A non-subjective approach to Hurst analysis

Much of Hurst’s workwas based on his spectral analysis of The DJIA. Using mathmatical bandpass and curve fitting techniques involving some “challenging” math, he was able to produce what I have always felt was nonobjective cyclicical analysis. He then went “the other way” in his course which most of us have studied and introduced, in my opinion, “art” and subjective interpretation into the process.This has always bothered me because it results in muliple analyses, with varying cycle lengths and different projections. How do we know what is right and what is wrong? Once one learns how to use Sentient trader, one can almost always come up with 2 completely opposite outcomes, depending on the starting point and the nominal model.
The starting point is the spectrum but all spectra are not alike

Here we have a peiodogram that represents weekly USD futures going back to 1967. It shows a dominant 4 year cycle.

Here is the periodogram with an emphasis on the more recent data. Note the prominant 4 year cycle is no longer dominant, replaced by an 8 and a 16 year cycle. This is demonstating an important characteristic of financial data: cycles are not necessarily persitent, but are born, live, and then die.

A mathmatical technique that can evaluate when cycles are active are wavelets, pieces of waves. The wavelet diagram confirms what the 2 periodograms demonstated, the temporary appearance of the 4 year cycle and the persistence of the 8 and 16 year cycle.

The chart has the 8 (8.2 to be exact) year cycle plotted and is satisfactorily demonstrating the last 3 troughs.

Enhancing this wave with its 7 harmonic overtones produces a reasonably accurate price trace with only 2 major (but exact) inversions.
Now I have objective parameters to perform a cyclical analysis using an 8 year dominant cycle and harmonic supra and subcycles factored by 2 and beginning on the week of 4/95.

The analysis is presented above. I don’t like the inversion at the 2008 low. The accurate tracking of price by the composite line is, however, a good sign. This analysis points to a price peak 1/2018.
Of relevance: I just attended Martin Armstrong’s 2016 conferance. It is, and has been, his contention that the USD will rise as the chaos that we have been experiencing increases and capital seeks the “safest” place to park until we end in a soverign debt crisis begining…2018.
Armstrong’s profound understanding of cycles is on par with Hurst’s, in my opinion, but that’s a topic for another post.


The problem is the title. You call it not-subjective approach and that implies everyone’s approach is subjective. Your own analysis however is based on 2 (two) 16? years cycles. Timing Solutions (i have the software) and the type of analysis applied, requires at list 3 and preferably more then 3 complete cycles of data. Personalty, I have a problem with objective analyses of the long term USD exactly because of my inability to find long term data series for the USD.

Best Regards

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Hi b3cker
The analysis is based on the 8 year cycle…a 16 year cycle results by Hurst’s principle of harmonicity.
More data is a double-edged sword because more means longer potential cycles v. averaging cycle lengths which may or may not be active. If you look at a long timeframe of data such as the DJIA which can easily be had at STOOQ.com back to 1898, you will see this: markets constantly change as do cycle lengths and amplitudes. I am interested in creating a tradable projection which will probably be valid for only a very short time in the future.
Finally, it is nonsubjective because it is built mathmatically…and it does not imply that ALL other methods are subjective. Anyone who has performed a great deal of Hurst analysis using the course and the pattern recognition method knows this as compared to the Profit Magic method.

Here is my subjective projection. It is subjective because larger cycles are under-weighted in the analysis and because cycle large then 16 years can not be correctly phased. However it seems that underlining trend larger than 16 years has bottom out and pushing up. Regardless, ether 32 or 48 years cycle has bottomed. Or I am totally confused here because of luck of data.

49 years of data for DX.F at STOOQ.com

B3cker Nice Enveloppes !

Assuming next larger cycle is 32 years and I suspect it is 48, I would need 2 full cycles or at list 64 years.

My DJIA data is reconstructed and going back to 1820 and DJIA model is second to none.

Opposite to USD I have about 100 years of data for the British pound and non-subjective long term analysis can be done and it is supersedes my USD analysis. Also it can be tested, There is enough data to run out of sample test.
out of sample

real time

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Hello Stuart,
Interesting topic and stimulating the methodological discussion.
At first, reading the thread suggested, I was puzzled about the meaning of the title. Then, according to the Aristotle’s principle of non-contradiction, a proposition must be true, and the other false. If the approach is not-subjective then it is an objective approach replicable by anyone using common scientific instruments.
IMHO, the central thesis of Stuart is

  1. the nominal model of Hurts does not exist without the spectral analysis of prices action
  2. the output of Hurst is a subjective cyclicical analysis, especially when in its course introduces the concepts of starting point, varying cycle lengths and its reflex in the nominal model.
  3. the starting point determines the spectrum but all spectra are not alike.
    This position makes me think to a different approach to the search for periodicity in the data first presented in 1999 by W.A. Sethares and T.W.Staley in a paper entitled “Periodicity Transforms”, downloadable at this link
    It resumes a classical technique, called the Buys-Ballot table, for the determination of “hidden periodicities”. None of the available methods directly searches for periodicities in the data. The set of basis vectors is not specified a priori, rather, the PT finds its own “best” set of basis elements. The PTs decompose a signal into a sum of periodic sequences by projecting onto sets of periodic subspaces. As the authors note, the results of the PTs depend on the order in which periodic signal components are extracted.

