One of the more difficult aspects of cyclical analysis in my opinion is correctly dealing with price wave expansion or contraction in a timely manner. If one waits long enough the difficulty will usually resolve itself in an additional cycle. However if the price wave in question is of intermediate length, one usually does not have the luxury of waiting. The S&P 500 in currently facing such a situation. It is somewhat unclear as to whether the 20 and 10 week price waves have expanded or contracted. Other analysts have postulated that the 20 week wave has expanded. It appears from a spectral viewpoint that the waves may have contracted, particularly the 10 week price wave.

Below is a daily chart of the ES futures covering approximately 9 months. The two price waves shown at the bottom of the chart are the 20 day (blue and white) and the 10 week (yellow). I superimposed the 10 week filter output onto the 20 day filter output. For the past several months the two waves have exhibited a textbook simple harmonic relationship and very closely synchronized troughs. The two most recent oscillations of the 10 week show a moderate decrease in period, particularly the most recent one which is one day shorter than the shortest 10 week oscillation over the past two years.

When the period of dominant price waves starts decreasing and the amplitude of the shorter waves starts increasing, the risk of a price inversion (i.e. price drops below the prior cyclical low while the the price wave is cycling up) is greatly increased. A price inversion of a dominant intermediate wave is a clear sign of a change in the trend underlying such wave. There have been no price inversions on the 10 week wave in the S&P 500 since the prior 4 year low, well over two years. The index is within shouting distance of the 3/11/15 low close. A daily close this week below that low may be more than from which the index can immediately recover. Time will tell.

Very timely post William as ES last night again visited the 2033 area with a sudden swoosh. This area was also seen Friday 13th in the day session and again early premarket morning Thursday the 26th at 4am. Nice bounce so far to 2050. Much appreciate the updated 20day and 10wk filters outputs and I like the superimposition. It is interesting to see that they are both in the process of peaking and the 5wk (not shown) is also heading down. You might just finally get a 10wk cycle that does not make a new high, but it would come at the tail end of an 80wk cycle! Thanks again for sharing your work.

Doc

Roughly the 18 Months / 78 Weeks / 390 Trading Days Cycle since the March 2009 Low is in average 20 % shorter than the “Theory”

Hi Alain,

When you say “Theory” I assume you mean Hurst’s nominal periods. I use the them for descriptive purposes only, not as references as some Hurst analysts. I use the actual average period determined from the filter output. For example the “80 week” price wave has averaged approximately 64 weeks over the past 3 or 4 oscillations which is very close to the historical average (it was 68 weeks on pg. 152 of Profit magic). Therefore I do not believe the wave is running “20% short”.

William

Thanks William for posting that. The 10 week oscillations look like a corkscrew and are converging in time. Each trough to trough and peak to peak interval is progressively shortening. At this rate the next nest of lows (10, 20, 40 wk) is due by late April. I think you will finally get your lower 10 wk low there. But is it a 40 or 80 wk coming due in April? That is the big question.

Have a good holiday break.

cheers,

john

“At this rate the next nest of lows (10, 20, 40 wk) is due by late April. I think you will finally get your lower 10 wk low there. But is it a 40 or 80 wk coming due in April? That is the big question.3

Hi John – a 20 % in average shortening of the “80 week” cycle means that this average will be meet for the current “80 week” cycle in 20 Trading Days.

That is end of April / beginning of May- May be it is an answer to your question ?

Alain,

Two questions.

1. You are counting trading days rather than calendar days and hence the label TD correct?

2. If so, how many TD are we along from your last 78wk low (nominal 80 wk low)? Thanks

Doc

Hi Doc,

a) yes I use Trading Days hence the TD abbreviation.

b) according to this count the last ” 78 Week” Cycle Low (Nominal “80 Week” Cycle) was on February 5 th 2014 – 1246 Trading Days after the Low in March 2009.

c) yesterday we were 1537 TD after the March 2009 Low.

d) 1537-1246 = 291 TD

e) as the average duration of the 4 last “78 Week” Cycle is 311 TD , IF the present 78 Week Cycle reaches is average, we have to wait 20 TD – 4 Weeks.

