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

Euro/US Dollar and Pound Sterling/US Dollar are obviously correlated currency pairs. Due to the symmetry of the cross-correlation peak, a move in either pair can in principle be used to predict a move in the other: EUR/USD foretells GBP/USD and vice versa.

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

time scale Asia-Pacific session European session American session
hour0.660.730.76

The Asia-Pacific session shows the least correlation between the two currency pairs.

EUR/USD and GBP/USD intermarket correlation

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

Fig.1 shows the intermarket correlation with one hour time scale and the range of lags of up to 12 hours, of interest to a day trader. The positive peak at the zero hour lag tells you that the currencies are correlated, or move in tandem. The height of the peak showing strength of the correlation varies session to session, we present the information textually in the table. The peak seems to be more than one bin wide, except for the Asia-Pacific session. The symmetry of the peak means that while it is true that a move in EUR/USD is followed by a move in the same direction in GBP/USD, it is equally true that an up or down move in GBP/USD may be followed by an up or a down move in EUR/USD. The market reaction is not instantaneous and it may take up to a couple of hours for the adjustment to finish (not true in the Asia-Pacific session). For trading EUR/USD and GBP/USD on the basis of the intermarket correlation strategy, the European and American sessions are the best time.

EUR/USD and USD/JPY 2002-2008: Intermarket Correlations (Leader-Follower)

Euro/US Dollar and US Dollar/Yen are obviously anticorrelated currency pairs. But, which one is the leader and which one is the follower? How long do the markets take to work out the anticorrelation? If the adjustment is not instantaneous, can one currency be used to predict the other?

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

time scale Asia-Pacific session European session American session
hour-0.40-0.53-0.55

EUR/USD and USD/JPY are, understandably, anticorrelated. What is not so obvious is the observation that the anticorrelation is the least pronounced in the Asia-Pacific session.

EUR/USD and USD/JPY intermarket correlation

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

In Fig.1, there is one feature worth noticing: that is the bin with the time lag -1. It is negative but not as negative as the time lag 0. But while time lag 0 can not be used for prediction, time lag -1 (as any non-zero time lag) can. We define lag as time for the market 1 minus time for the market 2. In this case, time for EUR/USD minus time for USD/JPY. A positive correlation at a certain time lag tells you: “same thing happens in two markets with a certain time lag”. A negative correlation at a certain time lag tells you “markets are doing the opposite thing with a certain time lag”. The fact that most of the correlation is concentrated at the 0 lag means that the correlation (reported in the table) works out mostly on the time scale of up to 1 hour. The time bin to the left of the 0 lag indicates that there is a “tail” of predictable action lagging behind. Finally the most important thing: time lag -1 hour means that EUR/USD is leading and USD/JPY is following — in the European and American but not the Asia-Pacific session.

EUR/USD and USD/JPY intermarket correlation compared with noise

Fig.2: Cross-correlation of EUR/USD and USD/JPY, 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 respecting the volatilities of EUR/USD and USD/JPY in this particular trading session.

As Fig.2 demonstrates, the main challenge while working with trading session-specific correlations is the non-linear (although quite predictable) behaviour of the noise level with time lag. This can not be ignored otherwise one risks over-interpreting the picture. The area around zero is fairly safe since the noise is at the minimum when the lag is at an integer number of days. The conclusion about the leader and follower currency pair, drawn on the basis of the asymmetry of the central peak, is significant despite the noise. For trading EUR/USD and USD/JPY on the basis of the intermarket correlation strategy, European and American trading sessions are the best time.

European (Eurasian) Trading Session

Forex trading sessions are loosely defined since there is no centralized market place in forex. In these forex trading system and forecasting studies we define trading sessions which are at least 13 hours long each (so that the time lag can be from 0 to 12). In our usage the Eurasian trading session is the period of time from the trading hour ending at 1am to the trading hour ending at 1pm New York time, or 2pm to 2am Tokyo time respectively, or 6am to 6m London time respectively.

