Good day to everyone
Today we would want to discuss the growth structure, the harmonic vibrations and fractals of the stock market, we would use DJIA in our illustration. This growth pattern is similar with all US Indices.
First we want to mention that the stock market is not disjoint from its past, its a continuous growth with log expansion at well defined locations within the growth. There is historic chart from 1792 but we will take our origin from the 03/08/1896 low.
From this point price advanced steadily in geometric expansions of Phi
Our first chart is the pattern between 03/08/1896 to 27/04/1942
We will define four important points between this time range all anchored to the origin
03/08/1896 - 03/11/1919 = 8491 days / 1213 weeks / 279 months
03/08/1896 - 02/09/1929 = 12082 days / 1726 weeks / 397 months
03/08/1896 - 04/07/1932 = 13118 days / 1874 weeks / 431 months
03/08/1896 - 27/04/1942 = 16702 days / 2386 weeks / 548.6 months
Putting this on a time line we have:
Notice that the 03/11/1919 and 27/04/1942 are indicated as 1/4 and 1/2 respectively
The next half of the chart is the cycle from 27/04/1942 bottom to 24/08/1987 crash top
We will indicate three important points within this timeline still anchored to 03/08/1896
03/08/1896 - 14/09/1953 = 20860 days / 2980 weeks / 685.3 months
03/08/1896 - 09/12/1974 = 28616 days / 4088 weeks / 940.2 months
03/08/1896 - 20/09/1976 = 29267 days / 4181 weeks / 961.5 months
03/08/1896 - 24/08/1987 = 33257 days / 4751 weeks / 1092.6 months
We will again put this on a time line
I left out the 1974 and 1976 points to make the chart clean
These two sides complete one primary cycle from 03/08/1986 to 24/08/1929 crash top
If the entire cycle duration is 1092.6 months then the Phi division lies exactly at the 1953 bottom. Another way of illustrating this is by dividing the time range into 8ths
(1092.6 / 8) = 136.58 units = 1/8
2/8th division = 136.58 X 2 = 273.2 units = 1/4
1/2nd division = 136.58 X 4 = 546.3 units = 1/2
5/8th division = 136.58 X 5 = 682.88 units = 5/8
On the fib scale 5 and 8 are in succession of Phi
This Phi division is very important in that it determines the extent of the next cycle after 1987 and its internal subdivisions.
The two halves are also mirror images and very identical to each other or fractals with points on the previous side alternating phase in the second half.
We can represent the two sides around a time circle. It is in this representation that the significance of the 1929 top, 1974 bottom and 2020 top becomes apparent.
Complete cycle = 1092.6 months = 360°
Half cycle = (1092.6 / 2) = 546.3 months = 180°
This circle representation puts the two points 02/09/1929 and 09/12/1974 at opposite points 180° apart, they are also at equal positions/distances from the origin in each half.
We mentioned that the 03/11/1919 top was at the 1/4 point which is 90° point on a circle and 279 months from the origin
From the 09/12/1974 point:
09/12/1974 - 08/10/2007 = 1713 weeks / 394 months
09/12/1974 - 10/02/2020 = 2357 weeks / 542 months
since half cycle = 180° = 546.3 months, this puts the next 180° from 09/12/1974 approximately at the 2020 crash top 542 months apart and very identical to 1929.
The quarter(1/4) cycle at 03/11/1919 then aligns perfectly with the October 2007 recession top 394 months from 1974 and also very identical
Now representing both cycles separately we get a picture of the identical nature of the stock market. The distance from 08/1896 to 09/1929 is an equal distance as 12/1974 to 0/2020
Both 08/1896 and 12/1974 are bottoms, 09/1929 and 02/2020 are tops
Representing both on linear scale we have:
This also shows three identical cycles averaging 546 weeks with their golden sections
1929 and 2007 are very identical because the lie at the same location within the repeating pattern. 1987 and 2020 also look alike because they are the ending nodes of the 546 weeks cycle. 1942 and 1974 are both bottoms and are alternate fractals 180° out of phase, that is, if we arbitrarily turn the 1942 and 1974 chart upside down we will have the same structure as 1929 and 2007.
1929 section
2007 fractal
1987 fractal
2020 Fractal
As we section the chart into cycles we come to locate the position of the 2022 top and current location within the growth cycle, check back in next post/update as we will find the current location and also subdivide into smaller cycles to find the current trend.
