The First Annual Summary of Forex Automaton Research Progress, April 2009

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Written by Forex Automaton   
Friday, 03 April 2009 13:22
Article Index
The First Annual Summary of Forex Automaton Research Progress, April 2009
Forex bipolarity
Leading indicators
Periodicity or oscillation
What did the crisis change?
Black-box algorithm paper-trading
Conclusions. Future.
All Pages

Forex Automaton was launched in April 2008 with the ambitious mission of leveraging the specific algorithmic know-how to create a trading signal service geared toward retail forex traders. From the very beginning a two-prong strategy was adopted: first, development of the trading system product whose usefulness relies on secrecy of the relevant know-how. Second, white-paper research focusing on statistical properties of the market time series, especially those aspects which are potentially interesting from the point of view of algorithmic trading, however counter-intuitive, technical and remote from the mainstream picture of forex trading they may be. As of now, it is mostly the second prong that's visible to the website visitor. This document summarizes the main findings to emerge so far from a year of studies, including some glimpses into the progress made on the black-box algorithmic trading system front.

Market inefficiency: a physicist's perspective

The efficient market hypothesis (EMH) postulates that the "easy" money is perpetually "already made" -- without specifying the time scale. This seems to be inspired by advances of natural sciences and has the look and feel of a conservation law familiar from physics. Indeed, isn't a wealth generating automaton akin to a perpetuum mobile, of either first or second kind, violating the law of energy conservation or the second law of thermodynamics? Isn't the statement that there is "no free lunch" akin to the energy conservation principle? Finance engineers use it to solve problems much the same way electrical engineers do.

Financial engineers usually begin the history of their discipline with Louis Bachelier's 1900 PhD thesis "The Theory of Speculation", where the concept of random walk and Fourier's heat theory were applied to the movement of prices. (I base my discussion of Bachelier's work on the account given by Mandelbrot in "The Misbehavior of Markets"). Ironically, the Victorian physics look and feel was being imported into finance just as physics was about to undergo a dramatic separation with Victorian age: an intellectual revolution marked by the advent of quantum mechanics and relativity in the early XX century. Experiments with subatomic particles and precise astronomical observations limited the applicability of many common sense concepts rooted in the everyday experience to the physical scales typical of, well, that experience -- and challenged Victorian confidence in their scale-independent universality.

Later, in what is sometimes called measurements of zero, experimentalists demonstrated that many naive symmetry statements (deemed to be conservation laws) are overstatements. In school, students of modern physics are confronted with the problem: an alien space ship approaches Earth. As the aliens do not want to annihilate into gamma-rays upon physical contact with our world, they want to know: is our world made of matter or of anti-matter? Of course we don't know whether our and their definition of matter and antimatter are the same. The fact that such a definition can be communicated in principle means that the physical world is fundamentally asymmetric.

In physics, P, C and CP symmetries turn out to be overstatements which may make us feel comfortable mentally, but are wrong. The physics paradigm of Enlightenment was promoting the sense of false symmetry and perhaps false security. A modern physics graduate suspects that the EMH is a similar overstatement making us feel comfortable emotionally: are you excited by the wealth generation opportunities offered by the speculative markets of today, but worried about inherent risks? Relax, consistent speculative profits are impossible statistically, say EMH proponents. As a mechanism of psychological adaptation, EMH is perhaps a useful part of social culture but a questionable part of science, even of the imprecise science such as economics -- since crowd dynamics can be studied even with liberal arts methodology. As a quantitative tool in sell-side finance business, EMH is part of "financial engineering" where the ideal symmetry rather than its real breaking, the supposed beauty of the world ("efficiency" of the market) rather than its actual ugliness seem to form the subject matter. Yet it is the ugliness (broken symmetry, lacking perfection) that makes the practitioner money in the real-life markets. It's easy to confuse perfection with stability (be it of cash flow or of scientifically reproducible results), and in search for stability to seek perfection and to end up idealizing the world. Meanwhile to the practitioner the main "business opportunity" is human imperfection -- and is it a stable one...

Symmetry (perfection) justifies reduction in information, symmetry breaking (an imperfection) on the contrary is always specific and brings in extra information. Let's look at specific patterns in real-life data.

The method of analysis

Data aggregation

Initial raw data comes as a series of bid and ask prices recorded at specific times. The series can be binned or aggregated on various time scales, the aggregation consisting of creating a series of consecutive, adjacent time bins (intervals) of the same length, and calculating the open, close, low and high levels of price for each of them. The time scale of analysis is the time duration of the bin.

Logarithmic returns

Long-term absolute level of the price is almost irrelevant to a forex trader, what matters is relative movements. I use logarithmic returns to eliminate one trivial source of non-stationarity of the correlation functions which is the possible long time-scale trend in the time dependence of the price. Ordinary returns eliminate it as well, but given the questionable convergence of second moments of the typical financial quantities (as discussed by Mandelbrot), keeping the analysis logarithmic is very important.

Statistical reference and statistical significance

On the hour scale, distributions of logarithmic returns look roughly exponential. The good news from this is that the second moments do converge, therefore the Central Limit Theorem and thus the usual machinery of statistical analysis, based on the normal distribution, applies to the correlation measurements (which are in this case sums of large numbers of products of quasi-exponentially distributed quantities).

The pimary reference is the so-called martingale, or a time series with no prehistory dependence. Non-zero auto-correlation values at non-zero time lags, when statistically significant, falsify this reference and signify predictability in the "weak" statistical sense.

The statistical errors, the measure of uncertainty of measurement, are calculated directly for each correlation function measured by simulating a large number of uncorrelated time series, reproducing the volatility of the forex time series under study. On each of these, the same analysis is performed, and the precision of the resulting quantities can be estimated by looking at their variation among such reference time series. This general solution allows one to handle all situations, regardless of the exact shape of the distribution of logarithmic returns, the resulting degree of closeness to the normal distribution for the correlation quantity, and the effects of the possible time window cuts applied to the time series. This also eliminates doubts related to the software implementation of the mathematical techniques. However, effects of variation in the properties of the original time series with time (non-stationarity) are beyond the scope of this solution, and have to be addressed by e.g. ad hoc splitting of the time series into "volatile" and "pre-crisis" pieces.

In the figures that follow what matters, to the first order, is the magnitude of non-zero lag features with respect to the level of statistical accuracy indicated by the red shade. The mean of the red band at each bin is the embodiment of the EMH for the market in question.

A self-delusion is possible when a subset of results of a particular flavor is chosen to support a particular conclusion with no due regard to the rest of cases which may support a contradicting conclusion. Repetition of the same analysis on different data sets, the number of those sets being as complete as possible, is typical for the Forex Automaton style and helps avoid such a pitfall. Speaking of inter-market correlations, a full complement of exchange rate pairs involving AUD/JPY, AUD/USD, CHF/JPY, EUR/AUD, EUR/CHF, EUR/GBP, EUR/JPY, EUR/USD, GBP/CHF, GBP/JPY, GBP/USD, USD/CAD, USD/CHF, USD/JPY has been analyzed for a particular time span from 2002 to 2008.



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