EUR/JPY 2002-2008: Predictability Overview

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

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

The basic autocorrelation

EUR/JPY correlation 1 hour time-lag bin

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

As usual we apply autocorrelation analysis as a straightforward, inter-disciplinary, non-proprietary technique to test market efficiency in the EUR/JPY market. In Fig.1 we look for features on the time scale of up to a hundred hours such as to suit the time scale of day trading or swing trading. The hatched red band shows the range of statistical noise (namely its expectation plus minus its RMS deviation). Statistical noise was obtained by simulating 20 independent time series of the length corresponding to that of the EUR/JPY series, each one constructed to reproduce the measured distribution of returns for the time period under study, but completely devoid of correlations ( martingale time series ). From these, the expectation and RMS or the autocorrelation amplitude in each time lag bin were calculated. Against this background, we see no reliable correlation signals in the all time-zone integrated autocorrelation.

EUR/JPY correlation 4 hour time-lag bin

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

24-hour trading cycle.

EUR/JPY bullish and bearish autocorrelation

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

In Fig.3 we construct autocorrelations of the subsamples of the full time series (the “bullish” and “bearish” ones) selected by taking only positive and negative returns respectively. The 24 hour cycle of market action is again clearly seen as the maxima of the correlation are located at multiples of the 24 hour lag: 24, 48, 72, 96, 120 hours and so on. Therefore, smart trend following means something more than following a trend that existed in the near past. It means following a trend that existed this time of the day yesterday, the day before yesterday, and so on — that gives you a better than average chance of winning. Conversely, buying because the currency went up 12 hours ago (or selling because it went down 12 hours ago), all the rest being equal, is the least recommended strategy. Needless to say, this effect is not present in the simulated martingale data. However, strictly speaking, this is not a prediction mechanism in itself because it does not take into account similar oscillations of the trend reversal.

EUR/JPY bullish and bearish autocorrelation long range

Fig.4: EUR/JPY bullish and bearish autocorrelations. Axes and color codes as in the previous figure. Range expanded compared to the previous figure to show the characteristic time length of this market memory effect.

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

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

Summary

EUR/JPY is fairly but not completely “efficient” from the point of view of the basic, time-zone integrated two-point correlation analysis. Long term prospects of EUR/JPY are the subject of fundamental analysis and are outside the scope of this article. Cross-correlations with other markets are to be discussed in the up-coming articles. In this report we used data for the period from 00:00 2002-08-20 to 00:00 2008-02-01 (New York time).

Why “Bullish” and “Bearish” Autocorrelations

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

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

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

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

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

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

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

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

EUR/GBP 2002-2008: Predictability Overview

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

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

The basic autocorrelation

EUR/GBP correlation 1 hour time-lag bin

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

As before we employ autocorrelation as a straightforward, inter-disciplinary, non-proprietary technique to test market efficiency in the EUR/GBP market. In Fig.1 we look for features on the time scale of up to 100 hours such as to suit the time scale of day trading or swing trading. The hatched red band shows the range of statistical noise (namely its expectation plus minus its RMS deviation). Statistical noise was obtained by simulating 20 independent time series of the length corresponding to that of the EUR/GBP series, each one constructed to reproduce the measured distribution of returns for the time period under study, but constructed to be free of correlations (the so-called martingale time series). From these, the expectation and RMS or the autocorrelation amplitude in each time lag bin were calculated.

The one-hour time lag “contrarian” feature (a significant anticorrelation) we saw in this type of plot for other currency pairs involving GBP ( GBP/JPY ) and EUR ( EUR/AUD, EUR/CHF ) is quite strong in the EUR/GBP autocorrelation. Moreover the width of the anticorrelation deep is not limited to just one time bin — the effect has a larger correlation length than usually seen. The autocorrelation being an average of a product of hourly returns taken with a lag, its negativity means that we are way too frequently (more frequently than in the corresponding martingale time series) taking a product of opposite sign returns for this time lag— or that the product of the opposite sign returns by far outweighs that of the same sign returns for this time lag. Because trend reversals on the time scale of about one hour happen either too often or are too lucrative, EUR/GBP, like EUR/CHF, EUR/AUD, GBP/JPY, AUD/USD and AUD/JPY analyzed before, may well be the market where winning strategy requires being a contrarian on a short time scale.

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

EUR/GBP correlation 4 hour time-lag bin

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

24-hour trading cycle.

EUR/GBP bullish and bearish autocorrelation

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

Next we split the full time series into “bullish” and “bearish” samples to examine correlations within those — in hope that this provides better insights into the mechanisms of decision making and trader psychology. These samples are simply sets of hourly time intervals (not necessarily contiguous) with an upward or downward trend. In Fig.3 we construct autocorrelations of the subsamples of the full time series (the “bullish” and “bearish” ones) selected by taking only positive and negative returns respectively. The 24 hour cycle of bullish and bearish action is again clearly seen as the maxima of the correlation are located at multiples of the 24 hour lag: 24, 48, 72, 96, 120 hours and so on. Therefore, smart trend following means something more than following a trend that existed in the near past. It means following a trend that existed this time of the day yesterday, the day before yesterday, and so on — that gives you better than average chance of winning! Conversely, buying because the currency went up 12 hours ago (or selling because it went down 12 hours ago), all the rest being equal, is the least recommended strategy. (See why this 24-hour correlation feature alone is not a prediction strategy. ) Needless to say, this effect is not present in the simulated martingale data, although bullish and bearish trends and rallies occur there as well.

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

EUR/GBP bullish and bearish autocorrelation long range

Fig.4: EUR/GBP bullish and bearish autocorrelations. Axes and color codes as in the previous figure. Range expanded compared to the previous figure to show the characteristic time length of this market memory effect.

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

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

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

Summary

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

Trading System

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

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

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

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

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Quote Currency

Quote currency is the second currency of the currency pair. When the pair is represented as a ratio, quote currency is in the denominator of the ratio. For example, in USD/CHF, CHF is the quote currency. The price quote shows how much of the quote currency a unit of the base currency will buy.

Base Currency

Base currency is the first currency of the currency pair. When the currency pair is represented as a ratio, like USD/CHF, or EUR/USD, the base currency is in the numerator. The price quote shows how much of the quote currency a unit of the base currency will buy.

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).

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).

Trend

To avoid excessive complexity, by “trend” associated with a given time interval we mean simply the sign of the difference in the price quote at the beginning and the end of this time interval, no matter how large or small that difference is.