EUR/USD 2002-2008: the Fairest Game in Town!

We begin with EUR/USD — the currency pair that keeps making head-lines. We skip the usual charts which the reader can easily find elsewhere and cut to the chase, that is to the specialty of this site — the ability to tell a martingale or a “casino” (or fair game) from the market in which you can profit in a sustainable way.

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

EUR/USD autocorrelation

Fig.1:Autocorrelation of logarithmic hourly returns in EUR/USD. The time lag is the lag is in “business time” (holidays are excluded).

In this figure we look for obvious arbitrage opportunities on the time scale of up to two days — and conclude that these are rather difficult to reliably locate in this particular currency pair. 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/USD series under study, each one constructed to reproduce the measured distribution of returns in EUR/USD for the time period under study (including the fat tails!), but completely devoid of correlations. From these, the expectation and RMS or the autocorrelation amplitude in each time lag bin were calculated. Market’s long-term bias in one direction (in favor of EUR over USD) is seen in the overall positiveness of the Monte Carlo autocorrelation. The level of noise (width of the red band) is dangerously high making it hard to draw reliable conclusions. However, if one is to trust that there is a negative signal for the range of lags from -30 to -14 hours, and a positive one from -14 and up to -6, then the strategy would be to bet on a reversal of the preceding trend which took place during time t-30 through t-14, if supported by dynamics of the past 14 hours. Or in other words if the market went against you 30 to 14 hours ago and changed direction in your favor about 14 hours ago, you are better off betting on such a trend to continue — that’s the dangerously noisy message of this particular autocorrelation.

Even if you can not use this pattern in your favour, not having it against you is part of a smart survival strategy.

24-hour cycle

EUR/USD bullish and bearish autocorrelation

Fig.2: Yellow: correlating only positive hourly returns. Blue: correlating only negative hourly returns.

The striking feature of this plot is the 24 hour cycle of bullish and bearish action, clearly seen as the maxima of the correlation are cleanly 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 pattern is equally strong in all time zones is a question that requires a separate study.

Market memory

EUR/USD bullish and bearish autocorrelation long range

Fig.3: Axes and color codes as in the previous figure. Range expanded compared to the previous figure.

The memory effect seen in the previous figure has a certain life time. This figure shows this life time. The effect definitely persists for as long as 1000 hours or well over a month of trading time. It seems that the bullish memories (more pleasant in case of EURUSD) last somewhat longer as one can see more yellow boxes sticking out on the tail at large lag.


We conclude that EUR/USD for the period 2002-2008 is fairly “efficient” (in the EMH sense) with limited potential in the short term (days). Intelligent trend-following may be a possibility. 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 up-coming articles.