Exploiting Stock Market Cycles: Cycle Analysis in the Stock Market Is Not New. However, This Fluid Technique Is Difficult to Quantify. Here, We Look at One Core Indicator Designed and Tested with Fixed Parameters, Which Eliminates the Daunting and Often Non-Scientific Task of Input Optimization and the Curve Fitting That Often Results
Lorca, Francisco J., Modern Trader
Al-Khwarizmi was a Persian mathematician, astronomer, astrologer and geographer whose contributions in these areas provided the foundation for later innovations in algebra and trigonometry. He is considered by many the inventor of algebra.
One of Al-Khwarizmi's major works was a treaty he wrote in 825 AD on Hindi numerals, which was translated into Latin by the Toledo School in Spain during the 12th century, titled Algoritmi de numero Indorum. This book explained for the first time in the Occidental world the simplicity of the Hindu mathematical calculation, which contributed to the birth of today's algorithmic calculus. His work substituted long and tedious mathematical demonstration with graphs or charts.
Nowadays, the use of algorithms in the financial community is extensive and dates at least to S. Kaplan's "Computer Algorithms for Finding Exact Rates of Return" (The Journal of Business, October 1967), which improved the methodology used by Lawrence Fisher when calculating simple investment rate of returns. In other sciences, algorithms have a multitude of uses, ranging from bibliographical and database searches, facial recognition, DNA sequencing, etc. In reality, it is possible for an algorithm to detect the oscillatory properties implicit in nature that have, in fact, been empirically observed in the oscillatory tendencies of financial time series.
There is plenty of statistical evidence that shows that financial time series possess what is known as "long memory," which could potentially make the search for reliable market patterns a reality. Consequently, the creation of a pattern recognition computational algorithm could be made to detect these oscillatory properties to give traders an edge in the competitive financial arena.
This pattern behavior is present in the Fourier series--more precisely, the Square Wave--that shows how a simple pattern reproduces a repetitive behavior. This can be seen in "History repeats" (right), which can be divided into five parts. The first represents the ascending phase; the second, the horizontal phase, or equilibrium; the third part is the falling phase that leads to a new equilibrium phase; and finally, another ascending phase. For practical purposes, both equilibrium phases are identical and both reproduce a sinusoidal wave that can be subdivided into small sinusoids, waves, and so on.
GENERIC PATTERNS ARE NATURAL
According to Joseph Fourier, who introduced the Fourier series to the world, the equilibrium phase allows for a certain margin of variation, but is always bound within its generic shape. Market analysts have given these variations many names. The most common are referred to as double bottoms or double tops. In our study, these pattern formations are the combination of two, or at most three, simple patterns in different sequences.
The pattern as defined by Fourier as a "U-shaped pattern" may be formed by either an ascent-equilibrium-descent or a descent-equilibrium-ascent. The phase of ascent or descent completes the formation, which has been extensively studied by theoretical mathematicians.
According to Per Bak in How Nature Works: The Science of Self-Organized Critically, the descent phase, which will be the last part of the inverted U-shape, is used to study the phenomena of explosion in non-linear differential equations. This is a falling phase that results from an unstable system that ends in an abrupt movement in the form of an avalanche. Academic studies that explain this explosive phenomena were inaugurated by H. Fujita and continued by the studies of "Brownian Motion" in fluids. These studies have set the basis for the multidisciplinary approach to the prediction field of financial times series.
There are examples in nature that, depending on how they are observed, can yield different results. For instance, the position of the observer can be determinant in the appraisal of the phenomenon. …