CHF/JPY and EUR/JPY 2002-2008: symmetric predictive cross-correlations

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Written by Forex Automaton   
Tuesday, 22 July 2008 13:31

Swiss Franc/Japanese Yen and Euro/Japanese Yen cross-rates share the quote currency and are strongly correlated. For time lags 3 to 5 hours, symmetric positive correlations can be in principle used to statistically predict either cross-rate on the basis of the other.

CHF/JPY and EUR/JPY volatility comparison

Fig.1: comparing volatilities of hour-by-hour logarithmic returns in CHF/JPY (top panel) and and EUR/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 CHF/JPY and EUR/JPY 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
EUR/JPY hour 1.1×10-3 1.3×10-3 1.2×10-3

Fig.1 and Table 1 show that the volatilities of CHF/JPY and EUR/JPY do not differ much. Volatilities of both exchange rates vary little with trading time zone (session). 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 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 EUR/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 0.90 0.90 0.90

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

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

Fig.2: Cross-correlation of CHF/JPY and EUR/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.

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, correlations with non-zero time lag would be of particular importance. The correlation pattern of the European session looks quite different from the rest in Fig.2: there is little next-hour correlation, but on the time scale of up to 5 hours the positive correlation becomes significant. This statement is quantified and supported by comparison with statistical noise in Fig.3.

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

Fig.3: Cross-correlation of CHF/JPY and EUR/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 CHF/JPY and EUR/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.

We inspect significance of the predictive correlation in the CHF/JPY and EUR/JPY exchange rates by comparing it with the expected statistical fluctuations (noise) in Fig.3, as explained in the figure caption. The positive feature in the -5 through -2 -hour lag bins, and symmetric counterpart at the positive lags look significant. The interpretation is that a move in either (due to the symmetry) exchange rate can be used to forecast the other rate. The cross-correlation is seen to turn negative at larger lags, again in a symmetric fashion, although the high level of noise would require a more detailed study with a change in the binning in order to draw a definitive conclusion.

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

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