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™. A live forecasting system operating on daily time scale, Danica, is online since late December 2009. An hour-scale forecasting system, Heidi, and a daily signal EUR/USD system running a model portfolio, Demi, were launched in August 2010.

Our secondary goal is to discover, quantify and monitor the very existence of sustainable opportunities for profit-making via systematic trading. 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.

The third year of ForexAutomaton's life has come to a closure. As usual, presented here is the summary of main problems that occupied me during the year, and the main achievements. For the first time, the annual report includes reviews of the actual trading and forecasting systems which have been running live on this web site since the beginning of 2010, free and accessible to the public. The report is structured around system performance and development while observational studies of market inefficiency take a back seat. The prediction engine remains a Black Box to the reader.

• Statistical predictability of the direction in which each of the extremes of the price-chart bar evolves is proved to be insufficient to  claim market inefficiency, and is understood to have mundane roots in the diffusion of price under conditions of limited price continuity,  as is borne out by the random walk model.

• Differences between hypothetically efficient and real FX markets manifest themselves in higher order correlations, namely fourth order cumulants among certain real data and their proprietary forecasts.

• A strategy attempting to take advantage of these properties of the real FX markets, Demi, has been designed and launched. Results of the first seven months of its live paper trading are reviewed.

• A system making predictions on the hourly time frame, named Heidi, has been launched.

• Following a detailed analysis of the intra-day seasonality patterns such as the alternation of trend following and mean-reversion, Heidi has been improved for at least some of the intra-day time periods by making it seasonality-cognizant.

• The oldest system, Danica, generating predictions on the day scale, has so far been unable to provide systematic positive correlations between its forecasts for the direction of daily close and the actual direction in live operation, but the cause seems to go beyond the choice of the adjustable parameter.

Data accumulation for the present incarnation of Heidi began on December 1, 2010 and the first predictions (in back-testing mode) were generated for March 16, 2011. The present system was announced and began live operation on May 23. Now, eight months later, I take a look at the first statistically significant performance figures of merit and make an adjustment to one of the system parameters.

  During December 2011, the last month of the second year of Danica's live operation, the system continued on auto-pilot without parameter changes. While the forecasts for daily low and high were strongly positively correlated with reality, the predicted changes in the daily close were on average anti-correlated with the actual ones. Thus the system has ended the year in which it functioned as a surprisingly stable "anti-system", a curious quantitative phenomenon which no doubt will be useful to research and possibly exploit, but not the intended one.  

This system performance review 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 the usual green-yellow-blue-red color-coded charts of the performance, such as shown below, for each currency pair.

For comparison with the previous month, you may want to take a look at the October 2011 performance review.

This post begins monthly peformance reviews for the Demi line of EUR/USD daily time frame trading systems. There are four systems in total, differing only according to the choice of the closing hour of the "day": 3, 5, 9 and 11 am Eastern time. The systems went live on August 25, 2010, after extensive back-testing. Since then, the parameters found in the course of the back-testing have been frozen. Even though the system output (see Demi section of the site) is available only to the registered members, the performance reviews will be available publicly.

Fig.1.1 Evolution of Demi's simulated equity with time for the system with daily updates at 3am Eastern time (8am London). The moment of going live is marked by a vertical line. Time axis is labeled in MM-YY format.

For clues as to what effects to expect in forex rates from the consequences of the March 11th earthquake in Japan, I look at historical data from 1995, the year of the Great Hanshin earthquake. Great Hanshin earthquake occurred on Tuesday, January 17, 1995, at 05:46 JST (16 January at 20:46 UTC). There are at least two topics to explore. We look for quantitative effects of repatriation of funds into Japan to fund the recovery efforts on the exchange rate of the Japanese Yen to the US Dollar. Another possible concern is the carry trade implications.

Hourly time scale in forex provides roughly 24 times more statistics, than the daily scale. Therefore, if a single adjustable parameter for all currency pairs is justifiable in the daily system optimization (Danica), 24 parameters can be adjusted for Heidi without jeopardizing significance of the results. The natural way of increasing the number of parameters is to split the 24-hour day into time window "seasons" and treat the seasons as independent pattern recognition problems in the code and as independent optimization problems on the stage of optimization.

This post is the first attempt to summarize intra-day seasonality findings from the six major exchange rates involving USD, focused on the hour-scale correlation structures. Taking advantage of the "non-trivial" (non-zero time lag) correlations in forex is complicated since their structure changes during the day, and a residual structure that survives the multi-day averaging is for this reason weaker than what may exist in a stable way at a certain time period during the day. Averaging is necessary to accumulate statistics and let the signals dominate the noise. But in doing that, I contain averaging within temporal classes or "bins", combining bars of the data recorded at the same or close times during different days, months and years of observation. When cyclicity of time is thus taken advantage of, a weak but significant and stable pattern of intra-day alternation between trend-like and mean-reversion behavior emerges.

Intra-day seasonality in JPY is researched by averaging hourly logarithmic returns, grouped systematically into temporal "bins" according to the time of the day. Two types of average, the average across years of observation for each instrument, and an average across instruments for each year, are presented. The instruments are USD/JPY and four popular crosses involving AUD, EUR, GBP and CHF. The effects look practically insignificant given the typical levels of trading costs available to a retail trader, and given the lack of time stability.

This GBP/JPY report contributes to a set of systematic intraday pattern results involving JPY as the base currency. GBP/JPY as most other currency pairs tends to experience mean reversion around CET midnight.

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.

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 characterized 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.

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.

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.

The "Kelly Criterion" in quant folklore is based on the exposition and development of Kelly's work done by Edward Thorp. Acknowledging Thorp's contribution, I find the original article by Kelly conceptually more relevant to the realities of algorithmic trading as developed by ForexAutomaton. Our forecasting algorithm, as any forecasting tool, can be very naturally considered a case of the hypothetic communication channel discussed by Kelly, and the related mathematical objects, such as joint and conditional probability density distributions for the communicated "symbols" (forecasts and real quotes), are being already monitored here, despite the fact that the Kelly Criterion for capital allocation to trades remains to be coded.

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.