S&P 500 – 4 Year Cyclical High 30

2015 is shaping up to be an exciting year. The Gannologists are expecting a 25-30% advance in the market due to this being the “5th year of ascension.” Robert Prechter and the Ellioticians are still looking for the elusive “Grand Super-Cycle Peak” which will usher in a catastrophic decline in the indices. Harry Dent and the Spending Wavers are expecting a great deflationary spiral which also preludes a catastrophic drop in the indices over the next several years. Then there are the Hurstonians (me) who are trying to pin down the 4 year cyclical high which may mark the end of this 6 year uptrend.


Below is a weekly chart of the S&P 500. The price wave at the bottom of the chart is the 4 year wave showing 4 and 1/2 oscillations. The output was run through a demodulator which provides a clean look at the dominant price wave. The underlying cyclical structure today is virtually identical to the prior four 4 year cyclical highs. It is my opinion that the probability of this being the 4 year cyclical high is very high.


^SP500 (Weekly)  Week 23_1998 - Week 10_2015

David postulated in his most recent post that the phasing of the 80 week wave is the determinative factor as to whether the indices are at or approaching the 4 year high. I do not share that view. The uptrend over the last two years has been so strong that the amplitude of the 80 week wave has been so greatly reduced that, alone, it has had very little influence on the price action from a filter perspective. However, in my opinion, the 10 week wave has been the most visually evident price wave since the November 2012 4 year low. In addition the 10 week price wave has painted 15 consecutive higher highs since the 4 year low. I believe the first indication that the 4 year high has formed will be a change in that pattern, i.e. a lower 10 week high. A lower 20 week high would be the final confirmation.


The chart below is a weekly chart of the S&P 500 showing the most recent oscillations of the 10 week wave. It is currently cycling down. How far down the price action will drop is unknown. The usual suspects are based on standard FLD projections. The shorter waves, which are showing big amplitude again, will greatly help in identifying approximately when the next 10 week low will occur as the price action approaches it. A weekly close below the bottom of the dominancy envelope will provide a strong indication that the next 10 week high may be lower.






^SP500 (Weekly)  Week 23_2013 - Week 10_2015


About William Randall

I'm a retired attorney who discovered the fascinating world of the financial markets almost two decades ago. After learning about Hurst, I've spent the last several years honing all the skills necessary to fully implement the techniques he taught.

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30 thoughts on “S&P 500 – 4 Year Cyclical High

  • Jeffrey Young

    We have surpassed the mid-channel and I am expecting at least 2000.00 to be reached but had a target possibility of 1990.00-2000.00. I do not agree that the 20 week low occurred in February. What are you using to generate band pass filter. I would really love to learn more about this William as I think it adds value to the Hurst cycle analysis. Could you help point me in the right direction? As always I find you work informative and well thought out. Always a pleasure reading your posts.

    • William Randall

      Hi Jeffrey.

      90% of what I know I learned from studying Profit Magic, particularly Chapter 11, the appendices, and some of the reference materials. Hurst gave a thorough explanation of how a bandpass filter works. I strongly advise using the filter parameters he provides to recreate the 4 year wave on page 152 in Excel. Once you do that you will have a very strong foundation about digital filters and should be able to construct any kind of filter you want (it is very easy once you grasp the underlying principle). My other great source of course was Google and Wikipedia! Do not rely on canned code. Learn how to do it yourself. Most of the commercial stuff I’ve seen is useless for very obvious reasons.

      As for February being the 20 week low, from a spectral viewpoint there is nowhere else to place it. That is one of the advantages of of a filter approach. You don’t have to guess where it is, the filter output will show you. It completely eliminates the need for “alternative analyses”, provided your filter parameters are reasonably accurate.

