#] 
#] *********************
#] "$d_web"'CompLangs/PineScript/PuetzUWS IntlStkIdxs multi-fractals notes.txt'  - ???
# www.BillHowell.ca  14Apr2023 initial 
# view in text editor, using constant-width font (eg courier), tabWidth = 3

# fibonacci [, retracement ratio]s see "$d_Qndfs"'math - [quick, handy] stuff.ndf'  
#48************************************************48




#24************************24
# Table of Contents, generate with :
# $ grep  "^#]"  "$d_web"'CompLangs/PineScript/PuetzUWS IntlStkIdxs multi-fractals notes.txt' |  sed "s/^#\]/  /" 
#


#24************************24
# Setup, ToDos,   

PineScript built-in functions : 
go to PineScript editor -> Menu -> ... (more) -> PineScript reference (pop up) -> Built-in functions


#08********08
#] ??Apr2023 


#08********08
#] ??Apr2023 


#08********08
#] ??Apr2023 


#08********08
#] 18Apr2023 revamp to simply plot SP500 1938-2022 inclined Puetz timeFractal
previous version : 
	"$d_web"'CompLangs/PineScript/230417 20h08m08s PuetzUWS IntlStkIdxs multi-fractals (noWork).txt'  






+-----+
olde code 

// ary_n_bar -> can cause scrunching of outputs!!!  very finicky to set - wish I had a robust n_bars, t_start!
//	 	 27May2022 PineScript provides no bug-free means of getting n_bars.  
//	 	 see '0_PineScript notes.txt' : 
//	 	 	 I did it by trial & error for each time period and even then...
// std TradingView timeScales	 ( 1D      5D     1M    3M     6M     1Y    5Y   All  "All, 01Feb1871")
// last_bar_index	 	 	  	 	 (24924	 21257	 28294	 20055	 22804	 4951	 1000	 230	 ????)  these vary a bit

// 20Jun2022 using last_bar_index (number of datapoints on time axis) DOESN'T work! 
//	 	 Study Error : This study references too many candles in history (eg 5001)
//n_bars  = last_bar_index 

// 20Jun2022 couldn't get these to work - problems with : 
//	 	 Study Error : This study references too many candles in history (eg 5001)

// 16Apr2023 normalize variances via (1 + rsd) - this is a pragmatic fudge


// Symbols' [priceRsd [normal, semi-log], priceRsd[Min, Max]]   
//     {[trend, relStdDev], priceRsd[Min, Max, Spread]Idx, etc} 
// refer to my webSite (good luck with the webSearch) for details
// 1871-present :  Wilhelm Abel ?1937?, David Fischer 1996, I've used the following split : 
//	 	 price equilibrium (stable prices)  1871-1926
//	 	 price revolution  1926-2020
// 11Aug2022 QNial work may show that the breakover should be in the 1950's?  
//		(maybe Breton Woods 1944?)

// calculate [priceNormalRsd, priceSemilogRsd] from priceNormal 
// Euler's number 2.7182818

priceNormal_regressParams_to_priceLogRsd(priceNormal, constant, slope) =>
	priceTrend   =  math.pow(10, constant + slope * year_fraction)  
	(priceNormal / priceTrend - 1) 

// 17Apr2023 needs verification! - guesswork for now
priceLogRsd_to_priceNormal(priceLogRsd, constant, slope) =>
	priceTrend  =  math.pow(10, constant + slope * year_fraction)  
	math.pow(10, (priceLogRsd + 1) * priceTrend)



// symbols - [,un] comment to [ex, in]clude


// CME:CUS2! housing price futures
//	CUS2 = request.security("TVC:UKX", timeframe.period, close)
//	CUS2_detrend  =  0.  
//	CUS2_detrend :=  priceNormal_regressParams_to_priceLogRsd(CUS2, -23.3117, 0.012713, 0.0273817)  
//	plot(CUS2_detrend, color=color.orange, title="CME:CUS2! housing price futures", linewidth=2)
//	rsdMinCUS2		=   10.  
//	rsdMaxCUS2		=  -10.  
//	rsdMinCUS2		:=  smalest(CUS2_detrend, n_bars)  

