Forex Automaton

Our primary goal is to create a public information service providing financial markets forecasts, based on our proprietary forecasting tools: an automated trading system -- a Forex Automaton™. Our secondary goal is to quantify and monitor the very existence of sustainable opportunities for arbitrage profit-making. Or simply put, to monitor the degree to which these markets are more predictable than a "fair game" -- to a trader without access to insider information.

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.

This is a brief follow-up to the previous post on how I know my forex forecasting works. In that post I disclosed a measurement of a figure of merit I use to monitor the forecasting quality and optimize the algorithm, the figure of merit being the covariance of predicted and actual logarithmic returns on a day scale. The measurements were carried out for 16 values of the control parameter nicknamed Fred, which is currently the only "make it or break it" parameter responsible for the forecasting, and the only one being currently optimized. (As an aside note, there are other quantities which control the process like for example how big a chunk of data you look at. Those are believed to be more mundane and are currently fixed as some "reasonable" values -- which is not to say that I won't decide to take a more quantitative look at how reasonable those values are sooner or later.)  

The covariance of predicted and actual logarithmic returns is not the best quantity to look at when aggregating data for the different forex exchange rates: because of the somewhat different volatilities of those markets (different even despite the fact that the logarithmic returns take the absolute value of the exchange rate out of the picture), the resulting numbers for the major forex were volatility-weighted averages. Moreover, a quantity like 10^-6, even if it's more than 2 standard deviations above zero, does not communicate the result to the non-expert in the intuitive way the result deserves.

These are the reasons why I went over from covariances to Pearson correlation coefficients, and today I am presenting the updated measurements.

I've gone through three rounds of historical data optimization (back-testing) for the major forex pairs, performing simulated trading in each pair independently. This mode of the market analysis, with the various exchange rates being treated by the algorithm in isolation from one another, is not the way the production trading system will operate. However, understanding the markets in isolation and optimizing the trading system in this simpler problem setting is seen as the first step towards optimization of the more complex algorithm, where the amount of information at every point in time will be radically increased by combining analyses of multiple exchange rates within the same algorithm. This study is a cross-check to see how the indvidual optima hang together, trying to define a coherent dry residue from the combined experience of the 150,423 simulated trading histories.

As any computer program, a forex trading system has input and output. This post is about the output -- what should be in it? What are the guiding principles of this communication? Here are the basic principles as we see them now:

• Regularity.
• Communicate actions, not prophecies.
• Communicate actions as they happen.
• Program the computer, not the user.
• Be accountable for the past performance.
• No misrepresentation.
• Access control.

While it is true that past performance does not indicate the future, the only reliable information we have is about the past. A few important things make a difference between unbiased trading-system testing and self-delusion. Here I summarize my current understanding.

An excerpt from the interview:

- How do you see the future of trading and markets in the XXI century?

I see the XXI century as an age of crowds of kaleidoscopically diverse individuals, empowered and inter-connected by technology, interacting in more and more complex, conditioned and mediated ways -- and at the same time more and more differentiated within personal "virtual realities." I anticipate further inter-penetration between the concepts of information and capital.

The intention of this post is to tie together several topics which appeared on my radar screen in the course of the trading system optimization. First, it has been understandably hard to fully rid oneself of  vestiges of the mainstream financial theory based on the postulate of market efficiency, while building a wealth-generating tool relying explicitly on demonstrable market inefficiencies. The realization that Sharpe ratio does not let one make an objective choice of a portfolio was  there from the beginning, and I recall perceiving this fact as a "necessary evil". Then came the understanding of the fact that an  artithmetic average of returns gives one a biased picture of long-term return, and consequently, Sharpe ratio is built around biased quantities.

 I approach pairs trading with the correlations tool-box and basic algebra. Let's consider two time series, a(t) and b(t). It will be understood that these are  taken on a fixed time scale (second, minute, hour, and the like). Most explanations of pair trading fail to communicate the importance of non-zero correlations at non-zero time lags --  let alone the importance of their constructive interference (to be explained). Meanwhile, it is these subtleties that make a difference between just another roulette-like source of random outcomes and a reliable, little-risk source of arbitrage profits. 

The key component of my forex trading system is the prediction engine. So far I have been trying to optimize the prediction engine in the overall context of simulated trading on the historical data where besides the parameter responsible for prediction, at least three other parameters were being optimized. With the large number of parameters, the CPU demands of optimization become prohibitive: as the dimensionalty of the parameter space grows, the number of parameter combination grows with it. As the pseudo-random time series are at the very heart of the problem, the randomness of changes in performance with respect to every parameter clouds the analyst's vision of any parameter in the course of the optimization. The adverse effect of that is possibly even more important than the combinatorial growth of the volume of the parameter space. It is therefore very helpful to factor the problem out into independent pieces which can then be optimized separately. The success depends, among other things, on the figures of merit used and on the degree of true independence between such pieces.

Predictions for every market under analysis are obtained at every decision-making step (in this case, a day). As always, the system has no access to the future of the time series and only learns from the past. Every step during the simulation is therefore a direct test of the applicability of the past learning to the present context, just as it will be in real life. In real life however, the system chosen for operation will bear in itself the bias associated with its selection. In the Monte Carlo tests, we don't select and deal with an entire array of systems. The statements made for such an a priori array are free of selection bias.

In order to conduct an unbiased test of the prediction quality and determine the best prediction parameter, I use the following procedure. At every prediction step, I record the prediction and one step later, when the future becomes reality as predicted or otherwise, I take the product of the real and predicted logarithmic returns for the day. The average of the product is the quantity plotted along the vertical axis in Fig.1 for the entire range of the prediction parameters.

In the recent forex/CFD data, USD/CAD is negatively correlated with light oil (WTI) CFD. This is the same as saying that CAD, one of the commodity currencies, is positively correlated with oil. This is old news. In this article I take a deeper look at the issue and analyze the shape of the correlation peak. Analyzed on the hour time scale, the correlation peak is broad and somewhat asymmetric, indicating that it is much safer to rely on the guidance of USD/CAD in predicting the oil price, rather than other way round. The necessary caveat is that this is a time-integrated picture, covering a period from late August 2008.

After inspecting the simulated track of the best selected algorithmic traders (see EUR/USD, USD/JPY, GBP/USD, USD/CHF, USD/CAD, AUD/USD, it becomes clear that a volatility-neutral approach is needed. The optimized robots trade only during the peak of financial panic so there is a risk that if such a system is launched and the volatility returns to normal, no trades will be placed.

This AUD/USD back-testing analysis concludes the series which began with EUR/USD. Simulated track records of six best Step Two algorithmic traders are studied graphically. For a more numbers-oriented approach to performance, see the article explaining the trading system optimization process which led to the selection of these six robots. This is the sixth, final report in the series and by now, the main area needing improvement is already clear: just as the system undertrades the less volatile currencies, it overtrades Aussie.

This USD/CAD visual back-testing analysis continues the series which began with EUR/USD. Simulated track records of six best Step Two algorithmic traders are studied graphically. For a more numbers-oriented approach to performance, see the article explaining the trading system optimization process which led to the selection of these six robots.

This USD/CHF back-testing analysis continues the series which began with EUR/USD. Simulated track records of six best Step Two algorithmic traders are studied graphically. For a more numbers-oriented approach to performance, see the article explaining the trading system optimization process which led to the selection of these six robots.

This GBP/USD back-testing analysis continues the series which began with EUR/USD. Simulated track records of six best Step Two algorithmic traders are studied graphically. For a more numbers-oriented approach to performance, see the article explaining the trading system optimization process which led to the selection of these six robots.