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

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

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

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

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

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

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

td = tUSD/TRY – tEUR/JPY.

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

USD/TRY and EUR/JPY hourly autocorrelations, zoomed

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

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

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

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

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

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

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

AUD/JPY and EUR/USD ntermarket correlation

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

The fact that most of the correlation is concentrated at the 0 lag means that the correlation (reported in the table) works out mostly on the time scale of up to 1 hour. The tail of positive correlation to the left of the 0 lag indicates that there is a “tail” of predictable action in EUR/USD lagging behind AUD/JPY. It is the strongest in the European and American sessions. Even though the Asia-Pacific session has the strongest correlation between the two currency pairs within the 0-lag time bin (see the table), it has the weakest correlation away from 0 and thus must be the worst for forecasting on the basis of this correlation feature.

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

AUD/JPY and EUR/USD intermarket correlation European session

Fig.2: Cross-correlation of AUD/JPY and EUR/USD, derived from the hour-by-hour logarithmic returns, for the European (Eurasian) trading session shown against the backdrop of statistical noise (red). The noise is obtained from martingale simulations based on the historical volatilities of AUD/JPY and EUR/USD in this trading session.

Fig.2 demonstrates the non-flat (although quite predictable) behaviour of the noise level with time lag. This can not be ignored otherwise one risks over-interpreting the picture. The area around zero is fairly safe since the noise is at the minimum when the lag is at an integer number of days. Based on the level of the noise, the tail in the first couple of bins to the left of the 0 peak (which means EUR/USD is trailing AUD/JPY) looks like a real effect. We are probably looking at the “risk aversion”/”risk appetite” mood swings where the AUD/JPY having a very strong interest rate differential can indeed lead the show.

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

Euro/US Dollar and US Dollar/Yen are obviously anticorrelated currency pairs. But, which one is the leader and which one is the follower? How long do the markets take to work out the anticorrelation? If the adjustment is not instantaneous, can one currency be used to predict the other?

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

time scale Asia-Pacific session European session American session
hour-0.40-0.53-0.55

EUR/USD and USD/JPY are, understandably, anticorrelated. What is not so obvious is the observation that the anticorrelation is the least pronounced in the Asia-Pacific session.

EUR/USD and USD/JPY intermarket correlation

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

In Fig.1, there is one feature worth noticing: that is the bin with the time lag -1. It is negative but not as negative as the time lag 0. But while time lag 0 can not be used for prediction, time lag -1 (as any non-zero time lag) can. We define lag as time for the market 1 minus time for the market 2. In this case, time for EUR/USD minus time for USD/JPY. A positive correlation at a certain time lag tells you: “same thing happens in two markets with a certain time lag”. A negative correlation at a certain time lag tells you “markets are doing the opposite thing with a certain time lag”. The fact that most of the correlation is concentrated at the 0 lag means that the correlation (reported in the table) works out mostly on the time scale of up to 1 hour. The time bin to the left of the 0 lag indicates that there is a “tail” of predictable action lagging behind. Finally the most important thing: time lag -1 hour means that EUR/USD is leading and USD/JPY is following — in the European and American but not the Asia-Pacific session.

EUR/USD and USD/JPY intermarket correlation compared with noise

Fig.2: Cross-correlation of EUR/USD and USD/JPY, derived from the hour-by-hour logarithmic returns, for the European (Eurasian) trading session shown against the backdrop of statistical noise (red). The noise is obtained from martingale simulations respecting the volatilities of EUR/USD and USD/JPY in this particular trading session.

As Fig.2 demonstrates, the main challenge while working with trading session-specific correlations is the non-linear (although quite predictable) behaviour of the noise level with time lag. This can not be ignored otherwise one risks over-interpreting the picture. The area around zero is fairly safe since the noise is at the minimum when the lag is at an integer number of days. The conclusion about the leader and follower currency pair, drawn on the basis of the asymmetry of the central peak, is significant despite the noise. For trading EUR/USD and USD/JPY on the basis of the intermarket correlation strategy, European and American trading sessions are the best time.

EUR/JPY 2002-2008: Predictability Overview

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

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

The basic autocorrelation

EUR/JPY correlation 1 hour time-lag bin

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

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

EUR/JPY correlation 4 hour time-lag bin

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

24-hour trading cycle.

EUR/JPY bullish and bearish autocorrelation

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

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

EUR/JPY bullish and bearish autocorrelation long range

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

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

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

Summary

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

CHF/JPY 2002-2008: Predictability Overview

The Swiss Franc/Japanese Yen in 2002-2008 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.

In this report we focus on the period from 00:00 2002-08-20 to 00:00 2008-02-01 (New York time). This is a pair of low yield currencies. The Bank of Japan held its discount rate at historic minima (hitting 0.1% in September 2001). Swiss National Bank’s three-month Libor rate target hit historic minimum in 2003-2004. On average for the period, the Swiss Franc enjoyed a higher yield.

