I have been looking at the temporal distributions of daily highs and lows in forex since for some time now (see the EUR/USD report, the first one on the subject). Later I began complementing the data with a similar distribution of variance and 1-hour lag autocorrelation (here is the distribution for EUR/USD), trying to infer whether there is a systematic change in correlation regime from trend following to mean reversion during the day. The inference would be based on combining second order statistics and daily extreme distribution data. It had been tacitly assumed that random walk would have a featureless temporal distribution of daily extremes. In this post I document the "base-line" shape of this distribution: due to peculiar memory effects found even in the random walk (continuity of price), the shape of such distributions has certain characteristic features.
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Even in the random walk, locations of daily high and low are non-uniformly distributed in time
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January 14 2011, 2:44pm | Comments »
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AUD/USD intraday seasonality overview, 2003-2010
A notable stable effect on the hour scale in AUD/USD is mean-reversion dominance during the morning hours of the Asia-Pacific trading session. Qualitatively this is common to all exchange rates studied in this set of reports so far, but qunatitatively, the 1-hour negative autocorrelation is very strong in AUD/USD. The pattern of residual non-zero average hourly returns in AUD/USD in 2003-2010 is similar to AUD/JPY.
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January 10 2011, 7:24pm | Comments »
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December 2010 performance review for Danica-9am algorithm
During the month of December, the twelfth month of live performance, the system continued on auto-pilot without parameter changes. This document consists of a summary section reporting the figures of merit for the forecasting quality, followed by 14 subsections, dedicated to the individual exchange rates tracked by the system. Those contain our usual green-yellow-blue-red color-coded charts of the performance (2 for the two hypothetic strategy triggers for each currency pair, 28 in total) and details pertinent to the specific currency pairs. For comparison with the previous month, you may want to take a look at the November review.
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January 3 2011, 7:53pm | Comments »
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USD/CAD intraday seasonality overview, 2003-2010
The regime change from mean reversion to trend following is seen to occur daily in USD/CAD. Like in other pairs studied so far, the statistically preferred time to bet on a trend reversal in USD/CAD is the morning hours of the Asia-Pacific trading session. Evidence for that comes from the comparison of temporal distribution of daily extremes with temporal distribution of volatility, and from time dependence of autocorrelations of logarithmic returns with 1-hour lag. The hour ending at 17:00 CET (11am ET) favours trend following.
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December 30 2010, 5:40pm | Comments »
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GBP/USD intraday seasonality overview, 2003-2010
This GBP/USD report continues a new series of reports about intra-day "seasonality" effects in FX, gathering facts on the ground for an upgrade of the hour-scale algorithmic forecasting system. From the point of view of this approach and the features it reveals, GBP/USD is somewhat similar to EUR/USD. Like in other pairs studied so far, the statistically preferred time to bet on a trend reversal in GBP/USD appears to fall on the morning hours of the Asia-Pacific trading session. Evidence for that comes from the comparison of temporal distribution of daily extremes with temporal distribution of volatility, and from time dependence of autocorrelations of logarithmic returns with 1-hour lag.
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December 28 2010, 5:52pm | Comments »
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USD/JPY intraday seasonality overview, 2003-2010
This USD/JPY report continues a new series of reports about intra-day "seasonality" effects in FX, reinforcing the emerging picture of peculiar "stationary" non-stationarity in these time series: even though there is no invariance of the time series properties with respect to an arbitrary time interval, there seems to be some degree of translation invariance with respect to the 24-hour time interval in both variance of logarithmic returns (expected), lagged covariance (not-so-well known) and mean logarithmic return (not-so-well known). Like in other time series studied so far, the hourly movements in USD/JPY do not average to zero for every hour of the day. Moreover, there seems to be a statistically preferred time to bet on a trend reversal in USD/JPY. Evidence for that comes from the comparison of temporal distribution of daily extremes with temporal distribution of volatility, and from time dependence of autocorrelations of logarithmic returns with 1-hour lag.