Goodluck
Today we would want to discuss the growth structure, the harmonic vibrations and fractals of the stock market, we would use DJIA in our illustration. This growth pattern is similar with all US Indices.
First we want to mention that the stock market is not disjoint from its past, its a continuous growth with log expansion at well defined locations within the growth. There is historic chart from 1792 but we will take our origin from the 03/08/1896 low.
From this point price advanced steadily in geometric expansions of Phi
Our first chart is the pattern between 03/08/1896 to 27/04/1942
We will define four important points between this time range all anchored to the origin
03/08/1896 - 03/11/1919 = 8491 days / 1213 weeks / 279 months
03/08/1896 - 02/09/1929 = 12082 days / 1726 weeks / 397 months
03/08/1896 - 04/07/1932 = 13118 days / 1874 weeks / 431 months
03/08/1896 - 27/04/1942 = 16702 days / 2386 weeks / 548.6 months
Putting this on a time line we have:
Notice that the 03/11/1919 and 27/04/1942 are indicated as 1/4 and 1/2 respectively
The next half of the chart is the cycle from 27/04/1942 bottom to 24/08/1987 crash top
We will indicate three important points within this timeline still anchored to 03/08/1896
03/08/1896 - 14/09/1953 = 20860 days / 2980 weeks / 685.3 months
03/08/1896 - 09/12/1974 = 28616 days / 4088 weeks / 940.2 months
03/08/1896 - 20/09/1976 = 29267 days / 4181 weeks / 961.5 months
03/08/1896 - 24/08/1987 = 33257 days / 4751 weeks / 1092.6 months
We will again put this on a time line
I left out the 1974 and 1976 points to make the chart clean
These two sides complete one primary cycle from 03/08/1986 to 24/08/1929 crash top
If the entire cycle duration is 1092.6 months then the Phi division lies exactly at the 1953 bottom. Another way of illustrating this is by dividing the time range into 8ths
(1092.6 / 8) = 136.58 units = 1/8
2/8th division = 136.58 X 2 = 273.2 units = 1/4
1/2nd division = 136.58 X 4 = 546.3 units = 1/2
5/8th division = 136.58 X 5 = 682.88 units = 5/8
On the fib scale 5 and 8 are in succession of Phi
This Phi division is very important in that it determines the extent of the next cycle after 1987 and its internal subdivisions.
The two halves are also mirror images and very identical to each other or fractals with points on the previous side alternating phase in the second half.
We can represent the two sides around a time circle. It is in this representation that the significance of the 1929 top, 1974 bottom and 2020 top becomes apparent.
Complete cycle = 1092.6 months = 360°
Half cycle = (1092.6 / 2) = 546.3 months = 180°
This circle representation puts the two points 02/09/1929 and 09/12/1974 at opposite points 180° apart, they are also at equal positions/distances from the origin in each half.
We mentioned that the 03/11/1919 top was at the 1/4 point which is 90° point on a circle and 279 months from the origin
From the 09/12/1974 point:
09/12/1974 - 08/10/2007 = 1713 weeks / 394 months
09/12/1974 - 10/02/2020 = 2357 weeks / 542 months
since half cycle = 180° = 546.3 months, this puts the next 180° from 09/12/1974 approximately at the 2020 crash top 542 months apart and very identical to 1929.
The quarter(1/4) cycle at 03/11/1919 then aligns perfectly with the October 2007 recession top 394 months from 1974 and also very identical
Now representing both cycles separately we get a picture of the identical nature of the stock market. The distance from 08/1896 to 09/1929 is an equal distance as 12/1974 to 0/2020
Both 08/1896 and 12/1974 are bottoms, 09/1929 and 02/2020 are tops
Representing both on linear scale we have:
This also shows three identical cycles averaging 546 weeks with their golden sections
1929 and 2007 are very identical because the lie at the same location within the repeating pattern. 1987 and 2020 also look alike because they are the ending nodes of the 546 weeks cycle. 1942 and 1974 are both bottoms and are alternate fractals 180° out of phase, that is, if we arbitrarily turn the 1942 and 1974 chart upside down we will have the same structure as 1929 and 2007.
1929 section
2007 fractal
1987 fractal
2020 Fractal
As we section the chart into cycles we come to locate the position of the 2022 top and current location within the growth cycle, check back in next post/update as we will find the current location and also subdivide into smaller cycles to find the current trend.
Goodluck
Comment:
So we will continue the discussions trying to model the current repeating cycle...
