From the predictability point of view, the Pound Sterling/Yen currency pair resembles the Australian Dollar/US Dollar and Australian Dollar/Yen pairs analyzed before and its patterns are similar to but not as strong as in AUD/JPY.

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 this figure we look for arbitrage opportunities on the time scale of up to two days (corresponding to day trading or swing trading) — and like in AUD/USD and AUD/JPY, there is a negative autocorrelation seen for the time lag up to an hour. 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 GBP/JPY series, each one constructed to reproduce the measured distribution of returns for GBP/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.

Now to the main non-random feature here: the negative correlation signal at one hour lag overshoots the level of noise by a factor large enough to make it look significant. The autocorrelation being an average of a product of hourly returns taken with a lag, its 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 GBP/JPY price quote is *a lot* more jittery than what “financial theorists” who preach market efficiency (expecting this plot to be similar to what is represented by the red band) believe.

Because trend reversals on the time scale of one hour or less happen either too often or are too lucrative, GBP/JPY may well be the market where winning strategy requires being a clever contrarian. In the next figure, we increase the time lag bin to four hours 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 — but the signal of trend repetition with a 14- to 18-hour lag is barely above the level of noise and must be judged as too risky to rely on. It is remarkable however that all currency pairs looked at so far ( EUR/USD, AUD/USD, and AUD/JPY ) had a positive autocorrelation bump (trend repetition signal) of varying strength but above noise level for the time lags from 6 to 18 hours in the four-hour time bin plot like this figure.

### 24-hour trading cycle. Trader memory effect.

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 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.)

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

### Summary

We conclude that while the GBP/JPY market is definitely not a random walk, this is not the easiest market to trade on the basis of the two-point correlations alone. 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.