American Trading Session

Forex trading sessions are loosely defined since there is no centralized market place in forex. In these forex trading system and forecasting studies we define trading sessions which are at least 13 hours long each. In our usage the Eurasian trading session is the period of time from the trading hour ending at 8am to the trading hour ending at 8pm New York time, or 9pm to 9am Tokyo time respectively, or 1pm to 1am London time respectively.

Asia-Pacific (Australasian) Trading Session

Forex trading sessions are loosely defined since there is no centralized market place in forex. In these forex trading system and forecasting studies we define trading sessions which are at least 13 hours long each (so that the time lag is between 0 and 12 full hours). In our usage the Pacific Asian trading session is the period of time from the trading hour ending at 7pm to the trading hour ending at 7am New York time, or 8am to 8pm Tokyo time respectively, or 12am to 12am London time.

Pearson Correlation Coefficient

Pearson correlation coefficient (or Pearson coefficient) between x and y is defined by:

Cov[x,y]/(Var[x]Var[y])1/2

where Cov(x,y) is covariance and Var(x) is variance.

For the forex time series we analyze, the mean is typically at least two orders of magnitude smaller than the RMS. For this reason we often neglect the mean. Then, Cov[x,y] is simply the amplitude of the zero-lag bin of the cross-correlation function and Var[x] is the amplitude of the zero-lag bin of the autocorrelation function. When dealing with covariance alone, one does not know whether its change reflect the change in the strength of correlation between x and y or in strength of their independent variation. Pearson correlation coefficient allows one to analyse the tightness of the correlation between two quantities as such, leaving aside the question of the overall strength of their variation (correlated or not).

EUR/JPY 2002-2008: Predictability Overview

With the basic two-point correlation approach to the Euro/Japanese Yen currency pair we see the asymmetry between the bullish and bearish trends reflecting the interest rate differential, like in most other currency pairs, and the 24-hour oscillation of activity.

The interest rate differential has been in favor of the Euro.

The basic autocorrelation

EUR/JPY correlation 1 hour time-lag bin

Fig.1: Autocorrelation of hourly logarithmic returns in EUR/JPY. The time lag is in “business time” (periods without update ticks are excluded). The red band shows the level of noise as iferred from martingale simulations (see text).

As usual we apply autocorrelation analysis as a straightforward, inter-disciplinary, non-proprietary technique to test market efficiency in the EUR/JPY market. In Fig.1 we look for features on the time scale of up to a hundred hours such as to suit the time scale of 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 EUR/JPY series, each one constructed to reproduce the measured distribution of returns for the time period under study, but completely devoid of correlations ( martingale time series ). From these, the expectation and RMS or the autocorrelation amplitude in each time lag bin were calculated. Against this background, we see no reliable correlation signals in the all time-zone integrated autocorrelation.

EUR/JPY correlation 4 hour time-lag bin

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

24-hour trading cycle.

EUR/JPY bullish and bearish autocorrelation

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

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 returns respectively. The 24 hour cycle of market 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 a 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. Needless to say, this effect is not present in the simulated martingale data. However, strictly speaking, this is not a prediction mechanism in itself because it does not take into account similar oscillations of the trend reversal.

EUR/JPY bullish and bearish autocorrelation long range

Fig.4: EUR/JPY 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.

Similar patterns have been seen before with most other currency pairs in this series of predictability reviews. It is interesting to note that typically, such correlation has higher amplitude whenever “bearish” refers to the currency with a higher interest rate. This has been seen with AUD/USD, AUD/JPY, USD/JPY, GBP/JPY, USD/CAD, (although the interest rate differential has not been that high, it is in favor of USD), CHF/JPY, EUR/AUD and EUR/CHF. While in the case of classic carry-trade currency pairs such as AUD/JPY this has been associated with the unwinding of the carry-trade, the underlying mechanism is likely to be similar for other currency pairs. The case of EUR/JPY is unlikely to be an exception, and indeed EUR commands an interest-rate premium with respect to JPY for the period under study.