// 14Apr2023 parameters updates to 

DAX40 = request.security("XETR:DAX", timeframe.period, close)
rsdMinDAX40		=   10.    
rsdMaxDAX40		=  -10.  
rsdDAX40			=    1.  
DAX40_detrend	=    0.  
DAX40_detrend	:=  priceNormal_regressParams_to_priceLogRsd(DAX40, -61.6481, 0.0325753)  
rsdMinDAX40		:=  smalest(DAX40_detrend, n_bars)  
rsdMaxDAX40		:=  biggest(DAX40_detrend, n_bars)  
rsdDAX40			:=  DAX40_detrend / ((rsdMaxDAX40 - rsdMinDAX40) + 1)  
plot(rsdDAX40, color=color.purple, title="DAX40 Germany stkIdx", linewidth=2)

//	GOLD = request.security("TVC:UKX", timeframe.period, close)
//	GOLD_detrend  =  0.  
//	GOLD_detrend :=  priceNormal_regressParams_to_priceLogRsd(GOLD, -29.0842, 0.015824, 0.197304) 
//	plot(GOLD_detrend, color=color.orange, title="GOLD long term price", linewidth=2)
//	rsdMinGOLD		=   10.  
//	rsdMaxGOLD		=  -10.  
//	rsdMinGOLD		:=  smalest(GOLD_detrend, n_bars)  
//	rsdMaxGOLD		:=  biggest(GOLD_detrend, n_bars)  

//	14Apr2023 garbage inputs for HSSSC taken from GOLD!!!
//	HSSSHSC300 = request.security("HSI:HSSSHSC", timeframe.period, close)
//	HSSSHSC300_detrend  = 0.  
//	HSSSHSC300_detrend :=  priceNormal_regressParams_to_priceLogRsd(HSSSHSC300, -175.9000, -0.085201, 0.028966, 0.007881) 
//	plot(HSSSHSC300_detrend, color=color.green, title="HSSSHSC300 China Shanghai-Shenzen-Hong Kong stkIdx", linewidth=2)
//	rsdMinHSSSHSC300	=   10.    
//	rsdMaxHSSSHSC300	=  -10.  
//	rsdMinHSSSHSC300	:=  smalest(HSSSHSC300_detrend, n_bars)  
//	rsdMaxHSSSHSC300	:=  biggest(HSSSHSC300_detrend, n_bars)  


INDIA50 = request.security("Vantage:INDIA50", timeframe.period, close)
rsdMinINDIA50		=   10.    
rsdMaxINDIA50		=  -10.  
rsdINDIA50			=    1.  
INDIA50_detrend	=    0.  
INDIA50_detrend	:=  priceNormal_regressParams_to_priceLogRsd(INDIA50, -61.6481, 0.0325753)  
rsdMinINDIA50		:=  smalest(INDIA50_detrend, n_bars)  
rsdMaxINDIA50		:=  biggest(INDIA50_detrend, n_bars)  
rsdINDIA50			:=  INDIA50_detrend / ((rsdMaxINDIA50 - rsdMinINDIA50) + 1)  
plot(rsdINDIA50, color=color.rgb(200, 100, 100, 0), title="INDIA50 nifty fifty stkIdx", linewidth=2)


NI225 = request.security("TVC:NI225", timeframe.period, close)
rsdMinNI225		=   10.    
rsdMaxNI225		=  -10.  
rsdNI225			=    1.  
NI225_detrend	=    0.  
NI225_detrend	:=  priceNormal_regressParams_to_priceLogRsd(NI225, -61.6481, 0.0325753)  
rsdMinNI225		:=  smalest(NI225_detrend, n_bars)  
rsdMaxNI225		:=  biggest(NI225_detrend, n_bars)  
rsdNI225			:=  NI225_detrend / ((rsdMaxNI225 - rsdMinNI225) + 1)  
plot(rsdNI225, color=color.rgb(250, 200, 30, 0), title="NI225 Japan stkIdx", linewidth=2)


//	SHCOMP is no longer available live via TradingView
//	I included it in with my QNial programs (I have historical), 
//		in which all code was initially developed, then adapted to PineScript
//	SHCOMP = request.security("TVC:SHCOMP", timeframe.period, close)
//	SHCOMP_detrend  = 0.  
//	SHCOMP_detrend :=  priceNormal_regressParams_to_priceLogRsd(SHCOMP, constant, slope, relStdDev) 
//	plot(SHCOMP_detrend, color=color.darkgreen, title="SHCOMP China Shanghai-Shenzen-Hong Kong stkIdx", linewidth=2)
//	rsdMinSHCOMP	=   10.    
//	rsdMaxSHCOMP	=  -10.  
//	rsdMinSHCOMP	:=  smalest(SHCOMP_detrend, n_bars)  
//	rsdMaxSHCOMP	:=  biggest(SHCOMP_detrend, n_bars)  