a short table of comparison

(*) In a paper “Orthogonal, Exactly Periodic Subspace Decomposition” on 2003 D.D. Muresan e T.W.Parks eliminates this problem by generating orthogonal periodic subspaces.
The PT is designed to locate periodicities within a data set by projecting onto the (nonorthogonal) periodic subspaces. The method decomposes signals into their basic periodic components, creating its own “basis elements” as linear combinations of delta-like -periodic basis vectors.
I have not seen it yet applied to the historical series of shares and futures.
I’m late with the study. I can not contribute so profusely like you, Alain and Gary. I completed the mathematical analysis underlying the Hurst’s envelopes, following the reference of PM. Currently, I’m hardly performing the algorithm in VBA, expected that programming languages are not one of my skills.
With kindest regards

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Hi Stuart.

This has always been one of my favorite Hurst topics so I thought I would add my two cents. I don’t believe Hurst “went the other way” with respect to the cycles course. I view it as a simplification of the complex math put forth in Profit Magic. Personal computers, streaming data, etc. were not available to the average trader in 1970! I feel Hurst did a masterful job of putting it in a form that the pencil and paper trader could use in 1970.

The “subjective” issue I see today is the definition of what it is one is looking for in the price action. What I (subjective) am looking for is the dominant price wave as defined by Hurst in Profit Magic. It goes without saying that differs from ST’s “pattern recognition” approach which is Hickson’s (subjective) interpretation of Hurst’s cycle course. These differ from some “spectral analysis” approaches which define the dominant “cycle” by fitting a single angular frequency through the price action. These approaches, which sometimes yield similar results, are not interchangeable in my opinion.

This debate will be endless. The deciding (objective?) factor for me was simple, the one that makes the most money with the least amount of risk over all market conditions, verifiable through extensive back testing. I picked my poison and am very satisfied with the results.



Hurst is all “subjectivity”

Subjectivity with the “spectral model” listed in Profit Magic page 199 Figure A I-8 where Hurst ignores a 5;7 year frequency result to keep a 4,3 year result which fits better with the 2 first results he got (17,3 year and 8,5 year) . you see the HALVING process - but what about the 5.7 year (6 year ?)

then he assembles together 3 results - 3.4, 2.9 and 2.4 which he averages in a 3 Year in the model. 3 year which after that disappears without explanation - why ?

if you read attentively the data (in months ) you notice that you can assemble together the results and build a slightly different model

with the same data you can introduce another serie of frequency 18 Months, 3 year, 6 year , 9 year which exists also and build a better case for the relation 2 and 3 between cycles.

other “subjective view” - page 33 Hurst writes that the 6 and 3 months cycles, sorry COMPONENTS (26 and 13 weeks) "often appear in data as a combined effect of a 18 week nominal duration "

why ?
can other “cycles” appear in data as a combined effect of x (weeks, months, years ) nominal duration ?


A mon avis, I do not think it is pure subjectivity. At the base there are harmonic relationships that develop according to two progressions for 2 or 3 and their reciprocals (odd and even legs ). The model is developed (vibrates) according to the issue, in this case the DJIA. I refer the Dewey’s scheme you certainly already know.

They are REdiscoveries of Dewey and Hurst of what the Ancients called the Pythagorean Lambdoma.
The frescoes “The School of Athens” by the artist Raffaello Sanzio, reports the Lambdoma near the foot of Pythagoras and Averroes.

In underlying Lambdoma, we have two series, one of the numbers (red color) that compose the Plato’s Tetractys and that based on the three multiple of the numbers Six, i.e. 36. The sum of the three numbers given to the vertices of the triangle is 1 + 8 +27 = 36.

Veuillez agréer mes salutations très distinguées


USD may be due for to a major top in Feb 2017

Dear b3cker,

Can you show more weekly projection view ? Your projection maybe right because the is a gap needed to be filled up. I have a different view.

Thank you.

Using projection longer then shortest cycle in the composit may produce unreliable results. To extend the composit in to the future I will have to repeat analysis on the monthly bars.

I view it in this way because of the cycle time is completed. If next week go lower and filled up the needle bar portion then it is in this way. If not it is in your way.:grinning: Still have another week to monitor. Next week is NFP. Fast move next week.

Goh, if, as your chart suggests, DX has made an 18 month peak, it needs to come to an 18 month trough before surpassing the 18 month peak again. Back to the drawing board for that analysis I would suggest.

I do not see it directly goes to the bottom. It cannot react like that. It must form a channel before move on. What composite line proposed is correct.