More interesting math and projections

In the previous essay price time areas were developed for the most recent bear and bull (ongoing) markets.  This follow up will look back to further bulls and bears to see how the QQQs and SPX behaved relative to the natural geometric growth measurements.

According to closing highs and lows, QQQs show striking growth patterns relative to the square root of 2 (1.414) and the square of the square of two or 2. 

The yellow highlighted number is the 2000-02 bear's area divided by that of the 1999-2000 bull.  Nearly exactly 2.  But the green highlighted periods did not show growth strictly according to the sqrt(2) or its multiples.  Very close, but not exact. 

Added to that table are projections for QQQs that would drive price to the next logical geometric milestones.  There are three projections that demonstrate how later dates will result in a lower projected closing price on each successive date.  Those projections started with what Frost and Prechter considered a debatable formation, an expanding ending diagonal triangle in QQQs (the black lines are the boundaries).

Aside from the well formed boundaries, there are 3 prominent Gann angles that are converging.  The dark grey downward sloping 1 cent X 2 angle is from the all time high.  The purple upward sloping angle is the zero line 2.236 cent X 1  (2.236 is the sqrt(5) up from the all time low in 2002.  And the yellow upward sloping angle is the zero line 5 cent X 1 from the 2009 low.  They converge at near the projections shown in orange in the table above. I believe these are powerful angles that will provide extreme resistance should the market choose to attempt these levels.  Yesterday QQQs closed at 86.60 so the projections are very unlikely to occur in the coming week.  But that's the math.

Now SPX.  Same table.

Similar to QQQs, the ratios in green are not perfect.  The 2002-07 bull is slightly more than the perfect doubling of the 1X1 square; we'd expect 2.000 not 2.06.  And I can't make heads or tails out of the .319 for 2007-09 bear.  However, if you relate 2007-09 bear to 2000-02 bear (697400 / 459427) you get 1.51.  Very close to the geometric and harmonic 1.5. 

Again, projections for dates next week in the high closing area of 1907 (Monday) to 1904 (Friday).   And again, these levels comport with a conventional ending diagonal triangle that was first posted about a month ago:

The red zero line $1 X 1 angle near perfectly bisects the triangle and, on Monday May 12, that angle is at 1890.  Projected closings in the area of 1907 (Monday) to 1902 (Friday) are just above that Gann angle and about 10 points below the upper boundary of the triangle.  Since we'd expect the intraday high to be higher than the high close (it certainly can't be lower), one might expect the all time high to be in the 1920 area.

Finally, the above tables can be replicated for extreme prices as opposed to closing prices and I've done that.  The projections would be 94.70-94.80 for QQQs highest intraday high and 1910 to 1912 for SPX.

And one more, one more thing.  Remember the green boxes in the tables?  Those prior years did not work out exactly right.  If I fudged in the prices that would force those statistics to exact geometric ratios in QQQs and then based projections on those base years, I'd all of a sudden have much higher projections in the 98.50 area.  That would delight me for a host of geometry reasons.  But I do not remotely consider that result because of those 3 Gann angles in the QQQs chart....and the fact that QQQs closed at 86.80 on Friday. 

Sheesh, just to get to 94.80s you need a 9% rally in 5 trading days....there (much less 98s) would be comparable to the last 4 days of the run-up to the dot.com bubble top (16% in 4 trading days).  Rotsa ruck.

Jim



 

Some interesting math

Price time areas in QQQs:

Price time areas in SPX:

The swag is in bold italics.  All prices and dates are the high or low close for that cycle; not the intraday.  A variety of price and time items can be inserted in their place to produce a notable geometric or harmonic result (green highlight). 

Have a great weekend,

Jim

Addendum.  Try replicating this worksheet and insert the closing prices for QQQs on March 7, 2014 and for SPX on April 4, 2014.  You won't find any notable relationships inferring they are not the final high.

Belaboring QQQs' price time area and the current March 7, 2014 high

The current high in QQQs is 91.36 registered on March 7, 2014.  At 5 cents per day (a ‘natural’ currency division, the nickel), it falls wonderfully on a Gann zero line 5 cents X 1 from QQQs low close on March 9, 2014:

Over the time period from the 3/9/2009 low close to the current March 7, 2014 high, QQQs exceeded the 5 cents X 1 by $.16.  And, as we know, was sounded rejected, bottoming on April 14, 2014.

But Gann angles are only "moving averages" and, while they are excellent points of balance at which price might form meaningful pivots, they do not, by themselves, signal the final high in a large trend.