Hi John,

Unless something very unusual happens in the next two weeks, I may finally see a lower 10 week high! It is going to be a very interesting sequence. You are correct in noting that the 40 and 80 week cycle lows are approaching. The 10 week price wave in the two 80 week cycles prior to the most recently completed cycle exhibited a 9 to 1 harmonic relationship so I do not automatically assume that the next 10 week low is also an 80 week low. Isolating the 80 week wave is very difficult due to its current lack of amplitude which is somewhat unusual. However I can evaluate what the sum of the longer waves are doing with a lowpass filter.

William

Hi William,

Yes I meant lower 10 week high of course. I was going to ask what you thought of the reduced amplitude. Looking at your past work it implies a strong trend and continuation of the trend if that amplitude does not increase here. How do you read it?

cheers,

john

Hi John,

The chart is a little misleading. The amplitude of the 10 weeks waves on the left of the chart is somewhat larger than the average which makes the current oscillations look disproportionately small. Next time I’ll show more data. Right now I’m focused on its period.

As for its implications, I try very hard not to have any “expectations” with respect to the market (not always successfully). I take what the market gives me. The 10 week wave is so dominant that I key most of my decisions on it. It will be very interesting to see how this all plays out over the next few weeks. I’ll try to keep you guys posted with respect to my technique.

William

Hi William,

By my estimation, we should now have had at least two full cycles of the 20day and the 10 week should be peaking about now. Things could get interesting this week.

Doc

Hi Doc,

My charts are reflecting the same thing. The short term wave that has been very dominant in terms of amplitude over the last 8 months or so has been the 40 day wave. 75% of the cycle legs over that time period resulted in moves in excess of 50 points. It is at a peak and I’m shorting it for the drop into the 10 week low.

William

Hello William,

Given the lack of downward pressure thus far so close to the anticipated 40/80wk low, and looking at past lengths of the 10wk cycle, I am thinking that March 26 was more likely the 10wk low. I had always felt that March 11 was a bit too early for the 10 wk low. I am looking for a 5wk low here soon. Would that phasing fit with your Bandpass filters at all?

Now I know you mentioned that the last couple 80wk cycles had nine 10wk cycles within and that might end up with the same result I am proposing with a late May-June target for the 80wk low. I just have a hard time getting my head around a non-harmonic 9:1 ratio between 10 and 80wk cycles.

All the best,

Doc

Hi Doc,

The 4/17/15 low close was the third 20 day price wave low in the current 80 day cycle. Assuming the market maintains its simple harmonic relationship, the next low will be the 10,20,40, and 80 week low, as unlikely as it seems. The amplitude of some of the longer waves have been compressed to almost nothing. That is why, theoretically, we are not seeing any heavy downward pressure.

A complex harmonic relationship usually occurs over very long runs of data. If the market always moved in a perfectly synchronized, simple harmonic relationship, any 10th grade algebra student could trade it. Hurst explains the cause with a very careful reading of the information in the appendices. Fortunately any complex harmonic relationship is very close to a simple harmonic relationship. You have identified the most important, and the most difficult, issue in my opinion, that being keeping an open mind. Let the price action show you what it is doing as opposed to forcing it into any preconceived model.

Hi William, John and Doc

From my point of view I would not write ” Isolating the 80 week wave is very difficult due to its current lack of amplitude which is somewhat unusual.”

a) there is no lack of amplitude for the current 78 Week Cycle – see the graph

b) it is not unusual – it is usual in what Ehlers call “price in trending mode”

First 78 Week Cycle: Measured Move + 337 points

Second 78 Week Cycle: Measured Move + 92 points

Third 78 Week Cycle: Measured Move + 237 points

Fourth 78 Week Cycle: Measured Move + 394 points

Current 78 Week Cycle: Measured Move + 328 points

So I would not say that the current 78 Week Cycle lacks of amplitude.

I agree that this 78 Week Cycle and those of shorter duration are difficult to isolate.

I will offer you an explanation in my next post.

