Basic Models of Complex Systems

Crux of the Duplex Method
plus Case Study
of the Dow Stock Index

We live in a world full of complex and chaotic systems. A good example concerns the stock market that stymies all manner of investors ranging from casual amateurs to gung-ho professionals.

According to the Efficient Market Hypothesis, the current price always reflects the totality of information available to the investing public. As a byproduct, no one can detect any clues for predicting the market in a trusty fashion.

Instead, the market is deemed to move in an utterly erratic way. In particular, a popular myth known as the Random Walk shuffle contends that the price level shifts with equal likelihood and to similar extent in either direction, whether to the upside or downside.

At first glance, the image of pure randomness does ring true in practice. For instance, the average investor is unable to beat the market averages such as the Dow Jones index. While the lack of success may seem like a letdown, the truth is even worse. In actuality, the participants in the aggregate lag comfortably behind the benchmarks of the bourse.

If we look more closely, the lousy performance of the actors springs mostly from their frantic efforts to beat the competition. Amid the frenzy, the demons of greed and fear prod the antsy players into making impulsive moves that are not only groundless and futile but actually counterproductive and harmful to their cause.

On the bright side, though, the market displays a smattering of patterns that can be exploited by a sober person. An example concerns the seasonal cycle behind the monthly moves of the Dow benchmark.

To fathom the elusive waves in a stringent fashion, we turn to the duplex method of modeling shifty systems. The sturdy framework makes use of the binomial test: the simplest and strongest, as well as safest and surest, way to profile chancy events regardless of the domain.

To this end, we first transform the conceptual models of the stock market into a trio of precise templates. The formal blueprints are then converted into R code: the top choice of programming language and software platform for statistical workouts. The trenchant results serve to debunk the fable of efficiency and confirm the existence of hardy patterns in the marketplace.

In short, the benefits of the seasonal model lie in simplicity and potency in sundry forms. The drawcards include the ease of acquiring the information required, the leanness of the dataset employed, the ubiquity of the software deployed, the universality of the experimental setup, and the strength of the conclusions at high levels of statistical significance.  

NOTE:  The full report is titled, “Basic Models of Complex Systems”. The document may be downloaded in PDF form at Smashwords or ResearchGate. Moreover, a digest of the report is available as a video at YouTube or Internet Archive.

 

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Duplex Models of Complex Systems

Binomial Framework and Case Study 

of 

Seasonal Waves in the Stock Market 

Duplex models can portray complex systems with the utmost of simplicity, clarity and efficacy. The drawcards range from the dearth of initial premises to the soundness of final conclusions. The mettle of the binomial approach shows up, for instance, in debunking the welter of myths and misconceptions that pervades the fields of finance and economics. According to the Efficient Market Hypothesis, the marketplace always reflects the totality of information available to the general public. Since every nub of know-what and know-how informs the latest prices, no single actor can improve on the valuation of assets ranging from stocks and bonds to commodities and realties. 

One consequence is the lack of trusty cues for forecasting the market: if every clue has been fully utilized, then any move henceforth has to come as a complete surprise. Another fallout lies in the Random Walk Model that pictures the path of the market as a form of Brownian motion whereby the price level is wont to shift in any direction with equal likelihood. 

Unfortunately, the Efficient credo abounds with flaws ranging from unreal assumptions and spurious concepts to inconsistent models and faulty conclusions. A counterpoint involves the wave motion of the stock market that belies the premise of utter randomness. As a recourse, a true science ought to build on hard data and staunch precepts, rigorous models and tenable results. To this end, the study at hand represents a small but fundamental step toward a coherent theory of the marketplace. 

To underscore the gulf between the mythos and reality, the work plan takes a minimalist approach. For starters, the inquest draws only on a minute fraction of the trove of information freely available at the most popular portal among the investing public. Moreover, the quantitative analysis relies solely on the simplest technique in statistical testing. From a computational stance, the attendant program invokes a skimpy subset of the built-in functions within the core module of the R system: the leading choice of programming language and software platform for data science in disparate domains. 

NOTE:  The ebook is available under the title of “Duplex Models of Complex Systems”. The document in PDF form may be downloaded from the Internet Archive or at ResearchGate. In addition, the title is distributed in EPUB format by Apple Books and other partners of Books2Read.

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