CHF/JPY autocorrelation 1 hour time-lag bin

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

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 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 CHF/JPY series, each one constructed to reproduce the measured distribution of returns for CHF/JPY 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 JPY ( GBP/JPY and AUD/JPY ) is also present in the CHF/JPY 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 taking a product of opposite sign returns — or that the product of the opposite sign returns 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, CHF/JPY, like GBP/JPY and AUD/JPY analyzed before, may well be the market where winning strategy requires being a clever contrarian. We increase the time lag bin to four hours in Fig. 2 to try and see if we can locate a trigger signal — something that could alert you to take a contrarian position with more confidence.

CHF/JPY autocorrelation 4 hour time-lag bin

Fig.2: CHF/JPY 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. This figure does not reveal any new reliable patterns, although one might argue there is a hint of a zigzag pattern with a period of about 2 weeks.

24-hour trading cycle.

CHF/JPY bullish and bearish autocorrelation

Fig.3: CHF/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 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 cyclic correlation feature is not in itself a prediction mechanism.) Needless to say, this effect is not present in the simulated martingale data.

Note that whether this trend following pattern is equally strong in all time zones (at all times during the day) is a question that requires a separate study.

CHF/JPY bullish and bearish autocorrelation long range

Fig.4: CHF/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 when “bearish” refers to the currency with 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. 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 fact that one can read the sign of interest rate differential off the public forex quotes via basic correlation analysis is — should this interpretation prove correct — astonishing 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

As most other currency pairs analyzed, CHF/JPY is not completely “efficient” from the point of view of basic two-point correlation analysis. Long term prospects of CHF/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.

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.

GBP/JPY 2002-2008: Predictability Overview

From the predictability point of view, the Pound Sterling/Yen currency pair resembles the Australian Dollar/US Dollar and Australian Dollar/Yen pairs analyzed before and its patterns are similar to but not as strong as in AUD/JPY.

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

Trend predictability

GBP/JPY autocorrelation

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

In this figure we look for arbitrage opportunities on the time scale of up to two days (corresponding to day trading or swing trading) — and like in AUD/USD and AUD/JPY, there is a negative autocorrelation seen for the time lag up to an hour. The hatched red band shows the range of statistical noise (namely its expectation plus minus its RMS deviation). Statistical noise was obtained by simulating 20 independent time series of the length corresponding to that of the GBP/JPY series, each one constructed to reproduce the measured distribution of returns for GBP/JPY for the time period under study (including the fat tails!), but completely devoid of correlations ( martingales ). From these, the expectation and RMS or the autocorrelation amplitude in each time lag bin were calculated.

Now to the main non-random feature here: the negative correlation signal at one hour lag overshoots the level of noise by a factor large enough to make it look significant. The autocorrelation being an average of a product of hourly returns taken with a lag, its negativity means that we are way too frequently taking a product of opposite sign returns — or that the product of the opposite sign returns far outweighs that of the same sign returns. In other words, the GBP/JPY price quote is a lot more jittery than what “financial theorists” who preach market efficiency (expecting this plot to be similar to what is represented by the red band) believe.

Because trend reversals on the time scale of one hour or less happen either too often or are too lucrative, GBP/JPY may well be the market where winning strategy requires being a clever contrarian. In the next figure, we increase the time lag bin to four hours to try and see if we can locate a trigger signal — something that could alert you to take a contrarian position with more confidence.

GBP/JPY autocorrelation

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

Now the negative correlation is absorbed in the 0 peak — but the signal of trend repetition with a 14- to 18-hour lag is barely above the level of noise and must be judged as too risky to rely on. It is remarkable however that all currency pairs looked at so far ( EUR/USD, AUD/USD, and AUD/JPY ) had a positive autocorrelation bump (trend repetition signal) of varying strength but above noise level for the time lags from 6 to 18 hours in the four-hour time bin plot like this figure.

24-hour trading cycle. Trader memory effect.

GBP/JPY bullish and bearish autocorrelation

Fig.3: Yellow: correlating only positive hourly returns. Blue: correlating only negative hourly returns.

In Fig.3 we construct autocorrelations of the subsamples of the full time series ( the “bullish” and “bearish” ones) selected by taking only positive and negative returnds respectively. The 24 hour cycle of bullish and bearish action is again clearly seen as the maxima of the correlation are located at multiples of the 24 hour lag: 24, 48, 72, 96, 120 hours and so on. Therefore, smart trend following means something more than following a trend that existed in near past. It means following a trend that existed this time of the day yesterday, the day before yesterday, and so on — that gives you better than average chance of winning! Conversely, buying because the currency went up 12 hours ago (or selling because it went down 12 hours ago), all the rest being equal, is the least recommended strategy. (See why the sub-sample correlation feature is not in itself a prediction strategy.)

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

GBP/JPY bullish and bearish autocorrelation long range

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

Summary

We conclude that while the GBP/JPY market is definitely not a random walk, this is not the easiest market to trade on the basis of the two-point correlations alone. Long term prospects of this currency pair are the subject of fundamental analysis and are outside the scope of this article. Cross-correlations with other markets are to be discussed in the up-coming articles.

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.