GBP/USD and USD/CAD 2002-2008: leader-follower correlation

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Written by Forex Automaton   
Tuesday, 09 September 2008 14:02

The case of Pound Stering/US Dollar and US Dollar/Canadian Dollar presents another leader-follower relationship. Naturally, GBP/USD and USD/CAD generally move in the opposite directions (showing negative correlations), what tends to "follow" GBP/USD is CAD/USD.

GBP/USD and USD/CAD volatility comparison

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

currency pair time scale Asia-Pacific session European session American session
GBP/USD hour 0.94×10-3 1.2×10-3 1.1×10-3
USD/CAD hour 0.88×10-3 1.4×10-3 1.3×10-3

Fig.1 and Table 1 show that the USD/CAD is generally more volatile than GBP/USD. Both exchange rates, and especially USD/CAD, show considerably less volatility 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/USD and USD/CAD 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 -0.31 -0.35 -0.37

GBP/USD and USD/CAD are negatively correlated on average for the period, throughout the three trading sessions studied. Understandably, the correlation is weaker somewhat during the Asia-Pacific session. This echoes the volatility trend noted in Table 1 although technically these are independent quantities.

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

Fig.2: Cross-correlation of GBP/USD and USD/CAD, 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/CAD 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. Indeed, looking at the European session, the correlation amplitudes at time lags -1 and -2 hours look promising in that they seem to be forming a tail of the peak extending into the area of negative time lags (according to our definition, time lags are

t1-t2

where "1" denotes GBP/USD and "2"-- USD/CAD. Thus, a negative correlation value at a negative time lag means that statistically there is a tendency for exchange rate "2" to do the opposite to exchange rate "1" at a later time.) A comparison with the same analysis performed repeatedly on the random data designed to mimic volatilities of GBP/USD and USD/CAD 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. Such a comparison is presented in Fig.3 below.

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

Fig.3: Cross-correlation of GBP/USD and USD/CAD 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/CAD 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 time lag 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 tail of the negative peak extending into negative time lags (-1 and -2 hours) is 3-4 standard deviations above the reference (uncorrelated time series with the volatilities of the real ones). This means that the "leadership" of GBP/USD with respect to CAD/USD is confirmed. Speaking of LIBORs, recall that for the period under study (2002-08-20 to 2008-02-01) the difference of LIBORs was generally higher between GBP and USD than it was between USD and CAD, although the former difference varied more strongly. A deeper study of the dependence of the correlation values at the time lags where such values emerge to be non-zero on average would go a long way towards understanding intermarket correlations in forex, since LIBORs appear to move in highly predictable patterns on a longer time scale. So far one can say that the "leadership" of an exchange rate with a higher interest-rate differential is also confirmed in multiple other cases studied in these series of notes.

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

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