I’ve proposed this before but believe the presentation was as confusing as the thought process at the time.  Price time areas compute the area of a bull or bear based on time and price.  A Gann angle evaluates a single vector and, by itself, does not provide a means to compare an ongoing market to a previous market to find relative proportions.  Bradley Cowan’s “Price Time Vectors” use price and time to create vectors based on the Pythagorean squares formulation of a right triangle and comparing PTVs between trends might signal the completion of trends in process.  Price time areas are similar to PTVs because, I believe, you can compare the ongoing market to previous markets to find proportions. 

Using an arbitrary end point of 5/14/2014 and $94.60, following are the price time areas of two markets; the 2007-09 bear and the ongoing 2009-14 bull:

The markets are related by one of the first iterations of Phi; 1.600 (fib 8 / fib 5).  Four growth cycles of Phi between the two markets.

What would the areas look like for the March 7, 2014 top at 91.36?

I can’t think of a notable number that works with 6.113 or roots of it.  In this methodology, March 7 looks pretty bad.

One last thought.  You can vary the arbitrary 5/14/2014 date and price of 94.60 and, of course the price time area varies from 1.600.  The 94.60 is a point found on the 5 cents X 1 line, so it has some attractiveness as does the 5/14/2014 date for other reasons.  Another attractive price might be 97.05 which is the 3/9/2009 low at 25.05 plus what I call QQQs initial vibration of 72.  The then all time low of QQQs on 3/24/1999 was 48.50 and exactly one year later on 3/24/2000 QQQs recorded the all time high of 120.50, a difference of 72.  You might also notice the 97.05 price is nearly twice the 3/24/1999 low of 48.50.  Hmmm  Here’s what that price on 5/14/2014 would look like in price time areas:

Closer to the ideal of Phi, 1.6118.  In my experience with looking at advances and declines within large bull or bear markets, I find the 1.600 more often than values closer to the ideal value.

Only a week left before 5/14/2014 and QQQs are way away from either 94.60 or 97.05.  If this methodology has validity, it could be presently used with leverage to create a large gain in a single week.  As it stands today (QQQs in the 86 range), that certainly does not appear to be the case.

Jim

QQQs - Two planets and a price on the square of 9

Every extreme high and low is explained by Saturn Earth since and including the first trade.  All charts are heliocentric with the date of the chart shown at the top left.  The two planets are Earth and Saturn.  Let’s start with the first trade date of 3/10/1999 at $50.59:

Price at longitude 230* exactly opposite Saturn and 45* Earth.

Now the all time high of 120.50 that occurred on 3/24/2000:

Price at 230* opposite Saturn and square Earth.

The all time low of $19.76 on 10/8/2002:

Price at longitude 334* is 40* to Earth and 108 (72* plus 36*) to Saturn.

The 2007 top at 55.07 that occurred 10/31/2007:

This is the messiest one.  Earth at 37*is 120* to price and Saturn’s longitude intersects price.  Saturn Earth is 6* short of trine with an angle of 114*.

And now for 2014.  Saturn Earth conjunct on 5/11/2014 at 230*.  Who’d a thunk that?

And where might you find my point projection of $94.60 QQQ’s top on about 5/14/2014?  I’m going to eyeball it and say 110* which is trine 230* longitude of Saturn Earth conjunct.

Of course, there are other prices that will form aspect to Saturn Earth on 5/11/2014, but the projection is certainly not disputed by Saturn Earth either. 

Unfortunately, the current high of 91.36 on March 7, 2014 can't be ruled out:

Jim

Price Time Area under the QQQ square; March 7, 2014 or May 14, 2014?

One item supporting the case that QQQs topped March 7, 2014

A good friend, and probably most people, prefer March 7 as the top in Nasdaq, NDX, QQQs.  I have them topping last or, certainly, not first of the major 3 indices, but you really have to look at the good case that March 7 is "it."  Here's one item supporting that case using QQQs as the proxy for Nasdaq/NDX.

A "natural" price element with which to define QQQs is the nickel.  In other words the 1X1 can be considered one nickel per day.  So, a zero line from QQQs lowest CLOSE (11/21/2008 was the low intraday but 3/9/2009 was a lowest close) looks like this:

And mathematically you have March 9, 2009 to March 7, 2014 (hmmmm, two days different after 5 years) is 1824 days.  1824 CDs X .05 = 91.20.  The March 7, 2014 high was 91.36.  Pretty darn good price and time balance.  Here's the math again:

 

Price Time Area under the Square

Here’s what my lawyer buddies or my Elliott buddies call an 'alternate case.'  I call it 'price time area under the square.'  I’m sure someone has tried to do this over the years but I have not read it.  The 'square' is the entire time duration of a bear or bull market.  The price is the highest high for that bear or bull.  Using an assumed price of 94.60 on an assumed date of 5/14/2014, here is my calculation of the price time area for the 2007-2009 bear and the 2009-2014 bull:

 

As we know, the 2009-2014 bull is a lot bigger than the 2007-2009 bear.  Duh.  It’s 6.5659 bigger than the area of the 2007-2009 bear according to the price time areas as I’ve computed them. 

