TRY (Turkish Lira) Intermarket Correlation: USD/TRY Follows EUR/JPY

A time-integrated study of hourly time-scale lagged correlation between USD/TRY and EUR/JPY reveals hints of a correlation whereby EUR/JPY leads and TRY/USD follows with a lag on one hour.

Compared to the series of intermarket correlation reports generated in 2008-2009 (not covering Turkish Lira), the new reports adopt a somewhat different approach to statistical uncertainty estimation. Instead of synthesizing mock time series with the volatility distribution of the real ones, producing their autocorrelations (and intermarket correlations), and inferring the uncertainty from a comparison of many such analyses, as was done in 2008-2009, I now infer the uncertainty of the correlation coefficients directly as a standard deviation of the sum, knowing the terms entering the sum. As before, hourly data are used and the quantity correlated is hourly logarithmic return.

The data used cover the period from November 14, 2010 till December 09, 2012.

USD/TRY and EUR/JPY hourly correlation 1.1 USD/TRY and EUR/JPY hourly correlation zoomed 1.2

Fig.1. Correlation in hourly logarithmic returns between USD/TRY and EUR/JPY, 2010-2012. 1.1: Lags from 0 to 200 hours. 1.2: Zooming on the signal. The correlation is normalized so that total correlation corresponds to correlation strength of 1, total anti-correlation — to correlation strength of -1 (see Pearson correlation coefficient).

The time lag between the USD/TRY and EUR/JPY time series is defined as

td = tUSD/TRY – tEUR/JPY.

The negative correlation content in the +1 hour time lag bin is seen with about 2.5 standard deviations. This means that a move (the present analysis is insensitive to the direction of that move) in USD/TRY and time t and a move in EUR/JPY at time t-1 are negatively correlated over the time of observation. This is the same as saying the TRY/USD follows (trails) a movement in EUR/JPY with a lag of one hour. Due to the discrete nature of binning, the actual ticks that create the effect could be separate by a time interval from anything about zero to anything below two hours and still land in the separate adjancent hourly periods, creating a 1-hour lag effect. The average such time interval is one hour.

USD/TRY and EUR/JPY hourly autocorrelations, zoomed

Fig.2. Autocorrelation in hourly logarithmic returns in USD/TRY and EUR/JPY, 2010-2012. The correlation is normalized as in Fig.1.

Speaking of pair trading, when forming a pair of EUR/JPY and USD/TRY, due to the negative correlation, both positions must be held short or long at the same time. The relative weight with which EUR/JPY and USD/TRY enter the pair must be optimized to increase the one-lag correlation with respect to the one at lag zero. Qualitatively speaking, the features around zero in Fig.2 (zero autocorrelation at 1-hour lag in EUR/JPY and negative autocorrelation at 1-hour lag in USD/TRY) will not cancel the feature in Fig.1 (also negative). The resulting pair will be a mean-reverting autocorrelated time series.

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

Australian Dollar/Japanese Yen and Euro/US Dollar are weekly correlated. A positive correlation tail with time lags up to 3 hours is seen indicating that EUR/USD tends to lag behind AUD/JPY.

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

time scale Asia-Pacific session European session American session
hour0.140.130.11

AUD/JPY and EUR/USD are weakly correlated on average for the period. The correlation is the least pronounced in the American session, most pronounced in the Asia-Pacific session.

AUD/JPY and EUR/USD ntermarket correlation

Fig.1: Cross-correlation of AUD/JPY and EUR/USD, 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 left of the 0 lag indicates that there is a “tail” of predictable action in EUR/USD lagging behind AUD/JPY. It is the strongest in the European and American sessions. Even though the Asia-Pacific session has the strongest correlation between the two currency pairs within the 0-lag time bin (see the table), it has the weakest correlation away from 0 and thus must be the worst for forecasting on the basis of this correlation feature.

To judge how reliable the correlation signal at the non-zero lags is, one has to compare the signal with the noise level obtained from the martingale simulations.

AUD/JPY and EUR/USD intermarket correlation European session

Fig.2: Cross-correlation of AUD/JPY and EUR/USD, 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 AUD/JPY and EUR/USD in this trading session.

Fig.2 demonstrates 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, the tail in the first couple of bins to the left of the 0 peak (which means EUR/USD is trailing AUD/JPY) looks like a real effect. We are probably looking at the “risk aversion”/”risk appetite” mood swings where the AUD/JPY having a very strong interest rate differential can indeed lead the show.

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
hour-0.38-0.42-0.43

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.

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/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.

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).

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).

EUR/CHF 2002-2008: Predictability Overview

The Euro / Swiss Franc in 2002-2008 is a currency pair with relatively low volatility. In the medium term (days and weeks), dynamics of EUR/CHF is visibly more random than one would expect on the basis of its long range behaviour — a feature not seen with more volatile currency pairs before.

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

The basic autocorrelation

EUR/CHF correlation 1 hour time-lag bin

Fig.1: Autocorrelation of hourly logarithmic returns in EUR/CHF. 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/CHF market. In Fig.1 we look for features on the time scale of up to two days 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/CHF 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. The one-hour time lag “contrarian” feature (a significant anticorrelation) we saw in this type of plot for other currency pairs involving CHF ( CHF/JPY) and EUR ( EUR/AUD ) is quite strong in the EUR/CHF autocorrelation. The autocorrelation being an average of a product of hourly returns taken with a lag, this 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/CHF, like 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.

