The S&P 500 seems to have weathered the frequency modulation that has plagued the index for the past several months from a spectral viewpoint. Below is a daily chart with the 40 day wave extracted at the bottom. The effect of the frequency modulation is clearly visible in the first four months of this year, evidenced by the spacing of the filter output lows. The 40 day wave has been very dominant the past four months, driving the price action up and down. The recent lower high and relatively equal lows of the 40 day wave are further evidence that the underlying trend is flattening. Trading against the 40 day wave is not advisable at this time in my opinion. A lower 40 day low, theoretically, will make it very difficult for the index to push to hew highs. The good news (for traders) is that the shorter price waves have plenty of amplitude which makes trading in the direction of the 40 day wave relatively easy(?) when applying Hurst’s principles.
The longer term picture remains the same. The 80 week wave still does not have any significant amplitude to drive prices regardless of where one phases the two most recent lows. Below is a weekly chart with what I believe to be the 10 week price wave extracted at the bottom. It has been very consistent over many years. Keep a close eye on the recent 10 week lows. A hard break below a prior 10 week low followed by a lower 10 week high should signal the start of the “correction” for which everyone seems to be waiting.
18 thoughts on “S&P 500 – Back on track, but …”
Hi William,
Thank you for posting your work and thoughts. I take it you are still not convinced that Oct. 2014 was an 18 month low, rather Feb. 2014 was the last 18 month low? Looking at your last chart, are you suggesting June 2015 was an 18 month low? That would be significant. I am watching for a 40 week low to form and whether it will fail (to hold that low for the next 40 week cycle).
cheers,
john
Hi John,
If one phases the 18 month low in October 2014, It would create a 100 week cycle from the November 2012 low! That would be unprecedented in the history of the market. In addition one would have to retroactively re-phase all of the shorter waves prior to October 2014 causing a distortion of the average period of those waves moving forward. That is why some analysts have had such a difficult time identifying the 40 week low, the average period is too long. The prior two oscillations would have averaged 50 weeks!
On the weekly chart I arbitrarily placed those yellow makers at every eight oscillations of the 10 week wave for those who believe the market waves sub-divide into a simple harmonic relationship. I’ve stated on a couple of occasions how difficult it is to phase the 80 week wave because currently it virtually has no amplitude. That is one of big advantages of using a spectral approach, one can see the amplitude of the wave, which is the driving factor, not merely the magnitude of the period.
The 40 week wave is a bit odd. If you look at Hurst’s 40 week filter output on page 152 of Profit Magic you will notice it does not have a simple harmonic relationship to the 20 and 10 week waves. The same is still true today. It rarely phases to major lows of the other longer or shorter waves (it did phase to the October 2014 low however). Of course the above is only applicable to a spectral approach to wave analysis. Even though they are very similar, there will always be these substantive differences between Hurst’s spectral approach and his time domain approach
William,
Okay well if February 2014 was the last 18 month trough and October was a 40 week trough and analysis of that indicates that this move lower should be the next 18 month low here at the end of this month early next (July). I am not in agreement with this and I think that things have definitely been distorted by QE. We have gone over 6 years without a bear correction which is also very rare. With October 2014 as a 40 week low wave periods are also distorted and do not align with magnitudes that would be characteristic. I really wish I understood what you were talking about with this spectral stuff because i always want to understand a more complete picture. Wouldn’t your analysis starting point figure into where those 80 week sequence lows were placed i the same way cycles are affected by where you start the data? Thank you for any insight.
Hi Jeffery,
Firstly, I think you may be correct about the QE distortion. QE is a fundamental aspect of market (included in the long term underlying trend) and it appears to have sucked all the amplitude out of the longer waves, particularly the 80 week wave, but it has not changed the underlying angular frequencies which comprise the price waves (spectral viewpoint). In my opinion, that is why the 10 week wave continues to be so consistent and visually evident, whereas the longer waves over the past three years or so have been very difficult to see in the price action, even though mathematically they are still there. They do not disappear.
David Hickson, in his excellent commentaries on the market, refers to how cycles “influence” the price action. That statement implies to me that they are exogenous to the price action. A spectral approach is fundamentally different. It assumes that the price waves are intrinsic to the price action and as such can be mathematically derived from the price action. I base my approach on the statement Hurst made on page 32 of Profit Magic. “Cyclicality in price motion consists of the sum of a number of (non-ideal) periodic-cyclical components.” A “periodic-cyclical component” is simply a sine wave and “non-ideal” means they are modulated.
Even though the two approaches are very similar and most of the time yield the same result, it is not advisable to mix them. It is mathematically impossible from a spectral perspective for the price waves to have a simple harmonic relationship by a factor of two, synchronized troughs, and amplitudes proportional to their periods. That was Hurst’s way of simplifying the complex mathematics of his price motion research to make it available to pencil and paper trader of 1970!
Unlike ST’s phasing algorithm, the use of a lowpass or bandpass filter does not require “anchoring” at a major low. All that is needed is sufficient data to accommodate the filter lag at each end of the output. The spectral approach to market analysis is much easier than you think. Maybe at some point in the future I’ll write a piece about it.
BTW, where do you think the 80 week troughs are?
Hi William,
The phasing in the US markets is challenging. It is much easier to see in other markets like the $TSX IMO. However, when I look at the Oct 2014 low, by many measures it was too much of a move to have been simply a 40 week low. TWT of course.
cheers,
john
Hi John,
I clearly understand your position with respect to the October 2014 low due to its visual prominence. We probably will not see a definitive answer until the next 4 year low! The chart below is the S&P 500 cash index showing the 80 week wave, based on Hurst’s filter design, back to the 2007 high. You can clearly see what I mean about no amplitude for the past couple of years and why I find it difficult to pinpoint the 80 week from a filter perspective . I too find phasing the US markets challenging, but also exciting.