The fact that one can read the sign of interest rate differential off the public forex quotes via basic correlation analysis indeed goes against the efficient market dogma as it indicates that despite large liquidity such interest rate differentials are not completely discounted by the markets and there remain profit opportunities for algorithmic trading — even though it remains to be demonstrated that knowledge of such an asymmetry can be transformed into an advantage in the actual trading.

Summary

EUR/JPY is fairly but not completely “efficient” from the point of view of the basic, time-zone integrated two-point correlation analysis. Long term prospects of EUR/JPY 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. In this report we used data for the period from 00:00 2002-08-20 to 00:00 2008-02-01 (New York time).

Why “Bullish” and “Bearish” Autocorrelations

Here are some further thoughts on the “bearish” and “bullish” autocorrelations.

  1. This is not, strictly speaking, a prediction tool because such representation of the data omits one important aspect of the picture — probability of trend reversals. The full two-point set can be split into subset of

    1. “bull-bull”,
    2. “bear-bear” but also
    3. “bull-bear” and
    4. “bear-bull” autocorrelations.

    I call a and b “trend following” and c,d “trend reversal” autocorrelations.

  2. The latter two also have the 24-hour cycle pattern which when combined with that of the “bull-bull” and “bear-bear”, gives the resulting, much more flat, full autocorrelation. For qualitative understanding, one can look at the total autocorrelation and either a,b or c,d since a,b can be deduced given the total and c,d. Likewise, c,d can be deduced given the total and a,b.

  3. The separation of “bullish” and “bearish” autocorrelations does reveal two important time scales which would otherwise remain hidden in the total autocorrelation: the 24-hour time scale and the less trivial “market memory” time scale.

  4. The separation of the “trend following” autocorrelations reveals the trend asymmetry associated with the interest rate differential. One can tell which currency of the pair has a higher interest rate by comparing the two “trend following” autocorrelations. I argue that this is an indication of a market inefficiency but it remains to be demonstrated that such an asymmetry can be reliably exploited to generate speculative profit.

  5. One can argue that once “inside” a long time trend, the relevant trend-following autocorrelation approaches the “total”. But if you know a priori what is and what is not a trend, that may be all you need.

EUR/GBP 2002-2008: Predictability Overview

From the point of view of two-point correlation analysis, the Euro/Pound Sterling exchange rate shows patterns which look similar to EUR/AUD.

During the period we consider (2002-2008), the BOE’s official bank rate was between 3.5 and 5.75% while the ECB’s key interest rate went from 2.25 to 3%.

The basic autocorrelation

EUR/GBP correlation 1 hour time-lag bin

Fig.1: Autocorrelation of hourly logarithmic returns in EUR/GBP. The time lag is in “business time” (periods without update ticks are excluded). The red band shows the level of noise as iferred from martingale simulations (see text).

As before we employ autocorrelation as a straightforward, inter-disciplinary, non-proprietary technique to test market efficiency in the EUR/GBP market. In Fig.1 we look for features on the time scale of up to 100 hours such as to suit the time scale of 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 EUR/GBP series, each one constructed to reproduce the measured distribution of returns for the time period under study, but constructed to be free of correlations (the so-called martingale time series). 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 in this type of plot for other currency pairs involving GBP ( GBP/JPY ) and EUR ( EUR/AUD, EUR/CHF ) is quite strong in the EUR/GBP autocorrelation. Moreover the width of the anticorrelation deep is not limited to just one time bin — the effect has a larger correlation length than usually seen. The autocorrelation being an average of a product of hourly returns taken with a lag, its negativity means that we are way too frequently (more frequently than in the corresponding martingale time series) taking a product of opposite sign returns for this time lag— or that the product of the opposite sign returns by far outweighs that of the same sign returns for this time lag. Because trend reversals on the time scale of about one hour happen either too often or are too lucrative, EUR/GBP, like EUR/CHF, EUR/AUD, GBP/JPY, AUD/USD and AUD/JPY analyzed before, may well be the market where winning strategy requires being a contrarian on a short time scale.

