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 in PDF form may be downloaded from ResearchGate or Internet Archive. Moreover, a digest of the report is available as a video at YouTube.

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