AUD/JPY and EUR/JPY 2002-2008: (trivial) intermarket correlations

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Written by Forex Automaton   
Thursday, 03 July 2008 13:59

Australian Dollar/Japanese Yen and Euro/Japanese Yen are correlated currency pairs. For the period under study, the correlation is limited to the 1-hour wide 0 time-lag bin.

AUD/JPY and EUR/JPY volatility comparison

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

Fig.1 shows how much more volatile AUD/JPY is, compared to EUR/JPY. Volatilities of both exchange rates vary little with trading time zone (session). Needless to say, the distributions 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. For the returns themselves (not the logarithms) this implies a distribution close to 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 scales of interest to such a trader) but so far we know nothing about our ability to make forecasts.

Table 2: Pearson correlation coefficient for the time series of logarithmic returns in AUD/USD and EUR/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 0.64 0.63

AUD/JPY and EUR/JPY are significantly correlated on average for the period. Looking at the 0-hour time lag, which is what the table represents, the correlation is the least pronounced in the American session, most pronounced in the Asia-Pacific session (unusual).

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

Fig.1: Cross-correlation of AUD/JPY and EUR/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 trading system development, correlations with non-zero time lag would be of particular importance. It is these correlations that allow us to make forecasts. Ability to detect them depends, among other things, on the time scale of the analysis (minute-by-minute, hour, day and so on) and signal to noise ratio. Alas, Fig.2 and Fig.3 (European session compared with martingale noise) present no indication of such correlations for this currency pair combination, given the level of uncertainty represented by the red band. The conclusion is dependent on the scale of the analysis used, this is the conclusion for the one-hour bin.

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

Fig.3: Cross-correlation of AUD/JPY and EUR/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 AUD/JPY and EUR/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.

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

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