The US Dollar/Canadian Dollar currency pair demonstrates some of the strongest cyclic patterns we’ve seen in the forex markets reviewed so far. This market must be an Elliott wave analyst’s delight, at least on the time scales of several days.

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 a hundred hours (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/CAD series, each one constructed to reproduce the measured distribution of returns for USD/CAD for the time period under study (including the fat tails!), but completely devoid of correlations ( martingales ). From these, the expectation and RMS of 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 present in the USD/CAD autocorrelation, and in fact it looks like it’s wider than an hour — at least the -3 bin has a signal almost as strong as the -1 bin. Translating into human language, this means that for better or worse, predictable trend reversals happen with a time lag more than an hour.

Fairly confidently we see 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 Elliot waves if that theory has predictive power). To have a better look at it we redo the plot (and recalculate the noise level) with 4-hour binning (see Fig.2), and extended time lag span.

The maxima lie in the [-166;-169] bin, the [-142;-145] bin, the [-118;-121] bin, the [-94;-97] bin, so one would expect the next maximum to lie in the [-70;-67] bin, and indeed that bin is pretty high, but the bump gets broader and the local maximum does not lie in this bin (and do not forget about noise level which is shown in the red). Similarly, the [-46;-42] bin is high but not the local maximum. The next maximum is, predictably at the [-22; -18] bin. It’s quite obvious how one could program a trading system to look for the market movements in the time intervals separated from the moment one is trying to forecast by the numbers just specified and count the instances of up and down trends and place a bet for the future based on their combined vote. Moreover one could look for significant negative minima of the autocorrelation in this plot, and similarly see what *their* respective trends *vote against*.

### 24-hour trading cycle.

In Fig.3 we again 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.

Not surprisingly the US Dollar bears seem to repeat their actions daily (24-hour cycle) for a lot longer than their opponents; the amplitude of the 24-hour cycle effect is very strong compared to other currency pairs. Perhaps this is related to the fact that both USA and Canada cover the same time zones.

### Summary

USD/CAD seems to be a poster child market for swing trading based on correlation techniques. Long term prospects of USD/CAD 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.