"$d_WebsiteRaw""Multi-fractal brew/0_multi-fractal brew notes.txt"
www.BillHowell.ca  18Sep2020 initial

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22Sep2020

How does one do "fractal regression"?




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21Sep2020  [Fourier, wavelet] analysis of [SP500, astro-sun-Earth, Puetz, Schumann]
(see list of items below "18Sep2020  Initial ideas")

08Nov2021 NYET!  piece of shit...  :  get matlab to work!



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20Sep2020 OK - with gnuplot, I can rapidly generate a series of 20-year graphs
I know I can use gimp to make a composite image 
	stack similar periods above one another
can do an automatic overlay on main (large) time series  
to focus on fractal fitting : 
	manually do composite of  5x2 images that are similar, 
/media/bill/SWAPPER/Website - raw/economics, markets/200920 SP500 composite graph comparisons.xcf

individually, imageSize	:=  '250, 200'   ;  
so create a 1250by 400 image in gimp, add component graphs
>> done!

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19Sep2020
bash script to extract data series from text file
"$d_bin""data - extract series.sh"
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18Sep2020  First step - build multi-fractal approach for patterns

A.	Real data : use patterns from :
"$d_WebsiteRaw""economics, markets/SP500/1872-2020 SP500 index, ratio of opening price to semi-log detrended price.html"
a)	1900-1925, 1950-1975		1900.05	1925.89		1950.05  1975.98
b)	1925-1940, 1990-2010		1925.89  1940.05		1990.05  2010.97
c)	1940-1960, 1995-2010		1940.05  1960.97		1995.97  2010.97
d)	1872-1890, 2000-2020		1871.22  1890.89		2000.05  2020.80
>> NUTS!!! these are only MONTHLY data - next to useless!!

B.	oil versus [XOM, HSE, IMO]...

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18Sep2020  Initial ideas

build on "$d_WebsiteRaw""economics, markets/SP500/1872-2020 SP500 index, ratio of opening price to semi-log detrended price.html"
multi-scale contiguous temporal patterns shuffled in time

title :  Cooking a multi-fractal brew of [Aristarchus, Fourier, Schwabe, Tchijevksy & Kondritieff, Elliot, Mandelbrot, Prechter, Dobra, Puetz]
rougly : 
I.		identify "time series paterns" at different timescales
II.	multi-fractal modelling of each pattern on the basis of Puetzian cycles
			produces list of key Puetz cycles for each pattern
III.	evolve meta-level modelling for full time series
			not just fit, but even more important is phase-change (pattern change) prediction

+-----+
I.		identify "similar periods" of time series at different timescales

A.	[Fourier, wavelet] analysis of [SP500, astro-sun-Earth, Puetz, Schumann]
1.	start with full-series wavelet - coefficients
2.	wavelets of sliding-[start, duration] windows according to full-series coefficients
3.	find "early-matches" of time periods
21Sep2020 :
4. Schumann - don't have historical  data before ~2000 AD?  in Russian
5. need daily SP500 data as well as current monthly?


B.	alternate & easier (manual)
1. eyeball "patterned periods"

C.	[fractal, Elliot wave] adjustments of "key Puetz periods" for each pattern
		evolutionary computation?

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II.	multi-fractal modelling of each "similar period" on the basis of Puetzian cycles
			produces list of key Puetz cycles for each pattern

1.	???

+-----+
III.	evolve meta-level modelling for full time series
			not just fit, but even more important is phase-change (pattern change) prediction

later to think about in broad-brush manner...



# enddoc