Forex Automaton

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.

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.

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.

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.

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