A Sentient Trader user recently asked some very interesting questions about the Cyclic Theory that underlies the analysis performed by Sentient Trader. With his kind permission I am putting his questions, along with my answers up on our blog.

*Question (1)***:** Is it correct to assume that cycles are drawn on the basis of troughs lining up together (i.e. they all start a the zero point)?

**Answer:** Yes, that is correct, although THT allows the option for using synchonized peaks instead of troughs, but the principle is the same. This is in fact one of Hurst’s original 8 principles that defined his theory, and is a distinguishing factor of his theory as opposed to other cyclic theories.

*Question (2)***:** Why can’t there be cycles of different lengths with troughs all occurring with different starting alignments?

**Answer:** According to Hurst’s Cyclic Theory this doesn’t happen (as one of his fundamental principles), but in the work that I have done on cycles I believe that it does happen, because I believe that complex harmonic ratios between cycles are possible (such as 3:2, or 5:2, etc.). The new version of the software enables this theory which is a departure from Hurst’s original theory. In fact I don’t believe that troughs have “different starting alignments” because I think that all cycles do have synchronised troughs at SOME point, which would effectively be the “same starting alignment” for those particular cycles. Even with very complex harmonic ratios, there are always times at which cycles must “beat together”, or experience synchronised troughs, although it is possible that the beats (synchronized points) occur very far apart. This is a mathematical fact.

*Question (3**)***:** You draw different cycles showing each one being half the amplitude of the other. What really is the relationship between cycle length and its amplitude? The random walk theory would suggest perhaps that amplitude size as related to time by its square root. So a 20 day cycle would have an amplitude 1.414 times the size of a 10 day cycle (SQR20/SQR10). What are your thoughts?

**Answer:** I haven’t done much work at all into the comparison between a cycle’s wavelength and its amplitude. According to Hurst’s theory the amplitude is directly proportional to the wavelength (in other words a cycle of double the wavelength of another cycle will have double the amplitude). The reason I haven’t done much research into this aspect of cycles is because when cycles are combined their individual amplitudes become largely obscured, or at any rate not of much value in terms of making trading decisions. Of course what one does need some understanding of when trading is the combined amplitude of all the cycles that will be active during a trade, and there is a calculation performed in the new trading process of THT that does exactly this. Perhaps the most important thing about amplitude is that (I believe) it is very variable – cycles go though periods of “dominancy” and “recession” which are simply times when they are exerting a large amplitude, and times of smaller amplitude. I think that this degree of variation makes a calculation derived from the wavelength fairly arbitrary.

*Question (4)***:** Why can’t longer cycles have both a larger and smaller amplitude than a shorter cycle?

**Answer:** In fact I think they can, because of the variation experienced in the amplitude of cycles as mentioned above.

*Question (5)***:** We typically show cycle summation using a simple chart of 3-4 cycles, each being half the other. Saying there are an infinite number of cycles doesn’t really make sense, because that would mean there was only one wave summation pattern that can ever be present in the market which I think is obviously not true. So if there is a limited number, why do we assume that there might be a dominant cycle say on each of the major time frame such as hourly, daily, weekly etc and then sum them? Why can’t there by 2 major cycles on say the daily which are very close to each other? I guess that in effect shows up as one cycle in most respects, but technically it isn’t true.

**Answer:** I am not sure that I understand the logic that an infinite number of cycles would mean that there is only one wave summation pattern. But I think I understand the point you are making in the rest of the question. In terms of Hurst theory, I believe the term “dominant” cycle is in fact a misnomer. There is nothing particularly “dominant” about the cycle, except that it must have an amplitude that allows the effects of the cycle to be evident in the price movement. In fact Hurst chose the dominant cycle as the longest “visually evident” cycle in the chart being analysed. The important point really is that it is a fundamental principle of Hurst’s theory that cycles are related to each other by something that I call the Harmonic Ratio – in other words, simply the ratio between their wavelengths. Another one of Hurst’s 8 principles is that cycles are related to each other by a small integer value (such as 2:1 or 3:1). I believe that in fact there are more harmonic ratios present in the market, which is why THT now works with “complex” Harmonic Ratios, and one can define a nominal cyclic model that includes ratios such as 4:3. This brings me to your point of “why can’t there be 2 major cycles on a chart?” I believe there can be – for instance I am fairly convinced that there is a 4 &1/2 year cycle and also a 6 year cycle active in the stock market at the moment (in other words their amplitudes are strong). These are two cycles that are fairly close together, and defy Hurst’s principle of a small integer harmonic ratio, and yet there is evidence that they exist. Of course these two cycles have a “beat” of 18 years … which is possibly the reason that the 18 year cycle (as identified by Hurst) is so prevalent in the stock market. What you are saying I think by “in effect shows up as one cycle” is in fact the beat of the two cycles.

All of this brings me to another point about the way in which cycles combine, and this is an aspect of my own personal theory which I call the “Fluid Cyclic Model”, something we discuss in the Sentient Trader workshops. This is the concept that there is no one true and correct nominal model. That in fact the cycles that we have come to know (the “18 year cycle”, the “40 week cycle” etc.) are in fact merely a small subset of all the cycles that are present. This is a “fluid” cyclic model because the cycles which are prevalent constantly shift in “dominance” (or prevalence, or simply in amplitude). This theory takes the approach that for every cycle there are also present a multitude of harmonically-related cycles. And that all we are doing when analysing the market is highlighting a small subset of all of these cycles.