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December 27 2010, 7:04pm | Comments »
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AUD/JPY intraday seasonality overview, 2003-2010
This report continues a new series of reports about intra-day "seasonality" effects in FX. Like in EUR/USD, the hourly movements in AUD/JPY do not precisely average to zero for every hour of the day. Moreover, there appears to be a statistically preferred time to bet on a trend reversal in AUD/JPY. Evidence for that comes from the comparison of temporal distribution of daily extremes with temporal distribution of volatility, and from autocorrelations of logarithmic returns with 1-hour lag.
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December 14 2010, 7:51pm | Comments »
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EUR/USD intraday seasonality overview, 2003-2010
In the past, we have looked at hour-scale autocorrelations and intermarket correlations in FX, averaged over observation intervals as long as several years. We have also looked at time evolution of interesting correlation effects, averaged over shorter time intervals. This report begins a new series of reports about intra-day "seasonality" effects in FX. We are interested in seasonality effects in both first (averages) and second-order (variances, correlations) statistics. If the correlation patterns happen to be meaningfully different during different times of the day, one can use this to one's advantage by programming the forecasting algorithms to work differently during those times, and by using different sets of parameters. Different models would be responsible for the different "seasons" of the day. This first report, dedicated to EUR/USD, begins accumulating such data.
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December 7 2010, 4:41pm | Comments »
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November 2010 performance review for Danica-9am algorithm
During the month of November, the eleventh month of live performance, the system continued on auto-pilot without parameter changes. This document consists of a summary section reporting the figures of merit for the forecasting quality, followed by 14 subsections, dedicated to the individual exchange rates tracked by the system. Those contain our usual green-yellow-blue-red color-coded charts of the performance (2 for the two hypothetic strategy triggers for each currency pair, 28 in total) and details pertinent to the specific currency pairs. For comparison with the previous month, you may want to take a look at the October review.
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December 1 2010, 7:58pm | Comments »
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October 2010 performance review for Danica-9am algorithm
During the month of October, the tenth month of live performance, the system continued on auto-pilot without parameter changes. This document consists of a summary section reporting the figures of merit for the forecasting quality, followed by 14 subsections, dedicated to the individual exchange rates tracked by the system. Those contain our usual green-yellow-blue-red color-coded charts of the performance (2 for the two hypothetic strategy triggers for each currency pair, 28 in total) and details pertinent to the specific currency pairs. For comparison with the previous month, you may want to take a look at the September review.
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November 11 2010, 3:47pm | Comments »
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JPY LIBOR 2007-2010: shorter maturities mean-revert, longer ones form trends
Statistically significant patterns in the Japanese yen LIBOR time series have been discussed on this site in October 2008, based on a data set ending in summer 2008. The financial panic of 2008 that followed (I reserve the word "crisis" for a broader context) left its imprints on the Japanese yen, one of the world's primary funding currencies. The data presented here cover the period from August 16, 2007 (the day Countrywide Financial made the news, triggering a change in the US Fed stance) through July 30, 2010. I focus exclusively on autocorrelations within the yen LIBOR time series for various maturities, and on the cross-correlations between them. Surprisingly, the patterns are very similar to those of the 2008 report, despite the fact that the most dramatic movements in JPY LIBOR took place in fall of 2008 and were not analyzed previously.
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October 29 2010, 2:44pm | Comments »
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USD LIBOR predictability 2007-2010: shorter maturities show the way
A series of LIBOR correlation articles published on this site in late 2008--early 2009 were very well received by the readers. The financial panic of 2008 was the most extreme event for LIBOR, and for reasons of timing, was not covered very well in these articles. Now, I am coming back to the topic with more data and the same statistical analysis framework. The data presented here cover the period from August 16, 2007 (the day Countrywide Financial made the news, triggering a change in the Fed stance) through July 30, 2010. The period chosen is the one charactirized by the US Fed single-minded focus on lowering the short- and longer-term interest rates. Not surprisingly, this definite trend shows up in the correlation analysis as a broad positive correlation peak. Cross-correlation analysis of different maturities shows shorter maturities to play the role of leading indicators for the longer ones. The effect has a characteristic time length of up to ten days. It is the most prominent when combining overnight LIBOR with the 1-month one, or combining the 1-week LIBOR with longer terms.
