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

Euro/US Dollar and British Pound/Yen do not seem to share any investment themes. Nevertheless these are correlated currency pairs, with a hint of a leader-follower relationship.

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
hour0.150.160.12

EUR/USD and USD/JPY are weakly correlated on average for the period. The correlation is the least pronounced in the American session.

EUR/USD and GBP/JPY intermarket correlation

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

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 tail of positive correlation to the right of the 0 lag indicates that there is a “tail” of predictable action in EUR/USD lagging behind GBP/JPY. It is seen in the European and American sessions. To judge how reliable it is, one has to compare the signal with the noise level obtained from the martingale simulations.

EUR/USD and GBP/JPY intermarket correlation European session

Fig.2: Cross-correlation of EUR/USD and GBP/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 based on the historical volatilities of EUR/USD and GBP/JPY 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. 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. Based on the level of the noise, betting on EUR/USD following the lead of GBP/JPY seems to be a risky strategy. But if you decide to do that, the European or American session would be the best time.

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/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).

GBP/USD 2002-2008: Predictability Overview

The US Dollar/Pound Sterling currency pair does not show much predictability from the point of view of basic two-point correlation approach adopted in these series of articles, besides the trend repetition signal with a 24-hour-multiple time lag seen in most other currency pairs.

In this report we focus on the period from 00:00 2002-08-20 to 00:00 2008-02-01 (New York time).

GBP/USD autocorrelation 1 hour time-lag bin

Fig.1: Autocorrelation of hourly logarithmic returns in GBP/USD. 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).

The basic autocorrelation

As before we employ autocorrelation as a straightforward, inter-disciplinary, non-proprietary technique to test market efficiency. In Fig.1 we look for features on the time scale of up to 48 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 GBP/USD series, each one constructed to reproduce the measured distribution of returns for GBP/USD for the time period under study (including the fat tails!), 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. The one-hour time lag “contrarian” feature (a significant anticorrelation) we saw on this plot in other currency pairs involving GBP ( GBP/JPY ) and USD ( USD/CAD, AUD/USD ) is not present in the GBP/USD autocorrelation.

GBP/USD autocorrelation 4 hour time-lag bin

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

GBP/USD autocorrelation 12 hour time-lag bin

Fig.3: GBP/USD autocorrelation as in Fig.1, but with time lag bin increased to 12 hours.

In Fig.2, the time lag bin has been increased to 4 hours, and in Fig.3 — to 12 hours. These figures do not reveal any reliable patterns.

24-hour trading cycle.

GBP/USD bullish and bearish autocorrelation

Fig.4: GBP/USD 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 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 periodic 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.

GBP/USD bullish and bearish autocorrelation long range

Fig.4: GBP/USD 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.

Summary

GBP/USD looks like a fairly difficult currency pair to trade on the basis of two-point correlations alone. Long term prospects of GBP/USD 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.

GBP/JPY 2002-2008: Predictability Overview

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

GBP/JPY autocorrelation

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

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.

GBP/JPY autocorrelation

Fig.2: Autocorrelation of hourly logarithmic returns in GBP/JPY constructed with 4-hour bin. The time lag is the lag in “business time” (holidays are excluded).

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.

GBP/JPY bullish and bearish autocorrelation

Fig.3: 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 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.

GBP/JPY bullish and bearish autocorrelation long range

Fig.4: Axes and color codes as in the previous figure. Range expanded compared to the previous figure.

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.