The US Dollar/Yen currency pair is another case of a relatively efficient market. While there are hints of non-trivial correlations, these remain hints and not reliable signals one could use for forecasting — at least not with the basic two-point correlation approach we stick with in this series of articles.

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

### Trend predictability

In Fig.1 we look for features on the time scale of up to two days (corresponding to 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 USD/JPY series, each one constructed to reproduce the measured distribution of returns for USD/JPY for the time period under study (including the fat tails!), but completely devoid of correlations ( martingales ). 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 on this plot in other currency pairs involving JPY ( GBP/JPY and AUD/JPY ) is not present in USD/JPY.

It looks like there could be another, larger scale, zigzag pattern in Fig.1 with a period close to a day (24 hours.) (It is this type of pattern one would expect to see for Elliott waves if that theory has predictive power). It is not well pronounced with this binning and we redo the plot (and recalculate the noise level) with 4-hour and 8-hour binning (Fig.2 and Fig.3, respectively).

With increased time-lag bin and the increased span of time lags as shown in Fig. 2 and 3, this periodicity signal remains marginally significant.

### 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 returnds 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 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 the sub-sample correlation feature is not in itself a prediction strategy.) Needless to say, this effect is not present in the simulated martingale data.

Note that whether this oscillation pattern is equally strong in all time zones is a question that requires a separate study.

As seen previously with other currency pairs involving Yen ( GBP/JPY and AUD/JPY ), being bullish on Yen as a way of trend following makes more sense than being bearish on Yen on the same basis — this is seen from the fact that the USD/JPY-bearish (JPY-bullish) correlation function (blue in the figures) has a confidently higher amplitude.

### Summary

We conclude that while the USD/JPY market is not a random walk, this is not the easiest market to trade on the basis of the two-point correlations alone. Bullish trend-following on Yen makes more sense than bullish-trend following on USD, based on the comparison of the sub-sampled correlations in Fig.4 and 5. 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 the up-coming articles.