Forex Automaton

Australian Dollar/US Dollar and Euro/Australian Dollar are negatively correlated currency pairs. However the correlation is a function of a time lag. A surprising feature of the their correlation is the positive next-hour correlation. In the hour-by-hour data, a movement in AUD/USD may foretell a same direction next hour movement in EUR/AUD next hour and vice versa.

AUD/USD and EUR/AUD are negatively correlated on average for the period, therefore sometimes to simplify the language we will talk about AUD/USD and AUD/EUR being correlated. Looking at the 0-hour time lag, which is what the table represents, the correlation is more pronounced in the Asia-Pacific session (unusual!), less pronounced in the European and American session.

The fact that most of the negative 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 are of particular importance. It is these correlations that allow us to make forecasts, and they are visible in the figure. The correlation signals in the bins adjacent to the 0-time-lag bin are quite strong and positive. This statement is quantified and supported by comparison with statistical noise in Fig.2.

We inspect significance of the predictive correlation in the AUD/USD and EUR/AUD exchange rate by comparing with the expected statistical fluctuations (noise) in Fig.2, as explained in the figure caption. The signals in the -1 hour and +1 hour time lag bins look quite comfortably significant. Their interpretation is as follows: AUD/USD leads and EUR/AUD follows in the same direction within 0 to 2. hours, or EUR/AUD leads and AUS/USD follows. I say within 0 to 2. hours despite the fact that we are looking at the 1 hour time lag because if the moves are such that one happens at the end of an hour, and the other -- at the very beginning of the next hour, they are separated by almost 0 time lag and yet they belong to the different time bins. They will contribute to a pattern with a one-hour time difference despite the actual separation being a lot smaller.

Fig.3 shows correlations on a longer scale. It seems that between 14 and 22 hour lags, the positive correlation gives way to a negative one, in other words the currencies again behave as one would naively expect. You can also note the striking symmetry of these features with respect to the sign of time lag, meaning that either pair can be used to predict the other.

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

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