD and USD/CHF, derived from the hour-by-hour logarithmic returns, for the three trading sessions. Time frames of the sessions are shown in New York time.

Fig.2 presents the cross-correlation of AUD/USD and USD/CHF over the time lag (hours), for the various trading session (time zones). The difference of the zero time lag peaks among the different time zones has already been discussed in terms of the Pearson correlation coefficients (normalized variance), the variance here being with good accuracy the zero-lag correlation amplitude. A comparison with the same analysis performed repeatedly on the random data designed to mimic volatilities of AUD/USD and USD/CHF lets one estimate the accuracy of the correlation measurements, see Fig.3 below.

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

Fig.3: Cross-correlation of AUD/USD and USD/CHF 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/USD and USD/CHF 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 feature at the zero time lag. Even in the European trading data, there is some peak asymmetry to the left, into the area of negative lags (wherby CHF/USD would be lagging behind AUD/USD). The asymmetry is seen to be stronger in the Asia-Pacific and non-existent in the American data. The reason negative lags are interpreted this way is the definition: the lag td is defined as

td = t1 - t2,

where index "1" denotes AUD/USD and index "2" denotes USD/CHF. Therefore, negative correlation value at negative lags means that opposite movements in AUD/USD and USD/CHF happen at an earlier time in AUD/USD, or AUD/USD is leading. The word of caution is in place: this is a time-averaged picture and an in-depth study of a time evolution of this picture may turn out to be more informative. This is the subject of a special section on the time evolution of forex inefficiencies.

The data used are from the period 2004-04-01 00:00:00 to 2008-10-01 00:00:00.

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