      • David

        After reading through these posts I decided to delve into Ch. 11 for the first time. I’ve worked through the Cycles Course a few times but am sensing that some of the contributing analysts here don’t put a whole lot of stock in it. My question is that when Hurst is discussing calculating angular frequencies on pp. 173 of Profit Magic he tells the reader to take the value of “Z” and divide it by the chosen digital data spacing. I’ve tried with no avail to figure out what he meant by digital data spacing. I’d appreciate it if you could define this. As a side note are there parts of the Cycles Course you do find of value.

        Thank you,

        • William Randall Post author

          Hi David.

          Firstly, I found the Cycles Course to be invaluable. I’ve been through it numerous times. Even today when I’m uncertain about something I’ll dig it out for clarification. That being said, it is my opinion that the Cycles Course is a simplified version of the complex math presented in Profit Magic with the addition of concepts such as the FLD. Keep in mind it is 1970 and there are no personal computers with Excel, trading platforms, or live data feeds. It would have been impossible for the average trader to complete the computations outline in Chapter 11 and the appendices. Hurst did a superb job of making it available to the pencil and paper trader. Today a smart phone probably has more computing power than the computer Hurst used, not to mention the power of a contemporary desktop. I say use it.

          Secondly, “digital data spacing” is very simple. Many years ago it took me a while to figure out to what Hurst was referring. In the example in Chapter 11 Hurst used “digital data spacing” of 7 in applying his filter. It simply means he used every 7th data point or every 7th weekly close. It can be applied to any sampling period. I like using daily data because I can fine tune the spacing to eliminate the shorter frequencies of no interest to me.
          I hope this helps.

  • Doc

    Hello William,
    Much appreciate your work. Do you think last Wednesday was a late five-week low or an early 10 week low based on your Bandpass filters? Since it was 5 1/2 weeks in duration off the early February low I’m inclined to think it was a late five-week low. In that case the shorter cycles may also be lengthening which would support the idea of a transition to a more bearish stance. We also bounced right at the VTL off the October lows and any future violation of this might also be another signal of a longer term trend shift.
    All the best,

    • William Randall

      Hi Doc.

      My filters tell me last last Wednesday was the third 20 day oscillatory low since the 1/30/15 low close (my filters are based on the close, not the absolute low). The shorter waves are not lengthening. The last two or three oscillations of the 10 week wave separate beautifully into simple harmonic relationships almost all the way down to my 30 minute action signal wave! It is not impossible for that to be a 10 week low, but it would be very early. With the 40 week wave cycling down and the 20 week wave cresting, the probability is low that Wednesday was the 10 week low.

      I’m not as big on FLD breaks being as definitive as Hurst suggests, however while the price action managed to stay above the 20 week VTL, it has broken below the 10 week FLD and has yet to break back above the 20 day FLD. I still maintain that the first clear signal that the trend is changing will be a lower 10 week high.

      • Doc

        Thanks for the prompt reply. I agree that the 10 week cycle do not appear to be lengthening at this time. In fact, they have been shortening. If I take August 7, 2014 as a 10 week low then the next 10 weeks low was also the 40 week low on October 15, 2014 and came 49 trading days later. The next 10 weeks low on December 16, 2014 came 44 trading days later. I count holidays such as Thanksgiving or Christmas as trading days. The next 10 weeks low was a rather short and early 20 week low on January 30, 2015 coming just 33 trading days later. The average length of these three 10 weeks cycles is 42 trading days. If March 11, 2015 was the third 20 day cycle in this 10 week cycle then it came at 28 trading days along this cycle. That would leave roughly 14 trading days before the completion of this 10 week cycle. That projects to roughly March 31, 2015. Does this summarize your current phasing of the near-term cycles? Thank you very much in advance.

