EUR/AUD and GBP/USD 2002-2008: intermarket correlations

User Rating: / 2
PoorBest 
Written by Forex Automaton   
Thursday, 07 August 2008 14:03

The pair of Euro/Australian Dollar and Pound Sterling/US Dollar exchange rates is one of those combinations whose correlation varies strongly among the trading session, being at the minimum during the Asia-Pacific trading session. With the hour time scale studied in this note, and talking of the European and American trading sessions, there is little predictive power in this cross-correlation as the confidently visible signal is limited to the 0-hour time lag. The Asia-Pacific session looks intriguing in that despite the overall very low 0-hour correlation, there are interesting signals with time lags.

EUR/AUD and GBP/USD volatility comparison

Fig.1: comparing volatilities of hour-by-hour logarithmic returns in EUR/AUD (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 EUR/AUD and GBP/USD in various trading sessions in 2002-2008.

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

Fig.1 and Table 1 show that, not surprisingly, GBP/USD is least volatile 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 CHF/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 0.048 0.13 0.13

EUR/AUD and GBP/USD are positively correlated on average for the period, throughout the three trading sessions studied, but the correlation being at the minimum during the Asia-Pacific session.

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

Fig.2: Cross-correlation of EUR/AUD 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.

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. In particular, one needs to compare the observed correlation amplitudes in the vicinity of the zero time-lag peak with the expectations from a totally random process.

EUR/AUD and GBP/USD intermarket correlation 1 hour time-lag bin with uncertainty estimate, European session

EUR/AUD and GBP/USD intermarket correlation 1 hour time-lag bin with uncertainty estimate, Asia-Pacific session

Fig.3: Cross-correlation of EUR/AUD and GBP/USD shown against the backdrop of statistical noise (red). The noise is obtained from martingale simulations based on the recorded volatilities of EUR/AUD and GBP/USD in the specific 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. Top: European (Eurasian) trading. Bottom: Asia-Pacific (Australasian) trading.

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 between the EUR/AUD and GBP/USD exchange rates by comparing it in Fig.3 with the random fluctuations expected on the basis of efficient market assumption, as explained in the figure caption. Curiously, in the Asia-Pacific session (bottom plot), the negative signal in the -1 hour bin is fairly strong compared to both the noise (measurement inaccuracy) and the 0-time lag correlation peak. It looks as though EUR/AUD is sending a "follow me" signal to USD/GBP (not the GBP/USD). It is not easy to rule this out as caused by a singular or rare occurrence, since the Asia-Pacific session is the one with very little volatility overall, as shown in Fig.1 and Table 1. It will be interesting to trace the time dependence of this signal. Similar features (correlations surrounding the 0 time-lag peak, but of the opposite polarity) have been seen in other combinations of exchange rates: for example, AUD/JPY and EUR/AUD. These are hard to interpret with confidence.

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

Bookmark with:

Deli.cio.us    Digg    reddit    Facebook    StumbleUpon    Newsvine