Newsletter: On Non-Periodic Cycles for Market Analysis
Detecting and measuring non-periodic cycles is crucial.
My most cited work are the papers and books on fractal analysis. In particular, rescaled range (R/S) analysis. Developed by Edward Hurst in the early 20th century, it was extended by Benoit Mandelbrot in the 1970s. I published work on R/S analysis and the Hurst Exponent (H) from the late 1980s through the 1990s. Academics have primarily focused on the H which measures whether a process is white noise or a different colored noise. It can be a measure of jaggedness in time series as well as define the shape of the probability distribution underlying the process. Since my work in the 1990s more sophisticated and accurate ways to determine H have been developed. R/S analysis has fallen by the wayside.
But R/S analysis can also be used to detect dynamical systems, generally referred to as deterministic chaos. In the hypertext book, I give an overview of these types of systems and their relevance. Chaotic systems also have trends and cycles but they are called “non-periodic” because they don’t repeat exactly each time. Detecting and measuring non-periodic cycles from a time series can be difficult. But I found that using R/S analysis, non-periodic cycles can be detected and measured even in the presence of large amounts of noise. These results were discussed at length in my books.
That most natural systems are non-periodic often gets overlooked. We have a natural tendency to want to make things regular so they’re more predictable. The ancient Greeks even went to so far as to say that the reason our world is full of irregular shapes is that our world is not the real world. It’s just a shadow of the real world where objects are perfectly smooth and symmetrical. Perhaps that’s why non-periodic cycles are not widely understood though they’re all around us.
That also may explain why R/S analysis’ ability to find non-periodic cycles has been largely neglected. But in my own work, it has been critical. I thought that in this newsletter I’d revive this methodology for those interested in market and business cycles/regimes.