*Question (6)***:** Do you believe that cycles shift? If you believe they do, then (1) MUST be wrong. Can it be possible for example, that an ‘event’ occurs, which cause one or more cycles to RESET to the point in time?

**Answer:** I suppose this depends on what you mean by “shift”. We are on tricky ground here, because of course we don’t really know what a cycle actually is! However, in an attempt to answer this question, I would say this: Yes, I believe that cycles do “shift” in that they experience a constant variation, both in wavelength and in amplitude. By “shifting” we are talking here particularly about variable wavelengths. There are a few points that I would like to make about how I believe (and how Hurst’s theory predicates) that cycles “shift”. The first is that cycles exist within a constant and fairly complex “web” of harmonic ratios, and so if one cycle “shifts” or experiences a shortening or lengthening of its wavelength, then ALL other cycles with which it has a harmonic relationship (possibly every “cycle” there is), also “shifts”. For this reason the shifting of cycles does not contradict your point #1. I envisage it as a huge and 3-dimensional fisherman’s net. If you pull at one part of the net in order to enlarge or twist that particular “cell” of the net, then all of the adjacent cells must accommodate for this, because they are all connected. The same is true of cycles – a shift in one cycle has an effect on nearby cycles … with a lessening effect the further one moves away from the cycle being observed.

I also believe that cycles do not “reset”. Here I am venturing into particularly unknown territory because I am speculating about what a cycle actually is … but if I may draw another analogy, I think that a cycle could be compared to a heart beat. There is a contraction (decline), the beat (trough), and then the expansion (rise). It is impossible for a heart to “reset” or to jump from expanding to beating, although it is of course very possible that the process will suddenly speed up, or slow down. For this reason I don’t believe that cycles “reset”, but of course they could speed up suddenly, resulting in what might seem like a “reset”. As a matter of interest I don’t believe that events cause any reaction in cycles, I believe that particular cause and effect relationship is incorrect, and that if anything, the current state of many cycles “causes” events – or at least creates situations in which certain events could occur. But that is also something that we discuss at the Sentient Trader workshops, and beyond the scope of this discussion.

*Question (7)***:** If cycles shift in time, how do they shift? As mentioned above, or via perhaps a gradual change in the length of the cycle?

**Answer:** I think this question has been answered by the above comment. I believe they shift because of an underlying change in wavelength. Whether this shift is gradual or sudden I couldn’t say, but it certainly appears fairly gradual in relation to the wavelength of a cycle (in other words a cycle’s “speed of variation” is linked to the cycle’s wavelength).

*Question (8)***:** Why do we always draw cycles as sine curves? Why can’t they be some other shape?

**Answer:** I think they could be some other shape, but there are two important qualities that they share with sine curves: Firstly, a regular and repetitive movement back and forth over at least 2 dimensions (I think it is very possible that in fact cycles might have more dimensions, but we are only able to observe two dimensions – a rise or fall in price, or up and down). And secondly they have a continuous shape, as does a sine curve, in other words they don’t jump from one “position on the curve” to another.

*Question (9)***:** My point to the above questions is basically, is there anything concrete we can say about:

- The number of cycles in the market;
- Is the relationship between time and amplitude fixed?
- Are cycle lengths fixed?
- Can cycles shift and/or change length?

**Answer:** My answers to this, as explained above are (as I believe):

- There are an infinite number of cycles
- There is a relationship between wavelength and amplitude, but not one that is fixed. In fact I think it is one of the most variable aspects of cycles.
- No, I don’t believe the cycle lengths are fixed. I think that they constantly vary, but that over a limited amount of time they could be considered to vary about a fixed length (Hurst’s nominal lengths).
- Yes, I think they do shift and change length constantly.

*Question (10)***:** If all the above variables and relationships are not fixed in any way, it makes our job of discovering what cycles are present at the time and going forward, and what it means summation wise, and therefore trading wise, very difficult. Impossible in fact. The random walk theory would dominate. If we feel the RW theory does not dominate, then it implies there must be something concrete we can say or define about the above variables. The question is, what is it that has been proven beyond a reasonable doubt?

**Answer:** You are absolutely correct in saying that it makes our job of discovering what cycles are present at any time very difficult. But I do not believe it is impossible. I think the important thing is to “understand what we can, ignore what we cannot, and have the wisdom to discern between the two” if I may paraphrase Niebhur’s famous “Serenity Prayer”. What I mean is that it is possible to making profitable trading decisions using the information that we can discern about cycles in the market. We cannot understand it all (that is indeed impossible), but using the information that we can glean from the markets, we can make profitable trading decisions.

You ask what has been “proven beyond a reasonable doubt”. I would have to say that nothing about cycles in the market has been incontrovertibly proven. There is no mathematical proof in the strictest sense, but there is overwhelming evidence that the prices of financial markets are moved by a combination of harmonically related cycles. What those cycles are nobody knows for sure, but when one is able to regularly make profitable decisions on the basis of this premise, or theory it means one of two things: either the premise is true, or the results are pure luck. The frustrating thing is that argument will never be resolved one way or the other, because how long is too long for it to be pure luck? One year, ten years, a hundred years?