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Puetz Universal Wave Series (UWS) model [time, price] multifractal of detrended SPX 1871-2020

"... History never repeats itself, but it rhymes. ..." (which author(s) down through history?)

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Stephen J. Puetz's "Universal Wave Series" (UWS - see references below) provides one of many generalized approaches to market [time, price] multi-fractals. I have implemented this in's Pine Script language to provide real-time market chart updates on [day, week, [1,3,6] month, [1,5] year, "All"] timescales.

Explanations of the detrended multi-fractal chart, and why you might consider using it, are provided in sections below.

The detrended view of market symbols is intended as a COMPLEMENT to semi-log charts that [investor, trader]s normally use, and NOT as a stand-alone view. Keep in mind that the process of detrending "throws out data", i.e. the trend, and the trend is of primary interest to [investor, trader]s. The detrended view converges to the normal view at timescales less than a month. As such, traders who focus exclusively on these shorter timeframes won't get much practical use form the detrended view.

Users only have to set up the basic chart and symbols in TradingView based on my chart PuetzUWS [time, price] multiFractal mirrors, SPX 1872-2020. To do so you must be a TradingView subscriber. After that, copy over my PineScript coding, which you can find on my TradingView page - click on "SCRIPTS", and select my script "PuetzUWS [time, price] multifractal of detrended SPX 1871-2020". Further setup details are given below.

It was my intent to provide [Fibonacci, Leibnitz] alternatives as basis for the [time, price] fractals, and to provide detrended series for [NASDAQ, USOIL, GOLD]. But it was enough of a struggle to get the current Pine Script coding to (mostly) work so I leave it as is for the foreseeable future.

This webPage is for users of the chart. Details about my Pine Script program to generate it, and how programmers can modify it for other [symbol, chart, fractal type, additional measure]s are provided on my TradingView PineScript of priceTimeFractals webPage..

What does my TradingView PineScript code do?

What are the objectives of a detrended view of a symbols, and of the generalized [time, price] multi-fractal, and why might this be of interest to you? Here is one example as a start to answering those questions :

Examples of TradingView charts : A series of the same chart at decreasing timescales is provided below :

The above images are snapshots of my TradingView chart.ot shown are diverse market symbols that I have added, simply by using the normal TradingView capabilities. For the purposes of this discussion, I will focus on the SPX US stock market index symbol. Both the symbol name and the chartline that represents it are colored light blue. For this chart, SPX is the "primary market symbol", so normally volume bars would appear at the bottom of the chart. However, these are not available for SPX (?), whereas SPX500USD does provide them.

The above charts are generated by my [written, adapted] Pine Script program that super-imposes fractal [time, price] grids : WARNING : You probably have to be a subscriber to TradingView to access the actual program that is being used. But you can also access an upload of my working copy (which I upload infrequently to my website).

I've posted the Pine Script program as "public", so TradingView subscribers who have paid for access to scripts, should be able to adapt the Pine Script program to their own needs, a view "live"

So, what does the user have to do to [get, adjust] output?

Nothing, as both the [time, price] fractals are "strongly anchored" :

What CAN the user change?

The normal TradingView "tools" (eg [pattern, indicator, strategy]s) can be added to the chart, but these will be anchored to the "normal" (not detrended) [SPX, USOIL, GOLD]. Too see your tools, the underlying symbol must be visible (I think?). You can therefore draw tools over the de-trended SPX, but these may be shifted around in time as the synderlying non-detrended symbol rescales? Some suggestions? : view the works of other TradingView Traders, for example here are some of my favourites :
Uers can add different symbols to the basic chart. These will display in a conventional style ONLY - producing detrended results requires Pine Script coding changes.

Users cannot easily change the SPX basis of the chart, or the PuetzUWS [time, price] fractals. That also requires changes to the underlying PineScript coding, as described on my webPage TradingView PineScript of priceTimeFractals. You can do that if you are reasonably comfortable with PineScript (hopefully more comfortable than I).

Initial observations

It helps to have experience with technical trading approaches as a basis for looking at the chart above, and the links to the same chart at other timescales. I am NO a trader, and I'm certainly no expert on technical trading methods, but after "watching-at-a-distance" post covid crash (unfortunately, as markets skyrocketed while I watched on), my first impressions were :

Initial questions

It is for >1 year analysis that the detrended perspective has its greatest potential benefits, although this remains to be proven :

PineScript comments

original comments 24May2022, posted on this webPage 28May2022

multi-fractals, Benoit Mandelbrot said :
[time, price] multi-fractals : Benoit Mandelbrot said that the true power of fractals only emerges when time is one of the fractal dimensions.

