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/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).

EUR/AUD 2002-2008: Predictability Overview

The Euro / Australian Dollar in 2002-2008 is a nice, textbook-clear case demonstrating what kinds of stable patterns one may expect in the currency markets, although none of the patterns seen with the two-point correlation analysis are unique to this currency pair.

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

The basic autocorrelation

EUR/AUD correlation 1 hour time-lag bin

Fig.1: Autocorrelation of hourly logarithmic returns in EUR/AUD. 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/AUD market. 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 EUR/AUD 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 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 AUD ( AUD/JPY and AUD/USD ) is quite strong in the EUR/AUD autocorrelation. It is noteworthy that the negative feature around 0 is more than one bin wide. 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 about one hour happen either too often or are too lucrative, EUR/AUD, 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. We increase the time lag bin to four hours in Fig. 2 to try to get a nicer picture of what seems to be a positive correlation (trend repetition) signal at -20 hours.

EUR/AUD correlation 4 hour time-lag bin

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

In Fig.2, the time lag bin has been increased to 4 hours. The “contrarian” feature around 0 remains visible. There is a couple of positive bins in the time lag range from -22 to -18. We have seen such features in other currency pairs, with a varying degree of confidence, and with a varying time lag with respect to 0. Here in EUR/AUD it looks reasonably significant and can be interpreted in the following way: a trend is likely to repeat itself with an 18-22 hour lag, regardless of whether this trend is up or down.

24-hour trading cycle.

EUR/AUD bullish and bearish autocorrelation

Fig.3: EUR/AUD 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 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. (See why this 24-hour correlation feature is not in itself a forecasting 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 time-zone specifics in trend following.

EUR/AUD bullish and bearish autocorrelation long range

Fig.4: EUR/AUD 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 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), and CHF/JPY. 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/AUD is not an exception, but this case is the opposite to the ones just mentioned in that the high interest currency — the Australian Dollar (aussie) — is the quote currency of the currency pair. As with other high yield currencies, you can “jump on the bandwagon” of selling AUD with more confidence than doing the opposite, as the higher amplitude and a bump in the AUD-bearish (EUR-bullish) 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 EUR/AUD currency pair has been showing a “contrarian” trend reversal tendency which may be part of a wave-like pattern. Therefore, EUR/AUD is not completely “efficient” from the point of view of basic two-point correlation analysis. Long term prospects of EUR/AUD 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 2002-08-20 to 00:00 2008-02-01 (New York time).

AUD/JPY 2002-2008: Predictability Overview

The correlation patterns we see in Australian Dollar/Yen have many similarities to AUD/USD but AUD/JPY should be easier to predict and trade as some of the important patterns are more pronounced.

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

Volatility. Fat tails.

For this currency pair, AUD/JPY, for the first time in this series of reviews we show a histogram of hourly logarithmic returns. It is similar to other currency pairs and you can find similar plots in the literature (for example, McCauley .)

For the option traders this is, in a sense, almost the final product as their business consists essentially in calculating probabilities and pricing the options accordingly (very much like insurance business). You can run a profitable insurance business without ability to predict events. The reason we do reproduce this here is to demonstrate which returns are contained in the data (gray histogram) and in the simulation (red crosses) used to judge statistical significance of the autocorrelation features in the subsequent plots. Large spikes (in case of erroneous data) in the hourly quote data (up and then down, or down and then up) could easily create artifacts like the anticorrelation with one-hour lag we see, but would create distant outliers distributed almost symmetrically around zero in Fig.1. Fig.1 (with no entries outside the range shown) boosts our confidence that the noise level shown in Fig.2 and 3 correctly accounts for the actual volatility, and that the anticorrelations we see are real.

AUD/JPY logarithmic return

Fig.1: Distribution of hourly logarithmic returns in the AUD/JPY exchange rate. Gray histogram: actual data. Red crosses: same distribution obtained from the correlation-free time series synthesized to mimic the AUD/JPY returns (20 independent simulated time series) and used in Fig.2 and Fig.3

Trend predictability

AUD/JPY autocorrelation

Fig.2:Autocorrelation of hourly logarithmic returns in AUD/JPY. The time lag is the lag is in “business time” (holidays are excluded).

In this figure we look for trading opportunities on the time scale of up to two days (corresponding to day trading or swing trading) — and, like in AUD/USD, 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/JPY series, each one constructed to reproduce the measured distribution of returns for AUD/JPY for the time period under study (including the fat tails — see Fig.1), 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 anticorrelation 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/JPY price quote is a lot more spiky than what “financial theorists” who preach market efficiency (expecting this plot to be similar to what is represented by the red band) believe — and spikier than AUD/USD.

Because trend reversals on the time scale of one hour or less happen either too often or are too lucrative, AUD/JPY, like AUD/USD analyzed before, may well be the market where winning strategy requires being a clever contrarian. And as we did for AUD/USD, we increase the time lag bin to four hours in Fig. 3 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/JPY autocorrelation

Fig.3:Autocorrelation of hourly logarithmic returns in AUD/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 — and it seems that there is a stronger-than-random repetition of a trend with a 14- to 18-hour lag. Compared to what we saw in the corresponding figure of the AUD/USD review, we see a much more robust trend repetition signal here.

AUD/JPY bullish and bearish autocorrelation

Fig.4: Yellow: correlating only positive hourly returns. Blue: correlating only negative hourly returns.

AUD/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.

Fig. 4 shows another surprise: the 24-hour period of bullish and bearish action seen in the AUD/USD and EUR/USD reports is not visible for AUD/JPY.

A similarity to AUD/USD (and something not seen in EUR/USD) is the long-range correlation of the bearish plot (probably related to the carry-trade unwinding). As in AUD/USD, you usually have several hours to “jump on the bandwagon” of the AUD/JPY bears relatively safely and possibly ride it for a couple of days or so (seen from the broadness of the blue peak in Fig.5).

Summary

We conclude that attempts to “beat the market” with AUD/JPY on the time scale of day-trading should work: this is not a “random walk” 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 up-coming articles — obviously cross-correlations with currency pairs involving NZD and CHF are the most interesting ones.

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.