The Euro / Australian Dollar in 2002-2008 is a nice, textbook-clear case demonstrating what kinds of stable patterns one may expect in the currency markets, although none of the patterns seen with the two-point correlation analysis are unique to this currency pair.

The interest rate differential has been in favor of the Australian Dollar.

### The basic autocorrelation

As before we employ autocorrelation as a straightforward, inter-disciplinary, non-proprietary technique to test market efficiency in the EUR/AUD market. In Fig.1 we look for features on the time scale of up to 48 hours such as to suit the time scale of day trading or swing trading. 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 EUR/AUD series, each one constructed to reproduce the measured distribution of returns for the time period under study (including the fat tails!), but completely devoid of correlations ( martingale time series ). From these, the expectation and RMS or the autocorrelation amplitude in each time lag bin were calculated. The one-hour time lag “contrarian” feature (a significant anticorrelation) we saw in this type of plot for other currency pairs involving AUD ( AUD/JPY and AUD/USD ) is quite strong in the EUR/AUD autocorrelation. It is noteworthy that the negative feature around 0 is more than one bin wide. The autocorrelation being an average of a product of hourly returns taken with a lag, this negativity means that we are way too frequently (more frequently than in the corresponding martingale time series) taking a product of opposite sign returns — or that the product of the opposite sign returns by far outweighs that of the same sign returns. Because trend reversals on the time scale of about one hour happen either too often or are too lucrative, EUR/AUD, like GBP/JPY, AUD/USD and AUD/JPY analyzed before, may well be the market where winning strategy requires being a contrarian on a short time scale. We increase the time lag bin to four hours in Fig. 2 to try to get a nicer picture of what seems to be a positive correlation (trend repetition) signal at -20 hours.

In Fig.2, the time lag bin has been increased to 4 hours. The “contrarian” feature around 0 remains visible. There is a couple of positive bins in the time lag range from -22 to -18. We have seen such features in other currency pairs, with a varying degree of confidence, and with a varying time lag with respect to 0. Here in EUR/AUD it looks reasonably significant and can be interpreted in the following way: a trend is likely to repeat itself with an 18-22 hour lag, regardless of whether this trend is up or down.

### 24-hour trading cycle.

In Fig.3 we construct autocorrelations of the subsamples of the full time series (the “bullish” and “bearish” ones) selected by taking only positive and negative returns respectively. The 24 hour cycle of bullish and bearish action is again clearly seen as the maxima of the correlation are located at multiples of the 24 hour lag: 24, 48, 72, 96, 120 hours and so on. Therefore, smart trend following means something more than following a trend that existed in the near past. It means following a trend that existed this time of the day yesterday, the day before yesterday, and so on — that gives you a better than average chance of winning! Conversely, buying because the currency went up 12 hours ago (or selling because it went down 12 hours ago), *all the rest being equal*, is the least recommended strategy. (See why this 24-hour correlation feature is not in itself a forecasting strategy .) Needless to say, this effect is not present in the simulated martingale data.

Note that whether this trend following pattern in all time zones is equally strong is a question that requires a separate study focusing on the time-zone specifics in trend following.

Similar patterns have been seen before with most other currency pairs in this series of predictability reviews. It is interesting to note that typically, the “bearish” correlation has a higher amplitude whenever the base currency has a higher interest rate. This has been seen with AUD/USD , AUD/JPY, USD/JPY, GBP/JPY, USD/CAD, (although the interest rate differential has not been that high, it is in favor of USD), and CHF/JPY. While in the case of classic carry-trade currency pairs such as AUD/JPY this has been associated with the unwinding of the carry-trade, the underlying mechanism is likely to be similar for other currency pairs. The case of EUR/AUD is not an exception, but this case is the opposite to the ones just mentioned in that the high interest currency — the Australian Dollar (aussie) — is the quote currency of the currency pair. As with other high yield currencies, you can “jump on the bandwagon” of selling AUD with more confidence than doing the opposite, as the higher amplitude and a bump in the AUD-bearish (EUR-bullish) plot demonstrate.

The fact that one can read the sign of interest rate differential off the public forex quotes via basic correlation analysis indeed goes against the efficient market dogma and indicates that despite large liquidity such interest rate differentials are not completely discounted by the markets and there remain profit opportunities for algorithmic trading.

### Summary

The EUR/AUD currency pair has been showing a “contrarian” trend reversal tendency which may be part of a wave-like pattern. Therefore, EUR/AUD is not completely “efficient” from the point of view of basic two-point correlation analysis. Long term prospects of EUR/AUD are the subject of fundamental analysis and are outside the scope of this article. Cross-correlations with other markets are to be discussed in the up-coming articles. In this report we use data for the period from 00:00 2002-08-20 to 00:00 2008-02-01 (New York time).