GBP/USD and USD/CHF 2004-2008: symmetric predictive correlation

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Written by Forex Automaton   
Wednesday, 07 January 2009 15:29

The negative correlation peak of Pound Sterling/US Dollar and US Dollar/Swiss Franc, when studied with hour time scale resulution, looks symmetric and wider than one bin. Therefore, either exchange rate may have predictive influence on the other. Of course, this is a time-integrated picture and the time evolution may have more complex structure: the symmetric peak may be composed out of a number of asymmetric ones.

GBP/USD and USD/CHF volatility comparison

Fig.1: comparing volatilities of hour-by-hour logarithmic returns in GBP/USD (top panel) and USD/CHF (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 GBP/USD and USD/CHF in various trading sessions in 2004-2008.

currency pair time scale Asia-Pacific session European session American session
GBP/USD hour 0.96×10-3 1.2×10-3 1.1×10-3
USD/CHF hour 1.1×10-3 1.5×10-3 1.4×10-3

Fig.1 and Table 1 show USD/CHF to be somewhat more volatile compared to GBP/USD, with similar shapes of the logarithmic return distributions. Volatilities of both exchange rates depend on the trading session and are at the minimum during the Asia-Pacific session. 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, with pronounced tails.

Table 2: Pearson correlation coefficient for the time series of logarithmic returns in GBP/USD and USD/CHF in various trading sessions in 2004-2008. Time frames of the sessions are shown in New York time.

time scale Asia-Pacific session European session American session
hour -0.58 -0.66 -0.71

GBP/USD and USD/CHF form a weakly correlated combination in Europe and the Americas and virtually no correlation in the Pacific.

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

Fig.2: Cross-correlation of GBP/USD and USD/CHF, 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 GBP/USD and USD/CHF over the time lag (hours), for the various trading session (time zones). As is often the case, the picture in the vicinity of zero-time lag looks the simplest for the Asia-Pacific session where the peak can not be resolved with the one hour resolution. A comparison with the same analysis performed repeatedly on the random data designed to mimic volatilities of GBP/USD and USD/CHF (Fig.3 below) lets one estimate the accuracy of the correlation measurements, and thus the potential value of these for any hypothetical trading strategy based on intermarket correlations.

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

Fig.3: Cross-correlation of GBP/USD and USD/CHF 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 GBP/USD and USD/CHF 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 feature at the zero time lag. The magnitude of correlation at the -1 hour and +1 hour time lag is comfortably (several standard deviations) above the red background, making the exchange rates in question look mutually predictive. The word of caution is in place: this is a time-averaged picture and an in-depth study of a time evolution of this picture may turn out to be more informative. That is the subject of a special section on the time evolution of forex inefficiencies. The data used are from the period 2004-04-01 00:00:00 to 2008-10-01 00:00:00.

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