GBP/JPY and GBP/USD 2002-2008: intermarket correlations

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Written by Forex Automaton   
Tuesday, 02 September 2008 16:00

The case of Pound Sterling/Japanese Yen and Pound Stering/US Dollar shows some marginally significant predictability in the latter rate on the basis of the former. For some reason, the signal is only seen in the European trading session. A candidate for a deeper study.

GBP/JPY and GBP/USD volatility comparison

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

currency pair time scale Asia-Pacific session European session American session
GBP/JPY hour 1.2×10-3 1.4×10-3 1.2×10-3
GBP/USD hour 0.94×10-3 1.2×10-3 1.1×10-3

Fig.1 and Table 1 show that the volatilities of GBP/JPY and GBP/USD are similar. Some decrease in the volatility of GBP/USD is seen 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. 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 GBP/JPY and GBP/USD 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 0.50 0.50 0.42

GBP/JPY and GBP/USD are positively correlated on average for the period, throughout the three trading sessions studied. Surprisingly, the correlation seems to weaken somewhat during the American session.

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

Fig.2: Cross-correlation of GBP/JPY and GBP/USD, 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/JPY and GBP/USD 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. To the left of the middle peak, there is a group of bins with the correlation amplitudes in the European session which stand out as a group and attract attention being collectively above the "grass" of mostly random fluctuations in other bins and trading sessions. These are located at the time lags ranging from -6 through -1 hours. What's unusual is the fact that these are seen to occur only in the European trading session. A comparison with the same analysis performed repeatedly on the random data designed to mimic volatilities of GBP/JPY and GBP/USD lets one estimate the accuracy of the correlation measurements and thus potential value of these for any hypothetical trading strategy based on intermarket correlations. Such a comparison is presented in Fig.3 below.

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

Fig.3: Cross-correlation of GBP/JPY and GBP/USD 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/JPY and GBP/USD 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, what looks like a group of predictive signals at the negative time lags is in fact merely 2-3 standard deviations above the reference (uncorrelated time series with the volatilities of the real ones) at each individual bin. It can hardly be dismissed as a group but it is not clear why this behavior is not seen in other trading sessions (Fig.2). Clearly this is not the most spectacular case of forex intermarket predictability. But it is of the "right" kind in a sense that a rate with a larger interest rate differential would show the way to the one with a smaller differential.

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

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