EUR/CHF is the currency pair where the martingale simulation “prescribes” an overall positive correlation — a feature which we have not seen pronounced so strongly with other currency pairs in this series of reviews. Its visibility is underscored by the overall relatively low volatility of EUR/CHF with consequently tighter noise range (width of the red band in the figures). The autocorrelation for the lag ranges we have probed is inconsistent with such a “prescription”. Therefore, short range dynamics of EUR/CHF 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/CHF correlation 4 hour time-lag bin

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

24-hour trading cycle.

EUR/CHF bullish and bearish autocorrelation

Fig.3: EUR/CHF 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 24-hour correlation feature alone is not a prediction strategy. ) Needless to say, this effect is not present in the simulated martingale data.

Note that whether this trend following pattern in all time zones is equally strong is a question that requires a separate study focusing on the best time zones for trend following in EUR/CHF.

EUR/CHF bullish and bearish autocorrelation long range

Fig.4: EUR/CHF 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 higher amplitude whenever the base currency commands 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. In case of EUR/AUD where the interest rate differenctial favors the quote currency, the “bullish” correlation is stronger. These two observations can be summarized in one sentence: the closing of long positions in a high yield currency can be a correlated and thus a relatively predictable process. 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/CHF is unlikely to be an exception, and indeed EUR commands an interest-rate premium with respect to CHF 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.

Summary

The EUR/CHF 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. EUR/CHF is not completely “efficient” from the point of view of basic two-point correlation analysis. Long term prospects of EUR/CHF 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).

EUR/AUD 2002-2008: Specific Patterns Of Trading Sessions

This article develops one of the themes in the EUR/AUD predictability overview, namely that of the daily cyclic pattern of market action. We analyze the patterns time zone by time zone — with curious insights into market dynamics.

For the purpose of analysis we define three time windows (or zones). Expressed in New York time, they are

  • Australasia (Asia-Pacific): 7pm-6am
  • Eurasia (from Near East to London; for simplicity we may also call these Old World traders Europeans, which is what they likely mostly are): 1am-12pm
  • America (South and North Americas, including West Coast): 8am-8pm

The labeled time intervals are inclusive, that is, e.g., 1am-12pm refers to a series of 12 time intervals, each 1 hour long, ending respectively at 1am, 2am, and so on through 12pm New York time. As the time series consists of logarithmic returns, the first item is always a return with respect to an hour which precedes the beginning of the series.

EUR/AUD bulls correlation short range

Fig.1:   Autocorrelation of hourly logarithmic returns in EUR/AUD for the time zones labeled using New York time and explained in text. The time lag is in “business time” (periods without update ticks are excluded).

In the figures below we show sub-sampled “bullish” and “bearish” autocorrelations, with further restriction of the time zone on the data. It is impossible to interpret the “bullish” and “bearish” autocorrelations without either the counterpart trend reversal autocorrelations or the total autocorrelation. Therefore we start with the total autocorrelation (Fig.1) where all the nontrivial structures are at least order of magnitude lower than the amplitudes of the oscillations in the bullish and bearish components (Fig.2). This means that to the first order, the oscillations in Fig.2 and 3 are caused by the daily oscillations of market activity. The features in Fig.1 should be compared to the Fig.2 of the EUR/AUD predictability review — it turns out that the individual sessions are much more correlation-rich than the overall picture.

EUR/AUD bulls correlation short range

Fig.2: Autocorrelation of positive hourly logarithmic returns in EUR/AUD for the time zones labeled using New York time and explained in text. The time lag is in “business time” (periods without update ticks are excluded). “America: random” shows a martingale   simulation time series subjected to the same time zone selection as “America”, but devoid of correlations (and time zone variation) by construction.

Fig.1 and 2 focus on the autocorrelations with time lags of 120 hours and less which would correspond to the time scale of interest to a day trader or a swing trader. Both “bullish” and “bearish” autocorrelations show spikes for Eurasian and Australasian trading sessions — with a remarkable difference of a roughly opposite phase! In other words, the minima of the Australasia correlation roughly correspond to the maxima of the Eurasian one, and vice versa. A simple explanation of this would be the time difference between the peaks of the trading activity in the Atlantic and Pacific regions, with most activity coinciding with the European afternoon. The time difference is 9 hours between London and Sidney and 8 hours between London and Tokyo. It is interesting that the histogram for the American session is fairly flat on the short time scale (time lags < 100 hours).

EUR/AUD bulls correlation extended time lag axis

Fig.3: Autocorrelation of positive hourly logarithmic returns in EUR/AUD for the time zones labeled using New York time and explained in text. The time lag is in “business time” (periods without update ticks are excluded).

In Fig.3 we extend the time lag axis — and see quite an interesting and unexpected change of picture. American traders do follow the developments which took place more than 100 hours ago, as seen from their histogram becoming spiky for the time lags over 100 hours. Moreover, their histogram becomes spiky in phase with that of the Australian and Pacific Asian traders, while spikes in the Eurasian histogram undergo a half a day change in phase and the pattern adjusts itself to the other two. (Peaks at -420 (17.5×24), -396 (16.5×24), -372 (15.5×24) and so on common to all three time windows are clearly seen.) Even if the oscillation itself and the phase difference between different trading sessions can be explained by the fact that the maximum of action occurs during a particular (Atlantic) trading session, the change of phase can not be explained so easily.

Perhaps the right interpretation is the following: short range trends are determined during the Atlantic session but on a longer range the markets shift the attention to look at the Pacific session for the guidance.

In this analysis, we used data from from 00:00 2002-08-20 to 00:00 2008-02-01 (New York time).