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

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Written by Forex Automaton   
Thursday, 24 July 2008 11:56

Swiss Franc/Japanese Yen and US Dollar/Canadian Dollar exchange rates are weakly negatively correlated. Correlations away from the 0 time lag bin resemble the case of EUR/USD and USD/CAD, and marginally significant predictive correlations are seen.

CHF/JPY and USD/CAD volatility comparison

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

currency pair time scale Asia-Pacific session European session American session
CHF/JPY hour 1.1×10-3 1.3×10-3 1.2×10-3
USD/CAD hour 0.88×10-3 1.4×10-3 1.3×10-3

Unlike CHF/JPY, volatility of USD/CAD depends noticeably on the trading session and is at the minimum during the Asia-Pacific session whose participants presumably have the least interest in USD/CAD. As always in forex, the distributions of logarithmic returns, at least on the 1-hour time scale considered, are not "bell-shaped", are strongly non-Gaussian. The distributions look roughly triangular on the log scale. Therefore a lot more appropriate model for the tails would be an exponent, meaning the returns themselves (not the logarithms) follow 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 CHF/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 -0.17 -0.23 -0.23

CHF/JPY and USD/CAD are strongly correlated on average for the period, throughout the three trading sessions studied.

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

Fig.2: Cross-correlation of CHF/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 localized 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. Such correlations appear to be present, especially in the European (Eurasian) trading session in the bins immediately surrounding the zero time-lag bin. But a completely random process (noise) could with certain probability create correlations of certain magnitude, which need to be discriminated against. Fig.3 presents a comparison with what can be expected from uncorrelated noise with the volatility properties shown in Fig.1.

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

Fig.3: Cross-correlation of CHF/JPY and USD/CAD for the European (Eurasian) trading session are shown against the backdrop of statistical noise (red). The noise is obtained from martingale simulations based on the recorded volatilities of CHF/JPY and USD/CAD 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.

We inspect significance of the predictive correlation in the CHF/JPY and USD/CAD exchange rates by comparing it with the expected statistical fluctuaitons (noise) in Fig.3, as explained in the figure caption. It seems certain that the correlation peak at and around the 0 time-lag bin is more than one bin wide. The interpretation is that a move in either exchange rate can in principle be used to forecast the other rate.

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

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