Hi Alain,

I was thinking more specifically about William’s last image posted and the oscillations of the 10 week cycle (yellow line) and its amplitude and that of the 10 week cycle itself. My take is that because the amplitude is converging and decreasing so much, it is unlikely that we are approaching an 80 week low (ie. compare it to say the low in Oct.) here on the next 10 week cycle low. I would expect increased volatility and amplitude in the 10 week cycle for an approaching 80 week cycle low and we are not seeing it just yet. Again, let me know your thoughts on this.

cheers,

john

Hi Alain,

I did not make myself very clear. The current 80 week wave is lacking amplitude relative to the three prior oscillations which had substantial amplitude, particularly the first two after the March 2009 low. That is what currently makes it somewhat difficult to isolate. It is unusual in that over the past 100 years the 80 week wave has usually exhibited a reasonable amount of amplitude. I agree that the strong underlying trend is responsible for the diminution of the amplitude. All of the shorter waves have a fair amount of amplitude which makes extracting them with a bandpass filter relatively easy.

About the Amplitude and the Underlying Trend

I would not go right now in long details which could be explained later on request.

Gann thought that every index or share was sensitive to a paricular “vibration”.

Let’s assume that up to now the S&P 500 had – on a long term basis – price fluctuating within a “Fractal of Price ” of (0-2000)).

Gann’Octave is 2000/8 = 250.

This Octave is the “vibration ” I use to build the 1 Year / 256 TD Enveloppe (brown) on the graph. The Octave (250 points ) is the depth of this Enveloppe.

The Enveloppe is build by adding ( sustracting) 125 points to the 256 TD Centered Moving Average in order to create the superior and inferior limits of the Enveloppe.

Same process is used to build the 6 Months (128 TD) Enveloppe dividing by 2 the Octave , which means adding and substracting 62,5 points to the 128 TD Centered Moving Average (Ocre)

As you can seeon the graph both Enveloppes includes most of the price fluctuations since March 2009.

(and before).

Roughly on the graph – you can visualize that right now that since March 2009 the 1 Year Cycle has added at the utmost 250 points to price fluctuations (1 square).

The Underlying Trend – here the sum of all cycles whose duration is longer than 12 Months – has added 5 squares (1250 points) to price fluctuations.

We can in fact observed that the 6 Months Enveloppes – depth 125 points – includes most of the price fluctuations.

This way if we go from the Low in March 2009 ( March 9, 695 points) to the March 31, 2015 high of 2084, this give us a Measured Move of (2084-695) = 1389 points whose only 125 points are due to the amplitude of the 6 Months Cycle.

Which means that less than 10 % of price advance since March 2009 is the consequence of the amplitude of the 6 Months cycle.

More than 90 % of price advance is due to the 6 Months Underlying Trend. This explain why visually you see almost nothing on the graph and have a lot of difficulties to isolate the 78 Week Cycle (and the shorter ones)

French CAC 40 Enveloppes

Medium Term Fractal of Price is (2500 – 5000) = 2500 points

Gann Octave is 2500 / 8 = 312,5 points which you add and substract to the 6 Months (128 TD) Centerd Moving Average(ocre) building the 6 Months Enveloppes which has a depth of 625 points

By doubling the Average (256 TD) and the Depth (1250 points) you build the 1 year Enveloppe

The Depth (1250 points) is equal to the Long Term Octave .

CAC 40 Long Term Fractal of Price is (0-10.000)

Gann Octave is then 10.000 / 8 = 1250 points

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.

Australian All Ordinaries Enveloppes

You can see a similar pattern on the Australian All Ordinaries

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 6 Months / 128 Trading Days – has contributed to 70 % of the Uptrend (2000 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.

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

Hi All

Some additional information and consideration. Attached is the spectral output of weekly ES from November 2012, a low of significance, showing, considering amplitude as the measure of cycle dominance, the importance of the longer waves as indicated

However, evaluation of the output using cycle strength as the measure of dominance tells a very different story(cycle strength=wave amplitude/wave period). As shown, the dominant wave(s) are the modulated group of oscillations ranging from 8-30 weeks consisting of the 10 and 20 week bands we are considering. Further considering statistical l significance(Bartels) yields a strong dominant wave of 10 weeks.