Like EUR/CHF, EUR/GBP is the currency pair where the martingale simulation “prescribes” an overall positive correlation. Its visibility is underscored by the overall relatively low volatility of EUR/GBP with consequently tighter noise range (width of the red band in the figures). As seen best in Fig.2, the autocorrelation for the lag ranges we have probed is inconsistent with such a “prescription”. Therefore, short range dynamics of EUR/GBP is quite different from what is prescribed by its long term “investment theme”. As always, one should not trade this pair short-range on the basis of long-range considerations alone.

EUR/GBP correlation 4 hour time-lag bin

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

24-hour trading cycle.

EUR/GBP bullish and bearish autocorrelation

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

Next we split the full time series into “bullish” and “bearish” samples to examine correlations within those — in hope that this provides better insights into the mechanisms of decision making and trader psychology. These samples are simply sets of hourly time intervals (not necessarily contiguous) with an upward or downward trend. 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 returns 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 this 24-hour correlation feature alone is not a prediction strategy. ) Needless to say, this effect is not present in the simulated martingale data, although bullish and bearish trends and rallies occur there as well.

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

EUR/GBP bullish and bearish autocorrelation long range

Fig.4: EUR/GBP 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.

Similar patterns have been seen before with most other currency pairs in this series of predictability reviews. It is interesting to note that typically, the “bearish” correlation has a higher amplitude whenever the base currency is the currency with a higher interest rate. This has been seen with AUD/USD, AUD/JPY, USD/JPY, GBP/JPY, USD/CAD, (although the interest rate differential has not been that high, it is in favor of USD), AUD/USD, CHF/JPY, and EUR/CHF.

In case of EUR/AUD, and now EUR/GBP, where the quote currency has a higher interest rate, the “bullish” correlation has a higher amplitude. Obviously this is the manifestations of the same effect: selling of a higher yild currency tends to be more predictable.

The fact that one can read the sign of interest rate differential off the public forex quotes via basic correlation analysis indeed goes against the efficient market dogma as it indicates that despite large liquidity such interest rate differentials are not completely discounted by the markets and there remain profit opportunities for algorithmic trading.

Summary

The EUR/GBP currency pair has been showing a “contrarian” trend reversal tendency in addition to the trend repetition signal with a 24-hour-multiple time lag seen in most other currency pairs. Like many other currency pairs we inspected, EUR/GBP is not completely “efficient” from the point of view of basic two-point correlation analysis. Long term prospects of EUR/GBP 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. In this report we used data for the period from 00:00 2002-08-20 to 00:00 2008-02-01 (New York time).

Trading System

In our usage, a trading system is an alogorithm to decide what, when, and with what allocation of capital needs to be bought or sold to maximize profit and minimize risk. Such decisions are made regularly and are based on a variety of input data, reflecting the changing market environment and prior history. The adequate level of complexity is high enough to require that a trading system be implemented as a computer program. The tasks of order execution may but do not need to fall into the scope of a trading system in our usage of the word.

Under conditions of complete market efficiency (when price quote time series is a martingale) there is no need for a trading system in our sense of the word — Modern Portfolio Theory will suffice. In some contexts the meaning of the term is reduced to denote an electronic or computer system that merely executes external orders, rather than generates them.

One may argue (as does Taleb) that everyday human experience which emphasizes cooperation in a more or less deterministic environment prepares us poorly for survival in the markets which are random to a very high degree. Our brain may be poorly equipped to deal with the randomness, let alone detect those traces of predictability and order which do exist in it. A response to this challenge may be to use higher faculties of our brain to build trading systems around abstract concepts (which are beyond the reach of computers) and then leave to computers the execution of routine decision making (counting odds) according to those systems.

Developing, back-testing and marketing buy-side trading systems for the forex traders is the main goal of the Forex Automaton™ project.

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