Determined Chaos is a non-linear method of analysis that has achieved a greater following in recent years. However, not only does this sophisticated and complex area of study require significant background to be applicable to the markets, it’s also plagued by another deficiency that affects many other nonlinear techniques. In its raw form, it’s only reliable for making extremely short-term forecasts.

One way to solve this problem is to apply additional analysis methods that have a wider field of view, amplifying the original signal, in a sense, to stretch it out over a more realistic term. However, this only makes the entire trading approach even more complex and time consuming.

A better solution begins with the theory of Determined Chaos itself. By taking a fresh look at the basics of this methodology, we can break it down to its essentials, keeping the model straightforward and making it more useful in the real world. Be forewarned, this is an advanced technique that assumes some background of chaos theory application that space precludes detailing here. That said, sufficient overview will allow the casual reader to follow along, while experienced analysts will find everything they need to use these methods, with sources cited for additional information. This process will be demonstrated by developing a system that exploits trends in the cash forex market.

PIECES OF THE PUZZLE

Among system traders, there is endless debate on the number and type of parameters that are best used to describe the market. Most trading systems are built using one parameter, the price. However, price-based models are notoriously unstable. Even if they return the expected results over the long term, no indicator based solely on price can explain or predict market movements with significant regularity.

Another approach is to try to model the supply and demand forces that act on price. On one level, this line of attack has its own problems, not the least of which is the efficacy of the supply and demand data streams themselves. However, we can eliminate many of those issues by looking at market data that reflect supply and demand dynamics without delving into the fundamentals: volume and open interest.

Market order flow can be accurately tracked by analyzing volume and open interest in conjunction with the market price. While price is an important aspect of this approach, it is more a product of how supply and demand interact rather than determining the direction future price follows.

For background on volume and open interest, see Kenneth Shaleen’s “Volume and Open Interest,” or Donald Cassidy’s “Trading on Volume: The Key to Identifying and Profiting from Stock Price Reversals.” By using open interest, though, it creates a problem when focusing on forex. Because cash forex is traded OTC and not through an exchange, as stocks and futures, open interest is not available. However, futures are derivatives of the cash market. Due to the obvious correlation between the cash markets and futures, we can use the open interest from the futures as a proxy.

FINDING THE TREND

The Trend Determining method takes into account different aspects of volume, open interest and price to produce trades with a high winning percentage. The first part of the Trend Determining method is based on the system of equations describing the market shown in “All in the family”.

For those who aren’t familiar with the analytical process of Determined Chaos, these equations bear some explanation. The system has five points of equilibrium. These are part and parcel of its strange attractor. In Chaos Theory, a strange attractor is a region to which a dynamic system is drawn after a long enough period of time.

In terms of system parameters, the strange attractor can be described as a set of trajectories. The modifier “strange” emphasizes singularity of attractor properties that describe its chaotic behavior. Such chaotic processes can be described by three or more parameters. Therefore, it is important to have at least three types of information produced by the markets, satisfied here by price, volume and open interest.

Although there are five points of equilibrium, one of them, E(Ce(t),Ve(t),Ie(t)), stands out as the most important for forecasts. In short, when the point defined by these equations transforms into a new region, it represents a significant evolution in the behavior of the entire system.

In terms of the price, this transformation signifies continuation or transformation in the direction of a trend, what we’re trying to predict for the forex market. This trend shift is described by the parameter Ce(t), which can be found by solving the given system of equations, holding values of the family of functions constant during each day.

By using the behavior of the function f(t) = k(t)(C(t) - Ce(t)), we can make the decision about the initiation or sustainability of a position. When its value gets to the buy (0.6, 1) or sell (-0.6,-1) area, we act on the opening of the next day. (The open and close are defined by the times for the futures market day sessions.) Note that this system uses function k(t) to normalize function f(t) for volatility. This isn’t necessary. A simple constant can be used for k(t) instead. Normalizing for volatility, though, does create a more dynamic model that delivers more stable results over time.

This is only the first part of the Trend Determining method, though. We need to use other methods to confirm or maintain the open position. This is done with digital filtration. First, the system filters a stream of prices, taking away all cycles of less than 10 and more than 40 days in length. It creates an oscillator, derived from the stream of prices, main trend and high-frequency noise. The universal interval from 10 to 40 days was found by researching spectrums of price streams of several currency pairs using Burg’s algorithm.

The digital filter is based on Park McAllen’s algorithm and is built by using MtxVec library programs. The digital filter is a band pass filter with the following parameters, some of which were indicated earlier: pass band cutoff frequency P(1) = 10; stock band frequency D(1) = 8; pass band cutoff frequency P(2) = 40; stop band frequency D(2) = 44; stop band attenuation A(1) = A(2) = -40dB; pass band ripple R = 0.08. The result of the digital filter is to generate the active market cycle. Next, we calculate lines of a root-mean-square deviation from its 25-day moving average. By using the extremes of active cycle in intervals from one to two standard deviations on each side, we can determine when we exit a position. When the active cycle has reached its extreme on the closing of a current day, we close our position on the opening of next day.

The stop loss is derived from the last 10 days of volatility and is seldom triggered. Its main task is to protect the account from an uncharacteristically large market movement; usually in those cases the system does not have enough time for reaction on its own.

SEEING IT WORK

Originally, the TD method was designed and backtested for the euro, with 2001-05 used as in-sample data. Then the method was applied to the pairs, using 2006-07 as the out-of-sample data, with one year of lookback. To demonstrate how this system works, we can look at spot trading in the GBP/JPY, from Nov. 6, 2007, through Jan. 9, 2008. All trades were made on the opening. The market data, along with the Determined Chaos function and active cycle indicator, are shown in “Point of chaos”

“Rising equity” shows a one-year period of backtesting performed on this currency pair, from Dec. 27, 2006, through Jan. 1, 2008. During this period, the system executed 22 trades, 17 of which were profitable with a return of 100.7%. Backtesting in base pairs during 2007 is shown in “Across the board”.

The Trend Determining system generates a high percentage of winning trades. Because of this, the risk of a significant drawdown is reduced and more stable profit expectations can be maintained. We can relax the restrictions of money management strategy and allocate a larger portion of initial trading capital to each trade while remaining at an acceptable level of risk.

Aleksey Yudin has been researching nonlinear methods as applied to markets since 2005. He can be reached at yudinaleksey@hotmail.com