Now the interesting part. When an ideal(unmodulated) 10 week wave is plotted(blue dashes) is compared to the actual spectral output fair correlation is noted but with some phase shift. But then last August and November, inversions occurred. As of the end of February, the 10 week wave had perfectly reverted phase correlating very closely with the ideal and indicating that a low(in the 10 week wave) is very close.

Creating a custom nominal model in ST using the dominant 10 wk on a 60 min chart yields the attached analysis. A 10 day nest of lows is expected but a break of 3/11 or even 3/26 in the current 10 wk cycle would be a bearish event.

Hi Stuart,

Looking at that table, if you took the 10 week as an outlier, then the 8, 14 and 30 week periods would rank the highest. If you bracket the cycle period +/-1 week, that would work best for me. It is hard to deny the early Feb. low as a 20 wk low for the $SPX, which may have even been a straddle with the mid-Jan. low. Looking at the $TSX, it appears to have made a 20 wk low mid-Jan. So another nest of lows is due in April or beyond. BTW, when I look at non-US assets or the $TSX for example, it is difficult to argue that they are making about to make both 40 and 80 wk lows here. And if you go with the concept of commonality, just what are you looking at for US markets? Thanks for posting the spectral work.

cheers,

john

hi Stuart

it seems that your spectral analysis gives very close results of the system I use

32, 64 and 128 Bars (trading days)

Hi John,

William averages the “80 Weeks ” Cycle at 64 Weeks which theoretically gives 320 Trading Days. My count gives me an average of 311 Trading Days – but take into account holydays. So it is basically the same.

Consequently if the “80 Weeks ” cycle averages at 64 Weeks , the “10 Weeks” Cycle should average at 8 Weeks (40 TD).

I do not use such cycle but a 32 TD Enveloppe !

As you can see on the graph the depth of the Enveloppe is 62,5 points and encapsulates almost all short term price fluctuations of the SP 500.

It is why I do not understand what you mean with “My take is that because the amplitude is converging and decreasing so much, it is unlikely that we are approaching an 80 week low (ie. compare it to say the low in Oct.) here on the next 10 week cycle low ”

For me it is not the Amplitude in points which is decreasing, it is the Period of the “visible” cycles

The Underlying Trend is so strong that it reduces the downtrending swing (or leg) of a cycle to almost nothing. This fact as William complexify the isolation of all the cycles , even the 78 Week one.

John:

The Bartels calculation correlates with the probability of the period most likely (but only possibly) present in the data-remember we are decomposing a complex collection of wavelengths and in theory a complex wave can consist of an infinite combination of components. The Bartels ranges from o-100 with anything over 50 starting to be significant but the higher the better. Then we must factor in amplitude so really what we looking for is max Bartels,amplitude, and strength. That is why I favor 10 weeks as the dominant price wave currently.

Alain

Thank you. My point was to provide corroborating evidence so that William’s limb was stronger. As he stated, some aspects of cyclic analysis are difficult enough. If we all share, we are helping not only each other, but ourselves as well.

Using exactly the same methodology the Brazilian BOVESPA tells us a totally different story.

You can at the first look that there is no commonality between the BOVESPA and the S&P 500

The Fractal of Price is (25.000-75.000) = 50.000 points

The Octave is 50.000 / 8 = 6250 points

The 1 Year / 256 TD Enveloppe (brown) has a depth of 12.500 points (2 Octaves).

These 12.500 points (2 Squares) represents roughly 40 % of the downtrend (5 Squares), the remaining points of the downtrend being add by the action of the underlying trend

cobined with the fact that the angle of descent is moderate., we have no difficulties to identify the major Cycles at work

William,

Are you still of the opinion that the 20 week trough was on 02/02/2015?

Hi Jeffery,

Yes I am. The way my filters are constructed I cannot place it anywhere else. (I use the low close as opposed to the absolute low which would place the low at 01/30/15)

In my last post of 3 April, I posted the wrong chart. The attached is correct. Sorry for any confusion.