The correlation patterns we see in Australian Dollar/Yen have many similarities to AUD/USD but AUD/JPY should be easier to predict and trade as some of the important patterns are more pronounced.

In this report we focus on the period from 00:00 2002-08-20 to 00:00 2008-02-01 (New York time).

### Volatility. Fat tails.

For this currency pair, AUD/JPY, for the first time in this series of reviews we show a histogram of hourly logarithmic returns. It is similar to other currency pairs and you can find similar plots in the literature (for example, McCauley .)

For the option traders this is, in a sense, almost the final product as their business consists essentially in calculating probabilities and pricing the options accordingly (very much like insurance business). You can run a profitable insurance business without ability to predict events. The reason *we do* reproduce this here is to demonstrate which returns are contained in the data (gray histogram) and in the simulation (red crosses) used to judge statistical significance of the autocorrelation features in the subsequent plots. Large spikes (in case of erroneous data) in the hourly quote data (up and then down, or down and then up) could easily create artifacts like the anticorrelation with one-hour lag we see, but would create distant outliers distributed almost symmetrically around zero in Fig.1. Fig.1 (with no entries outside the range shown) boosts our confidence that the noise level shown in Fig.2 and 3 correctly accounts for the actual volatility, and that the anticorrelations we see are real.

### Trend predictability

In this figure we look for trading opportunities on the time scale of up to two days (corresponding to day trading or swing trading) — and, like in AUD/USD, there is one thing that’s quite spectacular. The hatched red band shows the range of statistical noise (namely its expectation plus minus its RMS deviation). Statistical noise was obtained by simulating 20 independent time series of the length corresponding to that of the AUD/JPY series, each one constructed to reproduce the measured distribution of returns for AUD/JPY for the time period under study (including the fat tails — see Fig.1), but completely devoid of correlations. From these, the expectation and RMS or the autocorrelation amplitude in each time lag bin were calculated.

Now to the main non-random feature here: the huge anticorrelation signal at one hour lag overshoots the level of noise by a huge factor. The autocorrelation being an average of a product of hourly returns taken with a lag, this negativity means that we are way too frequently taking a product of opposite sign returns — or that the product of the opposite sign returns far outweighs that of the same sign returns. In other words, the AUD/JPY price quote is *a lot* more spiky than what “financial theorists” who preach market efficiency (expecting this plot to be similar to what is represented by the red band) believe — and spikier than AUD/USD.

Because trend reversals on the time scale of one hour or less happen either too often or are too lucrative, AUD/JPY, like AUD/USD analyzed before, may well be the market where winning strategy requires being a clever contrarian. And as we did for AUD/USD, we increase the time lag bin to four hours in Fig. 3 to try and see if we can locate a trigger signal — something that could alert you to take a contrarian position with more confidence.

Now the negative correlation is absorbed in the 0 peak — and it seems that there is a stronger-than-random repetition of a trend with a 14- to 18-hour lag. Compared to what we saw in the corresponding figure of the AUD/USD review, we see a much more robust trend repetition signal here.

Fig. 4 shows another surprise: the 24-hour period of bullish and bearish action seen in the AUD/USD and EUR/USD reports is not visible for AUD/JPY.

A similarity to AUD/USD (and something not seen in EUR/USD) is the long-range correlation of the bearish plot (probably related to the carry-trade unwinding). As in AUD/USD, you usually have several hours to “jump on the bandwagon” of the AUD/JPY bears relatively safely and possibly ride it for a couple of days or so (seen from the broadness of the blue peak in Fig.5).

### Summary

We conclude that attempts to “beat the market” with AUD/JPY on the time scale of day-trading should work: this is not a “random walk” by any stretch of imagination! Strategies should focus on trend reversals and detection of carry-trade unwinding. Long term prospects of this currency pair are the subject of fundamental analysis and are outside the scope of this article. Cross-correlations with other markets are to be discussed in up-coming articles — obviously cross-correlations with currency pairs involving NZD and CHF are the most interesting ones.