        • Doc

          By the way I might add that since the three oscillations of the 20 day cycle took 28 trading days that’s an average of 9.3 trading days per oscillation. That would mean technically that another 9.3 days after last Wednesday would be the expected fourth and final oscillation low to mark the 10 week cycle. That’s projects to next Wednesday or March 25, 2015. This means two things. First it means that this 10 week cycle would only be 37 to 38 trading days or little bit under the average of the last three oscillations. It also means the 10 week low will come about a week earlier than the calculations I presented above. How do you resolve such differences between the smaller cycles such as the 20 day cycle and the longer cycles such as the 10 week cycle in these cases where apparent discrepancies arise? This is an age old Hurst question I know. I’m just wondering how you resolve these discrepancies in your experience and with your tools.
          All the best,

          • William Randall

            Hi Doc.

            That is a very good question. It has a couple of simple answers. Firstly, I use calendar time when I apply my filters. I have found that if one uses trading days the shorter waves become distorted.

            When I project a wave into the future I project a range based on the deviation from the average, not just the average of the wave. I wait for the price action to enter the window of both the 10 week wave and the 20 day wave. At that point I dial down to a very short, harmonically related wave and wait for my action signal. This approach is necessary due to the constant modulation of the price waves. This effectively eliminates any conflict based on projecting just the average into the future.

            Another technique I use is to project the filter output into the future based on the current rate of curvature. Below is a daily chart of the ES with 20 day and the 10 week waves projected into the future. When both waves are projecting a trough, I wait for a highpass close below the lower deviation line on both charts. Once again I then dial down to a very short, harmonically related wave for my action signal. The margin of error decreases as the low is approached. Either of these approaches can be applied to any combination of dominant waves. They also very effectively handle the situation when the dominant waves do not exhibit a simple harmonic relationship.

          • Doc

            Thanks for the clarification on calendar days. I also like your ideas about using a range as well as projecting your filter waves into the future as well as dialing down to smaller cycles. I have used 30min charts in the past for such purposes. What you describe is undoubtedly your plan for going long at bottoms. Do you have a method you use for triggering going short prior to larger cycle lows such as a 10,20,40,80wk or 4.5 year lows in order to play the short side? There hasn’t been much meat on that bone in this bull market but as you eluded, that is likely coming to an end.

      • Doc

        Hello William

        Could you please update us on what your filters suggest for the 20 day cycles in relation to the 10wk? Price action is suggesting that March 11 may have indeed been a late 5 wk cycle low or an early 10 wk cycle low (less likely).
        Much thanks in advance.


        • William Randall Post author

          Hi Doc.

          As you can imagine this week’s price action threw a monkey wrench (or sabot) into the simple phasing of the intermediate price waves. However, the shorter waves remain relatively clear. The 20 day wave is at a peak and, barring a catastrophic drop next week, should cycle down and form a higher low. Identifying the low should be simple using harmonically related shorter waves. If the index is starting a new intermediate up leg, the amplitude of the shorter waves will shrink noticeably. It will take another few days before the phasing of the 10 week wave becomes clear.

          • Doc

            Thanks William. Your answer raises another simple question. You said before that we have already had 3 cycles of the 20day cycle since the Jan 30 low and the 4th one is now cresting. When this last 20day cycle does cycle down to its low in the coming days, wouldn’t that force you to conclude that the 10wk had also bottomed in order to keep the 4:1 relationship between the 2.5wk and the 10wk cycles intact? You wouldn’t allow five 20 day cycles inside a 10wk cycle would you? I guess another way of saying it is, if the 2.5wk cycle is clear and we are 3.5 of them along, this next 2.5wk low should also equal the 10 wk low and that should be just as clear due to harmonicity.

          • William Randall

            Filter outputs do not always operate in a simple harmonic relationship fashion. Many times they will form a complex harmonic relationship with the adjacent dominant waves. In addition they do not always synchronize at the absolute low. Hurst actually mentions this in the Cycles Course but for sake of simplicity we assume they do for descriptive purposes.
            All of the filters are independent of one another even though they share an internal consistency. The 10 week wave filter output will display the cyclical low irrespective of when the 20 day filter output displays the 20 day low. Due to the large amplitude of the shorter waves the 10 week low probably won’t synchronize precisely with the next 20 day low using daily data but it should be fairly close. I doubt if it will stretch to five oscillations of the 20 day even though it is possible.

