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<TITLE> Howell - PuetzUWS model for extended SP500 </TITLE>    
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<H2>Puetz Universal Wave Series (UWS) model for a back-extended SP500</h2>
<div class="a">
<I>"...   History never repeats itself, but it rhymes.   ..."</i> (which author(s) down through history?)
</div>


<h3>Table of Contents</h3>
<UL>
	<LI><A HREF="#Key [results, comments]">Key [results, comments]</a>
	<LI><A HREF="#How can the S&P 500 stock market index be correlated with "dead" system?">How can the S&P 500 stock market index be correlated with "dead" system?</a>
	<LI><A HREF="#Ratio of actual to semi-log detrended data : [advantages, disadvantages]">Ratio of actual to semi-log detrended data : [advantages, disadvantages]</a>
	<LI><A HREF="#Future related work">Future potential work</a>
	<LI><A HREF="#Comparison of [TradingView, Yahoo finance] data">Comparison of [TradingView, Yahoo finance] data</a>
	<LI><A HREF="#[data, software] cart [description, links]">[data, software] cart [description, links]</a>
</ul>
<BR>
NOTE :  The model here is DEFINITELY NOT suitable for application to [trade, invest]ing! It's far too [early, incomplete, immature, erroneous]!  See <A HREF="[#=; backtrack ;=#]!!linkError!!">Stephen Puetz</a> for the investment side ot the UWS. <BR>
<BR>


<HR><A id="Model results"> </a>
<h3>Model results</h3>


<A id="SP500 & DJIA indexes back to 1872"> </a>
<H4>"SP500 & DJIA indexes back to 1872"</h4>

Linear semi-log segments [1872-1926, 1926-2020]<BR>
<BR>
Fibonnaci levels versus log-levels <BR>
Larger Fibonnaci's at greater timescales<BR>
<BR>
How do I get negative numbers from a log transformation of the data?<BR>
<BR>
<BR>

<A id="PuetzUWS 2011 [normal, double]-wave series individually"> </a>
<H4>"Key [results, comments]"</h4>


<A id="PuetzUWS 2011 [normal, double]-wave series combined"> </a>
<H4>"PuetzUWS 2011 [normal, double]-wave series combined"</h4>
More and more like Fourier series analysis, but potentially with greater predictive capability? (see section below)<BR>
<BR>
<IMG SRC="[#=; backtrack ;=#]economics, markets/SP500/PuetzUWS/Puetz[,D]UWS 1870-2030 test01 standard.png"></a><BR>


<A id="PuetzUWS 2011  model - short-term ?2009-2020?"> </a>
<H4>"Conventional semi-log plot of the PuetzUWS model"</h4>

<A id="Conventional semi-log plot of the PuetzUWS model - mid-term 1872-2020"> </a>
<H4>"Conventional semi-log plot of the PuetzUWS model"</h4>

<A id="SP500 time-segment overlays"> </a>
<H4>"SP500 time-segment overlays"</h4>

My first semi-log detrended plot of the SP500 1872-2020 is in the webPage <A HREF="[#=; backtrack ;=#]!!linkError!!">title?</a>.  On that webPage, I overlay SP500 series from <BR>
<BR>
<IMG SRC="[#=; backtrack ;=#]!!linkError!!"></a><BR>

<BR>


<HR><A id="Puetz's UWS as a highly-constrained Fourier wave series analysis"> </a>
<h3>Puetz's UWS as a highly-constrained Fourier wave series analysis</h3>

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<h3>???</h3>

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<h3>???</h3>

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<h3>???</h3>

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<HR><A id="Was 2007-2009 the modern equivalent to the 1929 crash?"> </a>
<h3>Was 2007-2009 the modern equivalent to the 1929 crash?</h3>
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Was 2007-2009 the moderen equivalent to the 1929 crash, less the socialist abuse of the free market?
??MacKay?? reference

??MacKay??'s commments are certainly unconventional, but merit closer attention. 
Key points : 
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<HR><A id="How can the S&P 500 stock market index be correlated with 'dead' systems?"> </a>
<h3>How can the S&P 500 stock market index be correlated with 'dead' system?</h3>

<BR>

<HR><A id="What's missing from the current model?"> </a>
<h3>What's [missing from, wrong with] the current model?</h3>

<UL>
	<LI> The data set : 
		<UL>
			<LI> Currently uses historical data of the [SP500, 
			<LI> Needs to include the London Stock Exchange (LSE) and Bourse de Paris?
			<LI> Should perhaps be the SP International index back-extended?
			<LI> Pre-stock exchange proxies - agrultural commodities going back to Babylon
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	<LI> Update the UWS dataset - 
		<UL>
			<LI> currently uses the more complete parameters from Puetz & Borchardt 2011, for both the "normal" and "double" UWS series
			<LI> A 2014 paper changes the base UWS parameters, and applies a Half-wave (HUWS) seeries, rather thanDouble-UWS (DUWS) series
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		</ul>
	<LI> Why have I "eyeballed" the linear-log segments, yet I used Particle Swarm Optimization (PSO) for the parameter?  I even have routines for linear regression analysis, which are standard and very easy.  Laziness is the reason, but I also a fear of getting "artificially precise" at the start of the project when the basic concepts are being explored.  I'm not looking for false accuracy at this point.  It's much more important to simply get my hands dirty with the data and look for [challenges, questions, anomalies], and to see different approaches by eye.
	<LI> Using a hybrid [linear regression, PSO or other] optimisation approach
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	<LI> Down to the hour data - Trading models
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	<LI> Multi-fractal (Benoit Mandelbrot) and Fractional Order Calculus (Gottfried Liebniz) approaches
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<HR><A id="Inspirations"> </a>
<h3>Inspirations</h3>

Inspired by many historians and financial market analysts, most notably but not limited to (in order of appearance on the world stage) : <BR>
Ibn Khaldun "The Muqquadimmah"<BR>
?? Tijevski?<BR>
?? Kondriatieff <BR>
?? Elliot's waves<BR>
Arnold J. Toynbee "A Study of History" <BR>
	<LI> (the full 10-12 volumes, I was missing one or two, now I have only the abridged two-volume set</li><BR>
Ivanka Charvova - best concept I've seen of solar activity over 5-10 ky
Steven Yaskell and Willie Soon "Grand phases on the Sun" - wonderful descriptions of the Maunder grand solar  minimum and many scientists and others
Harry Dent - the most successful 10-40 year [economic, financial] forecaster that I am aware of<BR>
Robert Prechter's Socionomics, the first quantitative Sociology<BR>
Peter Fischers "The Great Wave" -  I forget which author (probably Stephen Puetz who used some of the data) mentioned Fischer's book, but it is a real gem, built on the meticulous work of numerous historians.  I consider it to be one of the great historical works. Stephen Puetz, and especially co-authors [Glen Borchardt, Andreas Prokoph, ??], <BR>
	<LI> and the system of 20+ Mayan calendars</li><BR>
Ray Dalio of ?BlackRock" Hedge fund "??"<BR>
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??Jan2020 initial posting<BR>
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