AUD/JPY and USD/CHF intermarket correlation, 2004-2008.

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Written by Forex Automaton   
Monday, 08 December 2008 13:27

The intermarket correlation between Australian Dollar/Japanese Yen and US Dollar/Swiss Franc does not exist in Asia-Pacific trading and is extremely week the rest of time. However, there is a hint of a delayed correlation at one hour lag, whereby USD/CHF would be leading and AUD/JPY -- following. Given the interest rates, this observation goes against the hypothesis that the stronger interest rate differential should be the leader. The AUD/JPY and USD/CHF combination resembles AUD/JPY and EUR/GBP where similarly week delayed correlation signaled statistical lagging of AUD/JPY behind GBP/EUR.

AUD/JPY and USD/CHF volatility comparison

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

currency pair time scale Asia-Pacific session European session American session
AUD/JPY hour 1.7×10-3 1.8×10-3 1.8×10-3
USD/CHF hour 1.1×10-3 1.5×10-3 1.4×10-3

Fig.1 and Table 1 show that the volatilities of AUD/JPY and USD/CHF are fairly different, AUD/JPY being one of the most volatile exchange rates. 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/JPY 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/JPY 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 -0.0048 0.037 0.045

AUD/JPY and USD/CHF form a very weakly positively correlated combination, although not for the Asia-Pacific traders.

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

Fig.2: Cross-correlation of AUD/JPY 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/JPY 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/JPY and USD/CHF lets one estimate the accuracy of the correlation measurements, see Fig.3 below.

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

Fig.3: Cross-correlation of AUD/JPY 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/JPY 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 peak at the zero time lag. What looks like a slight peak asymmetry to the right, into the area of positive lags (wherby AUD/JPY would be lagging begind USD/CHF) has significance of about two standard deviations (RMS). The reason positive lags are interpreted this way is the definition: the lag td is defined as

td = t1 - t2,

where index "1" denotes AUD/JPY and index "2" denotes USD/CHF. Therefore, positive correlation value at positive lags means that similar movements in AUD/JPY and USD/CHF happen at a later time in AUD/JPY, or AUD/JPY is lagging. 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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