Forex Automaton

We use autocorrelation to quantify market inefficiency. The autocorrelation function is an old, common knowledge method which anybody with access to the data can in principle apply. Therefore it is perfect for demonstration in that we do not reveal any proprietary know-how by using it, yet it is quite convincing as it relates directly to the concept of a martingale.

The autocorrelation is defined as the expectation value of the product

A(T)=E[x(t),x(t+T)]|_{over all available t}

where T is time lag. Most often we will be dealing with autocorrelation of logarithmic returns. Unless stated otherwise, the time lag we show is the lag in "business time" or in other words, week-end and holiday periods (periods with no data) are excluded.

By construction, an autocorrelation is symmetric around 0. Therefore, plotting only one side (either positive or negative lags) is sufficient. Because in most contexts we talk about prediction, it is more intuitive to plot the negative lag side -- that way one can interpret the axis of lags as a time axis, keeping in mind that what is about to happen (and is being predicted) is located at the 0 bin. Although in reality -- and this needs to be said for the more rigorous reader -- this axis is a diagonal direction of fixed time sums in the two-dimensional space of pairs of time points.

Forex Automaton™ has accumulated a collection of non-trivial autocorrelation data for the forex markets. We regard their existence as a sufficient, but not a necessary condition of predictability. Therefore, we do not suggest building a trading system bottom-up on the basis of autocorrelations (otherwise we would not make them public), and at least this is not what we did. But once the autocorrelations are found, ignoring them would be foolish.

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