EUR/GBP and AUD/JPY 2002-2008: another minimally correlated combination

User Rating: / 4
PoorBest 
Written by Forex Automaton   
Tuesday, 16 September 2008 13:53

Euro/Pound Sterling and Australian Dollar/Japansese Yen form an interesting combination where delayed correlation amplitude (representing AUD/JPY lagging behind GBP/EUR) happens to be as strong as the "instantaneous" correlation. The weak "instanteneous" correlation rivals AUD/USD and EUR/CHF previously identified as the least correlated forex pair. The statistical lagging of a stronger interest rate differential exchange rate such as AUD/JPY behing GBP/EUR is unusual. Good to know.

EUR/GBP and AUD/JPY volatility comparison

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

currency pair time scale Asia-Pacific session European session American session
EUR/GBP hour 0.76×10-3 0.93×10-3 0.79×10-3
AUD/JPY hour 1.5×10-3 1.7×10-3 1.6×10-3

Fig.1 and Table 1 show that the volatilities of EUR/GBP and AUD/JPY are quite different, EUR/GBP being, along with EUR/CHF, among the least volatile of the floating exchange rates. Some decrease in the volatility of EUR/GBP 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.

Table 2: Pearson correlation coefficient for the time series of logarithmic returns in EUR/GBP and AUD/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 -0.018 -0.013 -0.11

The correlation coefficients in EUR/GBP and AUD/JPY are negative and so week one would have to discriminate the significance of these measurements against random market expectation, as is done in Fig.3.

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

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

Fig.2 presents the cross-correlation of EUR/GBP and AUD/JPY over the time lag (hours). Even in at the 0 time lag, correlation is barely there. A comparison with the same analysis performed repeatedly on the random data designed to mimic volatilities of EUR/GBP and AUD/JPY lets one estimate the accuracy of the correlation measurements, see Fig.3 below.

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

Fig.3: Cross-correlation of EUR/GBP and AUD/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 EUR/GBP and AUD/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 you can see even the zero time lag signal is merely 2 standard deviations away from zero.

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