          • William Randall


            FYI you were correct. The move up out of the 3rd 20 day cycle was so strong it turned the 10 week wave up (subject to some nowtime error due to filter lag) even though the current cycle is very short. This is an example of a complex harmonic relationship. This approach is somewhat more difficult than a simple harmonic approach, but I believe it is more accurate.

        • SilentOne

          Hi Doc/ William,
          It would appear that a 10 week low is forming here. Could be in here this week or drag on into early next week. Then we should enter the last 10 week cycle for the current 40 week (off the October low). I’ll abstain from judging where the last 18 month low came in.

          • Doc

            Hello John,
            Nice to hear from you. Phasing the SPX has become a bit difficult lately. I was expecting the 10wk low around March 31, but William’s bandpass filters are apparently suggesting it might have come early, on March 11th. If so, that would be an extremely early 10wk low based on historical and recent lengths for the 10wk cycle. It would also mean that we just saw the 20day low this past week and there would only be another 3 20day lows before the upcoming 40wk low. I would welcome an update from William on his 20day and 10wk filters and perhaps it would be better if he started a new thread. It would be much appreciated.

  • Stuart Mendel

    “Secular High……sort of”

    I am of the opinion that in 2015 we are both fortunate yet possibly hampered but the work started by JM Hurst probably 50 years ago. A quick Google search incorporating his name, Cyclitec, and anything known about him yields very little that we don’t already know and so we must rely only on the work he left. And so inspired first by David and then by William, I have spent a great deal of time rereading and reconsidering what it all means and have come a conclusion which generates a new question.
    The conclusion: His work, and by that I mean the core, is profound yet securely guarded in chapter 11 and the appendices of Profit Magic; you know the part of the book that everyone who reads it skips due to the appearance of equations consisting of summation signs, polynomials regression, and worse .In fact, I would wager than the number of people who have worked through it all could be counted on the fingers of one hand (I have no factual data to back this up except to say not too many traders are profitable and not too many traders use Hurst(correctly). Profound? Sure…look at William’s work!
    But now the question: Hurst wrote in the 1970’s. Profit Magic, true to the time of its writing, references what to do in the event of a war, but does not deal at all what do with a world wide debt laden fiat money system clearly under control of Central Bankers. And he also wrote that most of the price action(75%) consisted of the long term, slowly changing trend with a small but significant additional component of “cyclicality.” But what happens to all of this under our present conditions where the concept of price discovery may be a fond memory causing the market to cruise in”trend” mode?
    Given the potential of a 4.5 year high, and going back to 1987 I can extract 2 long term oscillations: from 1987 a 92 mo wave and from 2002 a 41 mo wave. Not exactly perfect harmonicity, but that is what the math says so we go with it. I’m fine with 41 mo but 92 mo is outside of the approved Hurst range and so should be weighted less strongly in our consideration.
    Simply taking this information, informing ST to phase it not with “The Nominal Model” but with a model consisting this market generated data, results in 2 analyses that both call for a least an 18 mo cycle top. I have not adjusted ST to take any current sideband modulation into account; all I have done is “tune” it to dominant oscillations in the market.
    What I believe is notable in both of these analyses are the relative shallowness of these really long term troughs. If correct, we should not get too excited about a low risk, Graham and Dodd low PE entry point but should instead look forward to yet more time to be uncomfortably long.

    • William Randall Post author

      Hi Jim.

      First let me clarify that my chart is not a “top prediction”, but merely a cyclical high calculation. I believe that one of the biggest misconceptions people have about cyclical analysis is that cyclical highs and lows always equate to absolute highs and lows in the price action. I wish they did but they do not. The interaction is far too complex for such a simple result.

