*Cycle Analytics for Traders: Advanced Technical Trading Concepts*(Wiley, 2013).

Two types of traders should read this book: those who want to know why things work and those who are looking for new and improved indicators. Since I belong to the former category, I’ll quickly dispense with what probably interests most technical traders—indicators. The book comes with a PIN code to access and copy the EasyLanguage computer code found in the book, some of which is quite lengthy and would be exceedingly tedious to retype. Among the indicators whose code is provided are the decycler, decycler oscillator, band-pass filter, Hurst coefficient, roofing filter, modified (and adaptive) stochastic, modified (and adaptive) RSI, autocorrelation, autocorrelation periodogram, spectral estimate, even better sinewave indicator, convolution, and Hilbert transformer. There is code to compute the dominant cycle using the dual differentiator method, the phase accumulation method, and the homodyne method. There are also indicators for SwamiCharts. (If you don’t know what SwamiCharts are, a quick Google search will fill you in.)

As for the why. Ehlers is careful to explain the principles and the math behind these indicators. But he does more. He reflects on the very nature of the markets themselves. I was particularly struck by his thoughts on the drunkard’s walk hypothesis.

Ehlers begins with the claim embraced by proponents of the efficient markets model that price fully reflects available information. This claim “has been assumed to imply that successive price changes are independent of each other” and that “successive changes are identically distributed. Together, these two hypotheses constitute the random walk model. This model says that the conditional and marginal probability distributions of an independent random variable are identical. In addition, it says that the probability density function must be the same for all time. This model is clearly flawed. If the mean return is constant over time then the return is independent of any information available at a given time.” (p. 70)

In its stead Ehlers proposes a constrained random walk model. I can’t summarize it properly here, but let me highlight a few points that may serve as guideposts. First, “the equation governing the distribution of the displacement of the random walker from his starting point” is the partial differential equation known as the diffusion equation. It can be illustrated by a smoke plume leaving a smokestack, which is akin to the way a trend carries itself through the market. Second, Ehlers modifies the random walk model to allow the coin toss (which determines whether the drunkard takes one step to the left or the right) “to determine the persistence of motion. In other words, with probability

*p*the drunkard makes his next step in the same direction as the last one, and with probability 1-

*p*he makes a move in the opposite direction. … The interesting feature of the modified drunkard’s walk is that as the distance between the point and the time between steps decreases, one no longer obtains the diffusion equation,” but rather a different partial differential equation, the telegrapher’s equation.

The drunkard’s walk solution can thus describe two market conditions. “The first condition, where the probability is evenly divided between stepping to the right or the left, results in the

*trend mode,*described by the diffusion equation. The second condition, where the probability of motion direction is skewed, results in the

*cycle mode,*described by the telegrapher’s equation.” (p. 72)

I trust that this review, however sketchy, indicates that Ehlers’ book would be a very valuable addition to any trader’s library. It encapsulates decades of thoughtful work.

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