PuetzUWS comments

Puetz "Universal Wave Series" (UWS) timeFractals :
The Puetz "Universal Wave Series" (UWS) timeFractal applies to hugely diverse themes including (physics, astronomy, geology, major extinction events, history, war, psychology, sociology, financial markets).
If the "non-optimized time spikes" (vertical lines) appear to relate to market symbol movements at all standard TV timescales (eg 1D 5D 1M 3M 6M 1Y 5Y All), then :
- they may be saying something far (broader, deeper) about time series than anything other than Puetz that I know of (eg. far beyond the Mayan system of 20+ calendars)
- or is it just another example that human (senses, brain) always infer correlations and and patterns?

not used : (Ordovician, Devonian, Permian, Triassic, Cretaceous)

missing features :
23May2022 Puetz "Half-UWS" spikes were considered, but I fear would clutter the chart too much. Just imagine that there is a spike between each of the time spikes that do appear (which are UWS only: sequences of [*,/] by a factor of three)
23May2022 My intent was to give multiple fractal options for both time and price, adding [Liebnitz, Elliot, Prechter] to [Fibonacci, Puetz], but I won't get to that for now.

Fibonacci priceFractals
(= 1926-2020 stdDev semilog) :
Imy earlier mini-Project (??? hyperlink to provide later ???) Fibonacci priceFractals are hard-bound to the SP500USD 1926-2020 semi-log trend line and standard deviation.
So they are tied to the SPXUSD over the last 83+ years, but are NOT related to current market specifics. Fibonacci priceFractals are hard-bound to the SP500USD 1926-2020 semi-log trend line and standard deviation. (fib = number of stdDev)
So they are tied to the SPXUSD over the last 83+ years, but are NOT related to current market specifics.

Multi-fractal (Benoit Mandelbrot) and Fractional Order Calculus (Gottfried Liebniz) approaches. I've no time to elaborate on this now - this is just a concept-holder for a future date.

models can enlighten AND blind you :
WARNING: While models can help us better understand reality, they also (bias, blind) us to it as well. As science (fashions -> cults -> religions), the religions' (priests, disciples)*(suppress, destroy) the rare rebels who are our only hope for progress.

Spreadsheet of [data, trend, relStdDev] : SP500 1926-2020 semi-log trend, standard deviation :
SP500 1926-2020 semi-log trend = 10^(0.792392+2.89587*10^(-2)*(year - 1926.25)) price revolution* (~7%/y)
SP500 1872-1926 semi-log trend = 10^(0.784617+1.40925*10^(-4)*(year - 1871.08)) price equilibrium* (~0.03%/y)
OOPS! I forgot to put in the 1872-1926 relStdDev!!! I left it at the same as 1926-2020. so the graph will be skewed.
*David Fischer 1996 "The Great Wave, Price revolutions and the rhythm of history"

More and more like Fourier series analysis, but potentially with greater predictive capability? (see section below)

Puetz's UWS as a highly-[constrained, specific] Fourier wave series-like analysis?

Comments along these lines are provided in my very incomplete Howell - preliminary frequency analysis, Fourier series as origins of Puetz UWS. I don't actually "believe" my anal but it is very important to address it in some detail.

How can the S&P 500 stock market index be correlated with 'dead' system?

Was 2007-2009 the modern equivalent to the 1929 crash? Are we going there yet?

In my not-at-all-sure opininion, the Great Depression was a bad recession made vastly worse by FDR's socialist abuse of the free market and it's leaders. In my not-at-all-sure opininion, that could easiy happen again today given voter trends. In our societies, we now seem to destroy good men who build, and we make heros out of others who destroy and degrade. Nothing new there in light of the history kind.

A great presentation of that point of view that influenced me, even if I was already thinking more [broad, extreme]ly in that direction because of history projects of my father and I :
Lawrence W. Reed 2008 "Great myths of the Great Depression" MacKinac Center of Public Policy,, original edition 1981

Reed's commments are certainly unconventional, but merit closer attention, whether or not the politically-correct are happy about it. [Right, wrong, true, false] doesnt matter, I just want to argue over beer with my friends <grin>.

Anyways, you should form your own opinion, even if you are not allowed to.


Related background information on my other webPages : see [general, specific] links to [concepts, my software, data, results, etc] in :

Inspirations for this webPage

Inspired by many historians and financial market analysts, most notably but not limited to (in order of appearance on the world stage) :
Ibn Khaldun "The Muqquadimmah"
?? Tijevski?
?? Kondriatieff
?? Elliot's waves
Arnold J. Toynbee "A Study of History"
  • (the full 10-12 volumes, I was missing one or two, now I have only the abridged two-volume set

  • 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 (I'm not aware of much).
    Robert Prechter's Socionomics, the first quantitative Sociology
    Wilhelm Abel - earliest of the modern price historians who spoke of price [equilibria, revolutios, as far as I know. There were earlier researchers, and as [Abel, Fischer] point out, questions were being addressed throughout history.
    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, ??],
  • and the system of 20+ Mayan calendars

  • Ray Dalio of ?BlackRock" Hedge fund "??"