      I do not know how to separate “public participation” from the price action. All of my calculations are based solely on the price. Therefore “public participation” is irrelevant to my approach. I do not attempt to predict highs or lows but, thanks to Hurst, I can define and measure trends with a fairly high degree of accuracy. With the tools he has provided, I can react with a minimal amount of lag when a trend changes.

  • amir

    Hi Jeffery,
    Thank you for sharing your knowledge. I read Profit Magic few times but never got to Chapter 11, the math was above my head. My analysis focus on centered moving average with bands around it. I found that my biggest problem with centered moving average is repainting, do you have the same problem? of course, this is more notable on shorter time frame. (a repainting indicator is an indicator that changes the information it is displaying about past data as new data comes in).

      • William Randall

        Hi Amir.

        The math is not that difficult. It looks complex but it is mostly basic algebra.

        What trading platform are you using? All trading platforms will recalculate the indicator as new data comes in but programming is beyond the scope of this post. Maybe at some point in the future I can be persuaded to write a post on some of the mathematical techniques of Hurst.

    • alain


      what is exactly your problem(s) with “repainting” ?

      I use also Enveloppes based on Centered Moving Averages with Bands / Enveloppes.
      My “Basic Model” is 1 Year , 6 Months, 6 Weeks (256 TD, 128 TD, 32 TD) . This generally structures most of the data of most of the instruments (indexes, shares, commodities)

      I build the Enveloppes by adding or substracting to above Centered Moving Averages a Gann Octave (for the I Year CMA) or a subdivision of it for the Lower CMA.

      “Repainting” is not really (for me ) a problem it does not really modify the informations you can extract from such graphs.

      With these Enveloppes you can :

      a) easily estimate the short, medium and long term volatility
      b) estimate the proportion of the underlying trend in the present swing
      c) order and hierarchize the various Price Waves
      d) determine “cycle” periodicity the old fashion / Hurst way
      e) determine the Trend

      • amir


        I’m using the Centered Moving Average Bands on shorter time frames (60 min, 240 min).
        I noticed that the CMA/Bands actually shift location on the chart as new data comes in. When I scroll backward in time, the CMA/Bands actually move to different locations in comparison to where they were at when looking at them live. It means that the CMA/Bands give me (sometimes) a false indication.

        For example: Lets say prices start going down, then the indicator you using gives you a SELL signal, but then prices go up, all over sudden the signal that was displaying SELL changes to BUY instead of just remaining how it was (SELL).
        The one that does not repaints remain the same regardless the price change. Lets use the same example as above. Lets say prices went down and it displayed SELL, but all over sudden the prices went up, your signal displaying SELL remains SELL despite price change. So lets assume prices continue going up, then it should display another signal displaying BUY but your previous signal of SELL remained the same.

        My main issue is that live signals are less reliable – you cannot sufficiently backtest these indicators /system. When I plot the inverse half-span average for example and look at the chart history it can be quite deceiving, what may appear in the historical chart to be a great indicator that seems to create good signals on your chart when the lines cross, can actually turn out to be nowhere near as good in live trading because the historical chart only shows that indicator in a frozen moment in time. In practice you may find the indicator lines cross and uncross several times providing false signals that don’t show on the historical chart.

        Having said that, I believe the Hurst method is the best for me and I’ll keep learning it.


    • alain

      French CAC 40 Enveloppes

      since the significant 6 Year Low of march 2009 the Underlying Trend – in this cas the sum of all cycles whose period is longer than 12 Months / 256 Trading Days – has contributed to 50 % of the Uptrend (1250 points);

      You can notice that now the 1 Year Enveloppe (brown) shows a Directional Change.
      The Underlying Trend is now Neutral / Flat . This means that cycles longer than 12 Months do not add strength to the price fluctuations.
      Consequently the shorter cycles are more visible and tradable.

      You can see a similar pattern on the Australian All Ordinaries.
      In the Australian case the use of the Fractal of Price / Gann Octave allows us to determine that the volatility of the Australian Index is 50% more important than the volatility of the CAC 40