Far more importantly, the fourth root of 6.5659 has what connection to the Fibonacci growth cycle in nature.  It is the 1.60^4.  On May 14, 2014 and at a price of 94.60, that area of will have grown four natural growth cycles. 

[94.60 is based on 1892 calendar days X $.05 and the 5/14/2014 ending date is based on the previously suggested ending diagonal triangle.  Price and time are interchangeable in the area formula so an earlier time can be substituted and it requires only a higher price.  On Sunday May 11 helio Saturn is conjunct Earth, so that might provide a good date as well.]

Jim

Addendum.  The number of days is apparently so large, that when I put in 5/11/2014 as the end date, I do not get any substantial change in the ratio of 2014 area divided by 2009 area:

http://screencast.com/t/S4YPZh6Eb

It still boils down to 1.6001 instead of 1.6007.  It actually gets a tad better.

However, if I put in 3/7/2014 and the price high on that day of 91.36, the Phi ratio is totally destroyed.  I do not see anything notable about those ratios at first look.

http://screencast.com/t/WjwCwR6qt

Jim

 

A quicker DIA suggestion

May 5 at....   166.66666.  Too close to a spooky number not to choose it.   It's 2/3, the inverse of the fifth Fib number divided by the fourth Fib number (and hence an early approximation of Phi), and the diatonic "La", so I had to pick it.  Generally, I've been working with Price Time areas but I originally arrived at the time and price target via work with an ending diagonal triangle (EDT) in DJIA a couple weeks ago.  Here's the EDT in DIA that was originally posted in the context of the DJI chart:

There were some convoluted proportions of the 5 internal sub waves, but there wasn't anything particularly compelling to me.  On the other hand, the low of the EDT at point 3 to the low at point 4 is half the distance of the total height of the EDT (the 50% on the retrace tool).  That suggested to me the price proportions were acceptable with the 166.66 projection.

The Price Time area was my primary interest with the EDT having gotten me to a workable approximation.  Here's the big picture:

With the obvious equivalence of time between the two triangles (942 and 942), the areas are a perfect function of price (two price numbers multiplied by the same time constant of 942 days).  That makes it simple but I'll do the work long hand and show the areas of the smaller and larger rectangles as 12,117 and 15,694, respectively. 

The difference in those rectangles or 3,577 is the growth between them, duh.  Now, we can do this two ways; either by finding the growth to be 3,577 / 12,117 being 29.52% or 12,117 divided by 3,577 / 12,177 to find 3.3875.  Let's look at the 3.3875.  Simply, the cubic root of 3.3875 is.....1.502.  Back to the third and fourth Fibonacci numbers or 3 /2  = 1.500.  Cool.  Diatonic "SO".  Cooler. 

But remember when I said there wasn't anything in the internal proportions of the EDT was 'compelling' to me?  I lied.  Look at the waves...even and odd:

The odd waves of EDT have a proportion to the whole of 29.58%.  Rather similar to the proportion of the price growth in the larger rectangle to the smaller rectangle.... 3,577 / 12,117 = 29.52%. 

Spooky.  Err, only spooky if it works, that is.  Something to tell the kids...how do I translate it to Common Core counting?

Jim

A quickie SPY suggestion

Got to start looking at the freely traded markets instead of the indices.  So here's a biased (I'm a hopeless bear) look at SPY's move since the March 6, 2009 bottom:

Two rectangles that evenly divide the time period that is based on a suggested top on May 5 at 193.  As it turns out, the equal rectangles divide the suggested period on exactly the 2011 low and panic low of October 4, 2011.  Interesting.

More noteworthy, the price time area (at 10 cents per day) from zero forms the square root of 2.  Similarly, the 10 cents X 1 angle bisects a seeming expanding diagonal triangle (EDT) at the top right of the chart (black boundaries).

Here's a drill down on the suggested EDT:

Look at the time components of the internal waves of the suggested triangle:

Certainly, a rocket in 3 days could get SPY to 193 but.....

Jim