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.

NZD/USD 2005-2008: Predictability Overview

The correlation patterns we see in one of the world’s most volatile exchange rates, the New Zealand Dollar/US Dollar exchange rate, are very similar to those seen in AUD/JPY.

The interest rate differential has been in favor of the New Zealand Dollar.

The basic autocorrelation

NZD/USD autocorrelation 1 hour time-lag bin

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

As before we employ autocorrelation as a straightforward, inter-disciplinary, non-proprietary technique to test market efficiency in the NZD/USD market. In Fig.1 we look for features on the time scale of up to two days such as to suite 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 NZD/USD series, each one constructed to reproduce the measured distribution of returns for the time period under study (including the fat tails!), but completely devoid of correlations (martingale time series). 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 in this type of plot for other currency pairs involving USD ( AUD/USD ) is quite strong in the NZD/USD autocorrelation. It is noteworthy that the negative feature around 0 is more than one bin wide, it involves the -3 hour bin as well. 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 — or that the product of the opposite sign returns by far outweighs that of the same sign returns. Because trend reversals on the time scale of one to three hours happen either too often or are too lucrative, NZD/USD, like 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.

A group of time lag bins 12-24 hours away from show a significantly positive correlaiton. In other words, the currency pair has a tendency to repeat its moves 12-24 hours after they happened — a feature worth a closer look as a forecasting mechanism.

Bull/bear asymmetry in NZD/USD

NZD/USD bullish and bearish autocorrelation

Fig.3: NZD/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, clearly seen in most other currency pairs, is not well pronounced here for some reason. In this regard, NZD/USD is similar to AUD/JPY.

Typically, the “bearish” correlation has a higher amplitude whenever the base currency has 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/JPY, EUR/CHF. Conversely, the “bullish” correlation has a higher amplitude whenever the quote currency has a higher interest rate, as seen with EUR/AUD and EUR/GBP. While in the case of classic carry-trade currency pairs such as AUD/JPY I associated this feature with the unwinding of the carry-trade, the underlying mechanism is likely to be similar for other currency pairs. It seems, you can “jump on the bandwagon” of selling a high yield currency with more confidence than doing the opposite, as the higher amplitude and a bump in the NZD-bearish plot demonstrate.

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 and 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 NZD/USD currency pair has been showing a “contrarian” trend reversal tendency which is likely to be part of a stable wave-like pattern. Therefore, NZD/USD is not completely “efficient” from the point of view of basic two-point correlation analysis. Long term prospects of NZD/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. In this report we use data for the period from 00:00 2005-08-16 to 00:00 2008-02-01 (New York time).

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.

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.

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.

Summary

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.

USD/JPY 2002-2008: Predictability Overview

The US Dollar/Yen currency pair is another case of a relatively efficient market. While there are hints of non-trivial correlations, these remain hints and not reliable signals one could use for forecasting — at least not with the basic two-point correlation approach we stick with in this series of articles.

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/JPY autocorrelation 1 hour time-lag bin

Fig.1: Autocorrelation of hourly logarithmic returns in USD/JPY. 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 two days (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/JPY series, each one constructed to reproduce the measured distribution of returns for USD/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. 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 not present in USD/JPY.

It looks like there could be 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 Elliott waves if that theory has predictive power). It is not well pronounced with this binning and we redo the plot (and recalculate the noise level) with 4-hour and 8-hour binning (Fig.2 and Fig.3, respectively).

USD/JPY autocorrelation 4 hour time-lag bin

Fig.2: Autocorrelation as in Fig.1, but with time lag bin increased to 4 hours.

USD/JPY autocorrelation 8 hour time-lag bin

Fig.3: Similar to Fig.1 and 2, but with time lag bin increased to 8 hours.

With increased time-lag bin and the increased span of time lags as shown in Fig. 2 and 3, this periodicity signal remains marginally significant.

24-hour trading cycle.

USD/JPY bullish and bearish autocorrelation

Fig.4: 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 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/JPY bullish and bearish autocorrelation long range

Fig.5: 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.

As seen previously with other currency pairs involving Yen ( GBP/JPY and AUD/JPY ), being bullish on Yen as a way of trend following makes more sense than being bearish on Yen on the same basis — this is seen from the fact that the USD/JPY-bearish (JPY-bullish) correlation function (blue in the figures) has a confidently higher amplitude.

Summary

We conclude that while the USD/JPY market is not a random walk, this is not the easiest market to trade on the basis of the two-point correlations alone. Bullish trend-following on Yen makes more sense than bullish-trend following on USD, based on the comparison of the sub-sampled correlations in Fig.4 and 5. 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.

AUD/USD 2002-2008: Predictability Overview

The AUD/USD currency pair has been characterized by a high interest rate differential; indeed Australian Dollar is one of the highest-yielding currencies which creates very interesting patterns related to the famous phenomenon of carry-trade — and its violent unwinding.

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: try catching a falling knife!

AUD/USD autocorrelation

Fig.1:Autocorrelation of hourly logarithmic returns in AUD/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 (corresponding to day trading or swing trading) — and there is one thing that’s quite spectacular. 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 AUD/USD series, each one constructed to reproduce the measured distribution of returns for AUD/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.

Now to the main non-random feature here: the huge negative correlation signal at one hour lag overshoots the level of noise by a huge factor. The autocorrelation being an average of a product of hourly returns taken with a lag, this 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 AUD/USD 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, AUD/USD 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.

AUD/USD autocorrelation

Fig.2:Autocorrelation of hourly logarithmic returns in AUD/USD 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 — and it seems that there is a stronger-than-random repetition of a trend with a 6- to 10-hour lag (from the previos figure, it’s probably 6 to 7).

AUD/USD bullish and bearish autocorrelation

Fig.3: 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 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.

But there is something more: note the dramatic difference between bullish and bearish histograms. The bearsih (blue), besides exhibiting cyclic oscillations with a 24-hour period, shows a lot of correlation around 0 peak. This is most likely related to the phenomenon of carry-trade unwinding. The carry trades in the period under study are funded by borrowing in low-interest currencies like JPY and CHF and converting into high-yielding ones like AUD and NZD. These positions build up over time but once opened, the owners have a common interest in being able to close with a profit. Because of that, these positions tend to be closed over short time periods driving JPY and CHF up and AUD and NZD down (through excessive demand and supply, respectively) — and as a side effect, the AUD/USD rate goes down as well when this happens. What the plot shows is that once the AUD retreat began, it’s a safe bet that that the dynamics will continue for up to two days. This is not true with AUD rallies!

AUD/USD bullish and bearish autocorrelation long range

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

The 24-hour period effect seen in the previous figures 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.

Summary

We conclude that attempts to “beat the market” with AUD/USD on the time scale of day-trading should work: this is not a “fair game” by any stretch of imagination! Strategies should focus on trend reversals and detection of carry-trade unwinding. 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. Cross-correlations with currency pairs involving NZD, CHF and JPY will likely be among the most interesting ones.