USD/CAD and USD/JPY 2002-2008: "trivial" intermarket correlations

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Written by Forex Automaton   
Monday, 15 September 2008 13:13

US Dollar/Canadian Dollar and US Dollar/Japanese Yen are a weakly positively correlated pair of exchange rates. With the one hour time-scale analysis approach there is no evidence for predictive correlations in the time period under study.

USD/CAD and USD/JPY volatility comparison

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

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

Fig.1 and Table 1 show that the volatilities of USD/CAD and USD/JPY are not too different most of the time, with the notable exception of the Asia-Pacific session when the volatility of USD/CAD is known to drop dramatically. 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. 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 scale 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 USD/CAD and USD/JPY 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 0.15 0.21 0.20

USD/CAD and USD/JPY are positively correlated on average for the period, throughout the three trading sessions studied. The correlation is seen to weaken during the Asia-Pacific session -- the time period of relative quietude in the USD/CAD trading. Although there is no mathematical law requiring low volatility to result in low correlation, the connection may be causal since ultimately it is people and their opinion about the markets that create these correlaitons. When people sleep, so do the correlations.

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

Fig.2: Cross-correlation of USD/CAD and USD/JPY, 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 USD/CAD and USD/JPY over the time lag (hours). 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 forex trading system development, correlation amplitudes at non-zero time lags would be of particular importance. In Fig.2, there is no indication that such signals exist. This statement is confirmed by comparing correlation function of the real market with those of the simulated ones, simulation being based on the historical volatilities, but correlation-free by construction.

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

Fig.3: Cross-correlation of USD/CAD and USD/JPY 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 USD/CAD and USD/JPY 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. The correlation values obtained for non-zero time lags look consistent with noise expecations.

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

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