EUR/USD and USD/CAD 2002-2008: Intermarket Correlations (Symmetric Predictive)

Euro / US Dollar and US Dollar/ Canadian Dollar present another example of symmetrically cross-anticorrelated currency pairs.

Table: Pearson correlation coefficient for the time series of logarithmic returns in EUR/USD and USD/CAD in various trading sessions in 2002-2008.

time scale Asia-Pacific session European session American session

EUR/USD and USD/CAD are anticorrelated on average for the period. The anticorrelation is the least pronounced in the Asia-Pacific session.

EUR/USD and USD/CAD intermarket correlation

Fig.1: Cross-correlation of EUR/USD and USD/CAD, derived from the hour-by-hour logarithmic returns, for the three trading sessions.

The fact that most of the anticorrelation is concentrated at the 0 lag bin means that the anticorrelation (reported in the table) works out mostly on the time scale of up to 1 hour. The peak seems to be more than one bin wide, except for perhaps the Asia-Pacific session. In Fig.2, we show statistical significance of the signal.

EUR/USD and USD/CAD intermarket correlation European session

Fig.2: Cross-correlation of EUR/USD and USD/CAD, derived from the hour-by-hour logarithmic returns, for the European (Eurasian) trading session shown against the backdrop of statistical noise (red). The noise is obtained from martingale simulations based on the historical volatilities of EUR/USD and USD/CAD in this particular trading session.

As Fig.2 demonstrates, the main challenge while working with trading session-specific correlations is the non-flat (although quite predictable) behaviour of the noise level with time lag. The symmetry of the peak means that while it is true that a move in EUR/USD foretells an opposite direction move in USD/CAD, it is equally true that an upward or downward move in USD/CAD foretells a downward or upward move in EUR/USD, respectively. (As always on this site, “foretells” should be understood in the statistical sense). The market reaction is not instantaneous. But the width of the peak lets one estimate how much time the markets take to play out their recation: it may take up to a couple of hours for the adjustment to fully finish (not true in the Asia-Pacific session) — significant signals with two-hour lags are confidently visible in Fig.2.

Data from 2002-08-20 through 2002-02-01 were used in this report.

USD/CAD 2002-2008: Predictability Overview

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

USD/CAD autocorrelation 1 hour time-lag bin

Fig.1:Autocorrelation of hourly logarithmic returns in USD/CAD. The time lag is in “business time” (holidays are excluded). The red band shows the level of noise as iferred from martingale simulations (see text).

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.

USD/CAD autocorrelation 4 hour time-lag bin

Fig.2: USD/CAD autocorrelation as in Fig.1, but with time lag bin increased to 4 hours.

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.

USD/CAD bullish and bearish autocorrelation

Fig.3: USD/CAD bullish and bearish autocorrelations. Yellow: correlating only positive hourly returns. Blue: correlating only negative hourly returns.

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.

USD/CAD bullish and bearish autocorrelation long range

Fig.4: USD/CAD bullish and bearish autocorrelations. Axes and color codes as in the previous figure. Range expanded compared to the previous figure to show the characteristic time length of this market memory effect.

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.


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.