AUD/JPY and USD/CAD 2002-2008: intermarket correlations

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Written by Forex Automaton   
Tuesday, 01 July 2008 16:31

The time-lag analysis of cross-correlation between Australian Dollar/Japanese Yen and US Dollar/Canadian Dollar shows that these exchange rates have a leader-follower relation, with Aussie being the leader and CAD/USD (not USD/CAD!) the follower.

AUD/JPY and USD/CAD volatility comparison

Fig.1: comparing volatilities of hour-by-hour logarithmic returns in AUD/JPY (top panel) and and USD/CAD (bottom panel) for the three trading sessions: Asia-Pacific session,European session, and the American session. The sessions are defined in New York time. 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/CAD 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
USD/CAD hour 0.87×10-3 1.4×10-3 1.3×10-3

Fig.1 and Table 1 show how much more volatile AUD/JPY is, compared to USD/CAD. Needless to say the distributions 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 for the returns themselves (not the logarithms) would be power law. Volatility of USD/CAD changes visibly with the trading session, the Asia-Pacific session being the least volatile. This kind of data could be useful to an option trader but so far we know nothing about our ability to make forecasts.

Table 2: Pearson correlation coefficient for the time series of logarithmic returns in AUD/JPY and USD/CAD 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 -0.20 -0.24 -0.24

AUD/JPY and USD/CAD are weakly negatively 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/JPY and USD/CAD intermarket correlation 1 hour time-lag bin

Fig.2:Cross-correlation of AUD/JPY and USD/CAD, 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 the forex trading system development, correlations with non-zero time lag are of particular importance. It is these correlations that allow us to make forecasts, and they are visible in the figure: the peak around the 0 time lag bin is asymmetric and extends to the left. This statement is quantified and supported by comparison with statistical noise in Fig.3.

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

Fig.3:Cross-correlation of AUD/JPY and USD/CAD 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/CAD in this trading session for the period under study. The noise is presented as mean plus-minus 1 RMS, where the RMS characterizes the distribution of the correlation value obtained for each particular bin by analyzing 20 independent simulated pairs of uncorrelated time series.

We inspect significance of the predictive correlation in the AUD/JPY and USD/CAD exchange rates by comparing it with the expected statistical fluctuations (noise) in Fig.3, as explained in the figure caption. The signal in the -1 and -2 hour time lag bin looks quote comfortably significant. In our convention, the time lag is

t1-t2

where "1" denotes AUD/JPY and "2" denotes USD/CAD.

Therefore, the interpretation of the peak's tail extending to the left into the area of negative lags is as follows: AUD/JPY leads and CAD/USD follows in the same direction within 0 to 3. hours. Again we see a pair with the stronger interest rate differential show the way to a pair with a weaker interest rate differential. Likewise, in the AUD/JPY and EUR/USD analysis we see that it is the AUD/JPY who leads, because of the greater interest rate differential and despite the the fact the EUR represents the far greater economic power of the European Union. A similar conclusion is made about AUD/USD and USD/CAD as well as AUD/JPY and EUR/CHF. Interest rates dominate the forex dynamics, if the statement needs another quantitative proof, but it's amazing that the adjustments happen slowly enough to be detectable with one-hour time-bin analysis presented here.

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

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