CHF/JPY and GBP/JPY 2002-2008: (trivial) intermarket correlations

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Written by Forex Automaton   
Wednesday, 23 July 2008 12:54

Swiss Franc/Japanese Yen and Pound Sterling/Japanese Yen cross-rates share the quote currency and are correlated. The picture of the intermarket correlation over the time lag resembles that of the CHF/JPY and EUR/JPY, but the non-trivial features are weaker and we do not see predictive potential on the hour-by-hour time scale considered, from this pair of cross-rates.

CHF/JPY and GBP/JPY volatility comparison

Fig.1: comparing volatilities of hour-by-hour logarithmic returns in CHF/JPY (top panel) and and GBP/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 GBP/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
GBP/JPY hour 1.2×10-3 1.4×10-3 1.2×10-3

Fig.1 and Table 1 show that the volatilities of CHF/JPY and GBP/JPY do not differ much but GBP/JPY has been slightly more volatile. 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 (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 CHF/JPY and GBP/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 0.69 0.66 0.69

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

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

Fig.2: Cross-correlation of CHF/JPY and GBP/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 more pronounced, which resembles the case of CHF/JPY and EUR/JPY. Unlike the CHF/JPY and EUR/JPY however the positive correlation is not pronounced enough to confidently beat the statistical noise, as seen from the comparison with the noise in Fig.3.

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

Fig.3: Cross-correlation of CHF/JPY and GBP/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 GBP/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 GBP/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 -3 -hour lag bins, and its symmetric counterpart at the positive lags look only marginally significant. Therefore the bottom line has to be that there is no predictive correlations in this pair of exchange rates for the one hour time scale considered -- this conclusion is dependent on the time scale.

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

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