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

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Written by Forex Automaton   
Monday, 08 September 2008 13:53

Pound Sterling/Japanese Yen and US Dollar/Japanese Yen obviously are positively correlated but on the hour time scale, on average for the period of study, the correlation looks too tight to be of value for forecasting movements in one exchange rate on the basis of the other with any accuracy.

GBP/JPY and USD/JPY volatility comparison

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

Fig.1 and Table 1 show that the volatilities of GBP/JPY and USD/JPY are fairly similar, and in both cases the European trading session is the most volatile. 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 USD/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 0.66 0.57 0.60

GBP/JPY and USD/JPY are positively correlated on average for the period, throughout the three trading sessions studied. Somewhat surprisingly, the correlation is the strongest during the Asia-Pacific trading session.

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

Fig.2: Cross-correlation of GBP/JPY and USD/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, correlation amplitudes at non-zero time lags would be of particular importance. Such correlations are not seen in this pair of exchange rates on the hourly time scale considered. This statement is supported by comparison with martingale simulations (Fig.3) which quantify uncertainty of the correlation measurements.

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

Fig.3: Cross-correlation of GBP/JPY and USD/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 GBP/JPY and USD/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. 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, there is no significant predictive signal in this pair of exchange rates seen on the hour time scale, at least on average for the period studied.

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

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