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October 22 2010, 12:59pm | Comments »
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Fourth order cumulant study with more FX rates and time windows
The previous study revealed the positiveness of the fourth-order cumulant among the logarithmic increments for 24-hour highs and lows in EUR/USD and the respective ForexAutomaton forecasts. By expanding the scope of the study to include all of the 14 most popular exchange rates, and by splitting the time span of the simulated trading into five independent intervals, I demonstrate that the result is not just a feature of EUR/USD and is stable in time. The data hint at a correlation between the fourth-order cumulant under study and predictability of close (measured by Pearson correlation coefficient between predicted and actual logarithmic returns). However, the signal strength for these figures of merit, defined as the ratio of the value in question to the estimated precision of its measurement, appears to lend more credibility to the cumulant.
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October 13 2010, 5:13pm | Comments »
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September performance review for Danica-9am algorithm
During the month of September, the ninth month of live performance, the system continued on auto-pilot without parameter changes. This document consists of a summary section reporting the figures of merit for the forecasting quality, followed by 14 subsections, dedicated to the individual exchange rates tracked by the system. Those contain our usual green-yellow-blue-red color-coded charts of the performance (2 for the two hypothetic strategy triggers for each currency pair, 28 in total) and details pertinent to the specific currency pairs. For comparison with the previous month, you may want to take a look at the August review.
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October 4 2010, 11:38am | Comments »
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Fourth order cumulant in EUR/USD falsifies random walk hypothesis
Ability to predict the up-coming changes in daily and hourly high and low of price (of course, in a statistical sense, as measured by correlation coefficients between prediction and reality) by using adaptive black-box models has been well documented on this site. Observation of statistical dependence of the extreme levels of price (high and low) within a time bin on the immediate past of the time series, reported for the random walk model, explains and, particularly in the context of searching for market inefficiencies, even trivializes this achievement. Indeed, market inefficiencies are not required for the diffusion equation (cf. Black-Scholes theory) to work. Are we merely creating black-box equivalents of the popular tools of financial engineering? Enter higher-order cumulants. Shown here are measurements of the fourth order cumulants among the 24-hour high and low and the respective forecasts in real-life EUR/USD data; these can now be compared with the values they had in the random walk data. The difference revealed is dramatic.
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September 15 2010, 7:14pm | Comments »
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Markov property of the extremes in the binned random walk time series
Random walk is an important reference process in statistics and its properties have to be studied in financial applications, where hypothetic random walk of price remains an essential component of efficient market theories. Our day and hour time-scale predictive models demonstrated stable positive correlations between reality and prediction for returns taken in the time series of the respective (daily and hourly) lows and highs. However, same property is shown to hold for the simple Brownian motion random walk model. What are the origins and the implications of this effect?
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September 8 2010, 7:00pm | Comments »
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August performance review for Danica-9am algorithmic system
During the month of August, the eighth month of live performance, the system continued on the auto-pilot without parameter changes. This document consists of a summary section reporting the figures of merit for the forecasting quality, followed by 14 subsections, dedicated to the individual exchange rates tracked by the system. Those contain our usual green-yellow-blue-red color-coded charts of the performance (2 for the two hypothetic strategy triggers for each currency pair, 28 in total) and details pertinent to the specific currency pairs. For comparison with the previous month, you may want to take a look at the July review.
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September 8 2010, 1:13pm | Comments »
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High order cumulants
Cumulants are statistical measures of correlation designed to go to zero whenever any one or more quantities under study become statistically independent of the rest. Cumulants generalize the concept of a correlation measure; in particular, a correlation of two bodies, quantities and so on, the most intuitive one, can be represented and measured by the second-order cumulant. Higher orders can be conceived.
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August 30 2010, 7:30pm | Comments »
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Introducing Heidi, the hour-scale predictive model
ForexAutomaton has just expanded its portfolio of free predictive models into higher frequency domain. From now on, a forex forecast of low, high and close for the next hour will be posted on this site every 60 minutes. The new system is named Heidi following the naming convention where first names starting with H are assigned to systems with hourly decision-making scale.
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August 11 2010, 2:39pm | Comments »
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Explaining the output of Heidi trading system
This document explains typical output of Heidi -- an experimental free (payless but closed-source) ForexAutomaton hour-scale forex forecasting system or predictive model.
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August 9 2010, 2:04pm | Comments »