S&P Long Term Cycle Phasing


My interpretation is once the Summation turns up it must continue and exceed the previous high. Any failure here would be immediately bearish.

Beautiful 20 day component


Looks like your Hurstonian has matured quite a bit! congrats on some nice software. Curious if you can share what type of digital filter you are using to get such minimal lag while using 210 bars of data? I’ve been working on a combined spectral/graphic/visual phasing analysis method that uses Hurt’s nominal model and Butterworth filters to create an initial model that then ranks bottoms using various scoring methods to place diamonds at prominent lows that are hopefully synchronized. It works fairly well, but still requires judgement. Here’s a picture of one of my phasing analyses for the SP500 (daily).

For 40- 20 nominal cycle - 2 day pop from low is not enough, moving VTL to today’s low. Model top is still October 5 or 6 which most likely means Friday October 4th


The NYA did fail at the 9/24 low (see previous post) which was anticipated to be extremely bearish. Using the daily as the time frame short was entered near the close yesterday when is was obvious the close would be below the low of recent bars. The expectations are for the summation to decline below the 20 wk low of June and below 0.

Now, I am not that confident in the placing of the most recent 10 wk (end of Aug vs middle of Aug) and 5 wk low (9/18 vs 9/24,25,27). So I will defer to the the McO. The McO will hopefully begin to build divergences to mark the next 40 wk low, but it is not always the case. The last 80 wk low in December provided no assistance. Overall, the ambiguity in the placement did not alter the trade, just the timing. In hindsight since I was expecting a left translated 10 wk, a cross of the 2.5 wk FLD leading into the 5 week low (cat D) was the best trading opportunity to catch this big move rather than waiting for the failed bounce. Maybe next time.


The low 10/2, 10/3 was of at least 1.25 week magnitude
Expectations are for the McO to work back torwards the 0 line. That would be a good spot to look for a short. Right now 3-4 day FLD projections are @2967. Price just reached the 1.25 wk FLD. 2.5 wk FLD just above that 2970-2980.

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Market looks stronger then my models. One more retest of the lows next week still possible, but next opportunity is to the upside.

Yes, there are some signs of bottoming. McO did give a clue did anyone see it?
McO and summation have lower targets, but will let price decide.

Daily and intra-month trends are neutral at the moment.

Considering late 9 years , 54 month , and 18 month nominal cycles market is due for a panic.

Of course all bets are off if markets moves significantly higher than the July high.

It looks like next summer is where everything comes to fruition.

This is great Bill, can we expect a release? Is it standalone software? How about adding FLDs and VTLs into the mix - all based upon the foundation filter work you have done…?

The low pass filters used in mine to construct the BP are actually moving averages. The downsides of such a method (described in the appendix of PM) is offset by the short lag time!


This is done in Octave/MatLab. I do actually have an FLD function, but currently it’s manually activated by typing commands.Still working out the kinks and I don’t have any harmonicity and synchronicity programmed in yet. It kind of just happens with the cycle lows and the sort of voting algorithm that I used to select the cycle bottoms. It also doesn’t do all the cycles automatically, you do them one by one. I have some algorithm’s in mind for those and to perhaps tighten up the bottom finding. I think it still needs more finesse for others to use.

Some of the text output can be quite useful as well. Like statistics on the digital filter tops/bottoms. Here’s the 10wk Cycle for daily data on the SP500 (ignore amplitude, it’s not right). Also, below that is a table of the current nominal model durations based upon the filter output.

10w Cycle 
46.92 x 1.4542 bar data spacing
Filter Order: 4
Filter Cutoff Period Range: 35.19 to 58.65
529 filter troughs
Average filter trough spacing = 43.5028 x 0.029038% Amplitude
StdDev of trough spacing = 7.7913 (12.8557)
Statistical Max/Min = 30.6471 - 56.3585
Min/Max filter trough spacing = 19 - 65
Average of last 6 trough spacings = 45.4286
Variation of last 6 = 36 - 53
Up to Last 4 Trough Dates:
19-Mar-2019 53
03-Jun-2019 52
08-Aug-2019 47
09-Oct-2019 43
Next Predicted Trough:11-Dec-2019 06:14:27
Up to Last 4 Peak Dates:
05-Feb-2019 46
29-Apr-2019 57
08-Jul-2019 48
10-Sep-2019 45
Last Data Point = 18-Oct-2019
Next Predicted Peak:12-Nov-2019 06:06:32

This table is from a separate, but related program which I want to tie into the main one. ‘td’ is trading day.

Ticker Symbol: SPX
Timeframe (td/cd/w/m/y): td
Hurst Cycle Report using Butterworth Filters
Ave       Std       Stat      Stat      Mean      Min       Max       
Period    Dev       Min       Max       L10 Per   L10 Per   L10 Per   
40w Cycle (188.11td) | 131 samples
175.53    27.14     130.89    220.18    170.14    148.00    201.00    
Last 3 Filter troughs: 07-May-2018 /03-Jan-2019 /07-Aug-2019
20w Cycle (94.06td) | 260 samples
88.44     15.31     63.26     113.63    91.86     68.00     128.00    
Last 3 Filter troughs: 02-Jan-2019 /16-May-2019 /13-Sep-2019
10w Cycle (47.03td) | 528 samples
43.59     7.86      30.65     56.52     46.86     36.00     54.00     
Last 3 Filter troughs: 04-Jun-2019 /08-Aug-2019 /09-Oct-2019
5w Cycle (23.51td) | 1054 samples
21.86     4.08      15.16     28.56     21.57     14.00     28.00     
Last 3 Filter troughs: 06-Aug-2019 /05-Sep-2019 /04-Oct-2019
20d Cycle (11.38td) | 2169 samples
10.62     2.00      7.34      13.91     8.29      3.00      11.00     
Last 3 Filter troughs: 12-Sep-2019 /23-Sep-2019 /07-Oct-2019
10d Cycle (5.93td) | 4158 samples
5.54      1.10      3.74      7.35      5.71      4.00      8.00      
Last 3 Filter troughs: 02-Oct-2019 /10-Oct-2019 /17-Oct-2019
Last Data Point: 18-Oct-2019
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Very cool Bill. I love this.

Interesting question: of the troughs identified in the ‘10w cycle’ how many of those are actual price lows?



Most do not coincide exactly with price lows. Some nest fairly closely, but still may not match price lows. I’m working on trying to make this spectral method as the basis for Hurst pattern recognition. Here’s a chart of how the filter outputs match. Probably should have posted this stuff in the other group “Using Hurst Bandpass Filters”. I generally don’t trust the “now time” portion of the Butterworth filter. It often seems distorted as a result of the filtfilt command which centers the spectral filter output on the data by filtering backwards and forwards.

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Thanks Bill, strikes me this could be a chance to introduce some alternative to the diamond notation introduced by Hurst to something based more on probability or zones of opportunity etc. Whiskers mk.2!

Hi Bill,

Nice work. How did you derive your filter cutoffs?


The cutoffs were more or less arbitrary. I used a 25% spread on the nominal period. So if I set the 40 day cycle to 34 days the spread would be 34+/-34/4.


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SPX weekly

Essentially, we should make a significant low ether way, and my comments are more theoretical in nature. Latest unexpected bullishness in the market can be explained by upward momentum from 18-year cycle and top of the 18-year cycle is still a puzzle. Left or right translation of the 18-year cycle is ultimately decided by the direction of the larger cycle.
Hurst has never mentioned cycle larger than 18 years. I don’t think we have enough data to decisively declare it to be a second harmonic (36 y), and we are in the middle of new golden age or a third harmonic (54 y) and we are about to fall of the cliff.