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

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Written by Forex Automaton   
Monday, 01 September 2008 14:48

Euro/Japanese Yen and US Dollar/Canadian Dollar is hard to classify as either "signal" or "no signal" on the basis of the time-averaged data alone -- we have certainly seen more convincing signals in these series of reviews. The predictive intermarket correlation signal seen on average in 2002-2008 is marginally significant and warrants further study of its evolution with time and LIBOR rates.

EUR/JPY and USD/CAD volatility comparison

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

currency pair time scale Asia-Pacific session European session American session
EUR/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

Fig.1 and Table 1 show that the volatilities of EUR/JPY and USD/CAD are similar, exept for the Asia-Pacific trading when USD/CAD is noticeably less volatile -- apparently due to lack of interest in this exchange rate from the Pacific traders and businesses. 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 EUR/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

EUR/JPY and USD/CAD are weakly negatively correlated on average for the period, throughout the three trading sessions studied. The correlation is at the minimum during the Asia-Pacific session when the USD/CAD is presumably not so heavily traded.

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

Fig.2: Cross-correlation of EUR/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 forex trading system development, correlation amplitudes at non-zero time lags would be of particular importance. Such correlations may be visible in this pair of exchange rates in the vicinity of 0 time lag where the amplitude at the -2 hour time lag looks conspicuous. Martingale simulations (Fig.3) quantify uncertainty of the correlation measurements.

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

Fig.3: Cross-correlation of EUR/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 EUR/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. 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. As the comparison with noise indicates, the signal at the -2 hour time lag is about 3 standard deviations above the noise level; we have seen more convincing signals in this series of reviews. The pattern is a bit unusual as the -1 hour time lag shows a less significant signal -- typically in cases with asymmetric correlation peaks one sees an tail of correlation decaying away from the 0 time lag, with the largest signal next to the 0 time lag. Old news do not move the markets.

Nevertheless, if we were to take Fig.3 at the face value, the interpretation would be that EUR/JPY leads and CAD/USD follows (USD/CAD tends to move in the direction opposite to that of the EUR/JPY): since the time lag is defined as

t1-t2

where "1" denotes EUR/JPY and "2" denotes USD/CAD, the negativeness of the time lags associated with the negative correlation signal means that similar things tend to happen to rate 1 (EUR/JPY) at an earlier time before they happen to the inverse of rate 2 (CAD/USD) at a later time.

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

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