Here are some further thoughts on the “bearish” and “bullish” autocorrelations.

This is not, strictly speaking, a prediction tool because such representation of the data omits one important aspect of the picture — probability of trend reversals. The full two-point set can be split into subset of

- “bull-bull”,
- “bear-bear” but also
- “bull-bear” and
- “bear-bull” autocorrelations.

I call a and b “trend following” and c,d “trend reversal” autocorrelations.

The latter two also have the 24-hour cycle pattern which when combined with that of the “bull-bull” and “bear-bear”, gives the resulting, much more flat, full autocorrelation. For qualitative understanding, one can look at the total autocorrelation and either a,b or c,d since a,b can be deduced given the total and c,d. Likewise, c,d can be deduced given the total and a,b.

The separation of “bullish” and “bearish” autocorrelations does reveal two important time scales which would otherwise remain hidden in the total autocorrelation: the 24-hour time scale and the less trivial “market memory” time scale.

The separation of the “trend following” autocorrelations reveals the trend asymmetry associated with the interest rate differential. One can tell which currency of the pair has a higher interest rate by comparing the two “trend following” autocorrelations. I argue that this is an indication of a market inefficiency but it remains to be demonstrated that such an asymmetry can be reliably exploited to generate speculative profit.

One can argue that once “inside” a long time trend, the relevant trend-following autocorrelation approaches the “total”. But if you know a priori what is and what is not a trend, that may be all you need.