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

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Written by Forex Automaton   
Tuesday, 08 July 2008 14:40

Australian Dollar/Japanese Yen and US Dollar/Japanese Yen are positively correlated currency pairs. The non-zero time lag features of the correlation function seen in this currency pair combination appear to be only marginally significant with the hour-by-hour time scale.

AUD/JPY and USD/JPY volatility comparison

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

currency pair time scale Asia-Pacific session European session American session
AUD/JPY hour 1.5×10-3 1.7×10-3 1.6×10-3
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 AUD/JPY and USD/JPY differ, although not by much. Volatilities of both exchange rates vary little with trading time zone (session). As always in forex, the distributions of logarithmic returns are not "bell-shaped", are strongly non-Gaussian. A lot more appropriate model for the tails would be an exponent, as the tails look roughly linear on the logarithmic scale. This implies that a good model of returns themselves (not the logarithms) would be 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 AUD/JPY and USD/JPY in various trading sessions in 2002-2008.

time scale Asia-Pacific session European session American session
hour 0.55 0.50 0.49

AUD/JPY and USD/JPY are significantly correlated on average for the period. It is unusual to see the correlation coefficient to be the strongest in the Asia-Pacific session.

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

Fig.2: Cross-correlation of AUD/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, correlations with non-zero time lag would be of particular importance. It is these correlations that allow us to make forecasts. It seems that the negative amplitudes surrouding the zero time lag bin in Fig.2 are little bit too strong and symmetric to look random, especially for the American session. In Fig.3 we compare the signals with noise estimates obtained from martingale simulations.

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

Fig.3: Cross-correlation of AUD/JPY and USD/JPY for the American trading session shown against the backdrop of statistical noise (red). The noise is obtained from martingale simulations based on the recorded volatilities of AUD/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.

Comparison with noise in Fig. 3 shows that the negative signals surrounding zero time lag are at best marginally significant.

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

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