Thanks for the nice discussion. If my old friend Airedale 88, Bob Chonski were alive he would point out a couple important things. He was a resident master of Hurst cycles when I first got introduced to them back in 2005. In fact he did little besides Hurst cycle analysis for months during the time he was recovering from a spinal surgery gone bad.
First he would point out that the bull market rally since the 2009 bottom is in some respects a pseudo-trend created by the Fed with its zero interest-rate policy coupled with quantitative easing amplified by many of the worlds central banks doing the same.
Secondly, the October 2014 low is most likely a cycle straddle due to the Ebola panic. This created a larger amplitude cycle low then might have ordinarily been expected for a cycle of low degree than an 80 week low.
As an aside, I wanted to put this comment at the bottom of the thread but for some reason some of the comments do not have a reply box to click on. Any ideas on how to overcome that?
Doc
Thanks Doc!
I had been wondering if there was a fundamental interaction explanation for the exacerbated low in October 2014. Seem like you may have identified a possible explanation.
William,
So I have come back to reading this post several times and configuring different analysis start points to include the possibility that October 2014 was an 18 month low which indicates that the low we are forming now according to Sentient Trader would be an 18 month low. What I think I am able to realize is that my understanding and inclination of identifying lows is purely based on their magnitude hence October 2014 is identified as the 18 month low based on magnitude. if October 2014 is an 18 moth low then that places some lesser and higher magnitude lows in what according to my approach from a visual perspective in some unusual places that do not look visually appealing or accurate. William can you shorten that 80 week cycle chart down to starting at the November 2012 low and post it please. With a tighter range we may be able to see the dips and peaks since then. So unless I am totally misunderstanding Hurst concepts of magnitude i still believe that these are the 80 week lows since March 2009-69 weeks until (07/2010)-65 weeks until (10/2011)-58 weeks until (11/2012)- 100 Weeks (10/2014). Admittedly, the February 2014 date seems historically more in line @ 63 weeks than the October date but I think your 80 week wave with its lack of magnitude accurately depicts this phenomena and is certainly reflective of the central banks influence on investment. Technically this 18 year period should have be a secular bear market and instead has move to extreme new highs with little correction at all in over 6 years.Regardless of the phasing either each analysis suggests that either a 40 week or 18 month low is likely due by July 15-20. In a couple sentences what do you feel are the advantages of a spectral analysis versus the conventional cyclic analysis and can you give some concrete examples that indicate this advantage as reflected in trading decisions? Thanks again for sharing and I look forward to learning as much as I can about this.
Hi William,
I’m looking back to our exchange in this posting or yours. I was expecting a 40 week cycle to fail here this summer which now appears to have occurred (not much doubt in it anymore). Do you feel the June low was the 40 week low, as your filter seemed to suggest that earlier this summer? I have an important low forming early next year which IMO is going to be a nest of lows for a number of larger cycles. My work and view on the $TSX seems to be playing out as expected.
cheers,
john
Hi John,
I know the following will sound heretical in the Hurst community but I put very little emphasis on phasing the 40 week wave . The reason is twofold. Firstly, the dominance of the 80 week and 20 week price waves ordinarily overshadow the 40 week wave. Secondly, and more importantly, all filter outputs do not always synchronize perfectly at lows as in Hurst’s simplified model and the 40 week wave is the worst offender. Currently the 40 week wave is exhibiting a diminution of amplitude, though not as severe as the 80 week, making its impact on the the price action de minimus in my opinion.
The market action played out perfectly as I mentioned above. I shorted the lower 40 day high at 2100 and, fortuitously, the bottom fell out! The next year is going to be very, very interesting from a cyclical standpoint. Based on its historical average, the 4 year wave is due to make a low next year. The average deviation creates a fairly wide window but I’ll expect the pattern to be exactly the same as it has been for the last 140 years until it shows me otherwise.
Hello Wiiliam,
Thanks for sharing your analyses! Maybe this is of help. I have taken SP500 data back to 1895 and extracted the spectral model, which includes average 41.9 Years and 15.3 months cycles. The 15 month cycle has sidebands at 16.9 and 14.4 months.
Then a bit more modern filter than the one Hurst used, with some automatic gain control, gives a reasonable readout for the 15 months cycle, see the graph. In addition, the time-frequency analysis at the bottom gives a loud and clear 42 months dominant cycle.
The lowest time-frequency plot sows a rather broad 15 mo signal at present. It looks as if both side bands at 16.9 and 14.4 are of comparable strength as the 15.3 carrier.
The filter (aka spectral model) output is difficult to reconcile with a nominal 18 mo trough in oct 2014.
Best,
Huub
Beautiful work Huub!
Your results are virtually identical to mine. I show a historical (>100 years) 4 year wave average of approximately 44 months. I must admit I haven’t calculated the average deviation (I’ll do it this weekend!). The 80 week wave wasn’t exactly 3 to 1 over almost 100 oscillations, but it was so close one can assume 3 to 1 for simplicity sake. It is gratifying to see Hurst’s work verified using different methods.
I do not believe the spectral model output can be reconciled with a nominal model 18 month trough in October 2014. One must decide which flavor Kool-Aid to drink!
Hi William,
This is my frequency analysis for the SP500, like in the appendix in profit magic, except that I use the bottom trace, where the omega-squared dependence is divided out.
Best,
Huub
correction: it is 1/omega envelope, not omega-squared dependence
And this is an ST analysis grafted on the long term spectral analysis – Huub
Hello,
Here is my take on the S&P.
40 w has lost it’s amplitude as expected when forming the bottom.
Regards
DJIA monthly nominal model and probable 9 year cycle top