"$d_WebsiteRaw""Multi-fractal brew/0_multi-fractal brew notes.txt"
www.BillHowell.ca 18Sep2020 initial
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22Sep2020
How does one do "fractal regression"?
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21Sep2020 [Fourier, wavelet] analysis of [SP500, astro-sun-Earth, Puetz, Schumann]
(see list of items below "18Sep2020 Initial ideas")
get matlab to work!
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20Sep2020 OK - with gnuplot, I can rapidly generate a series of 20-year graphs
I know I can use gimp to make a composite image
stack similar periods above one another
can do an automatic overlay on main (large) time series
to focus on fractal fitting :
manually do composite of 5x2 images that are similar,
/media/bill/SWAPPER/Website - raw/economics, markets/200920 SP500 composite graph comparisons.xcf
individually, imageSize := '250, 200' ;
so create a 1250by 400 image in gimp, add component graphs
>> done!
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19Sep2020
bash script to extract data series from text file
"$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
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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. ???
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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