The Fractal Behavior of the Financial Markets
Henry F. Wernicki
Introduction
Natively, the financial markets are comprised of fractals. A fractal is a continuous pattern. They are “complex patterns” that are self-similar across all different (time) scales. These specific patterns are images of dynamic systems – the “pictures” of Chaos. Fractal patterns are very familiar in nature. For example: trees, rivers, coastlines, mountains, clouds, seashells and hurricanes. The financial markets exhibit this extraordinary characteristic. There are also Abstract fractals that can be generated by computers.
What is Chaos Theory? It is the science of surprises of the non-linear and the unpredictable. Certainly, the stock markets fit into this category. Traditional science deals with supposedly predictable phenomena, like chemical reactions. Chaos theory addresses non-linear events that are impossible to predict, i.e., the various financial markets across the globe, weather, turbulence. Accepting the chaotic fractal nature of the financial markets offers insight and wisdom. For example, by understanding the weather and winds, a balloon pilot can land in an exact location. And by understanding the chaotic dynamics of the stock market one can then make informed investment and trading decisions.
Unpredictability: we can never know the initial condition of a complex system (a particular stock market or instrument). Hence, we cannot predict the ultimate outcome. Order / Disorder in the financial markets is not a simple disorder. Fractals explore the transitions between order and disorder in surprising ways.
Feedback: Systems become chaotic when feedback is present. A prime example is the behavior of the stock market. As the market rallies and declines traders are inclined to buy or sell. This further results in more chaotic behavior (more rising and falling).
Fractals are a visual manifestation of chaos theory. The hypothesis here is: can common fractals identify the trends of a stock market? Are they useful for identifying the markets' turns? Specific rules and examples will be presented to support a proven trading system using fractals in any market.
The World of Fractals
Defining The "Hidden Fractal Order" in the Financial Markets.
Fractals as a Visual Manifestation of Chaos Theory.