// special setup for multi-segment regressions  
//		12Aug2022 may have a problem with detrends within if?
SPX500 = request.security("TVC:SPX", timeframe.period, close)

rsdMinSPX500Lo		=   10.    
rsdMaxSPX500Lo		=  -10.  
rsdSPX500Lo			=    1.  
SPX500Lo_detrend	=    0.  
if  year_fraction  <=  1940.06   // yrFrac regressions [1872-1940] 
	SPX500Lo_detrend :=  priceNormal_regressParams_to_priceLogRsd(SPX500, -14.9701, 0.00830613) 
rsdMinSPX500Lo		:=  smalest(SPX500Lo_detrend, n_bars)  
rsdMaxSPX500Lo		:=  biggest(SPX500Lo_detrend, n_bars)  
rsdSPX500Lo	:=  SPX500Lo_detrend / ((rsdMaxSPX500Lo - rsdMinSPX500Lo) + 1)  
plot(rsdSPX500Lo, color=color.blue, title="SPX500Lo stkIdx 1871-1940", linewidth=2)

rsdMinSPX500Hi		=   10.    
rsdMaxSPX500Hi		=  -10.  
rsdSPX500Hi			=    1.  
SPX500Hi_detrend	=    0.  
if  year_fraction  >  1940.06   // yrFrac regressions [1872-1940] 
	SPX500Hi_detrend :=  priceNormal_regressParams_to_priceLogRsd(SPX500, -56.7736, 0.0298315) 
rsdMinSPX500Hi		:=  smalest(SPX500Hi_detrend, n_bars)  
rsdMaxSPX500Hi		:=  biggest(SPX500Hi_detrend, n_bars)  
rsdSPX500Hi	:=  SPX500Hi_detrend / ((rsdMaxSPX500Hi - rsdMinSPX500Hi) + 1)  
plot(rsdSPX500Hi, color=color.blue, title="SPX500 USA stkIdx 1926-2022", linewidth=2)


// DON'T take log of interest rates! but invert them with respect to stock indexes
//	TNX = request.security("TVC:TNX", timeframe.period, close)
//	TNX_detrend  =  0.
//	TNX_detrend :=  priceNormal_regressParams_to_priceLogRsd(TNX, -0.1025, 210.209000, 0.201597) 
//	plot(TNX_detrend, color=color.red, title="TNX 10yr T-bond USA", linewidth=2)
//	rsdMinTNX			=   10.  
//	rsdMaxTNX			=  -10.  
//	rsdMinTNX			:=  smalest(TNX_detrend, n_bars)  
//	rsdMaxTNX			:=  biggest(TNX_detrend, n_bars)  

//	USOIL = request.security("TVC:UKX", timeframe.period, close)
//	USOIL_detrend  =  0.  
//	USOIL_detrend :=  priceNormal_regressParams_to_priceLogRsd(USOIL, -25.517, 0.0145591, 0.0245999) 
//	plot(USOIL_detrend, color=color.black, title="USOIL long term price", linewidth=2)
//	rsdMinUSOIL		=   10.  
//	rsdMaxUSOIL		=  -10.  
//	rsdMinUSOIL		:=  smalest(USOIL_detrend, n_bars)  
//	rsdMaxUSOIL		:=  biggest(USOIL_detrend, n_bars)  

UKX100 = request.security("TVC:UKX", timeframe.period, close)
rsdMinUKX100		=   10.    
rsdMaxUKX100		=  -10.  
rsdUKX100			=    1.  
UKX100_detrend		=    0.  
UKX100_detrend		:=  priceNormal_regressParams_to_priceLogRsd(UKX100, -61.6481, 0.0325753)  
rsdMinUKX100		:=  smalest(UKX100_detrend, n_bars)  
rsdMaxUKX100		:=  biggest(UKX100_detrend, n_bars)  
rsdUKX100			:=  UKX100_detrend / ((rsdMaxUKX100 - rsdMinUKX100) + 1)  
plot(rsdUKX100, color=color.rgb(200, 150, 250, 0), title="UKX100 long term stkIdx", linewidth=2)


// FRED:WLFN - Federal Reserve, Liabilities and Capital
//	WLFN = request.security("FRED:WLFN", timeframe.period, close)
//	WLFN_detrend  =  0.  
//	WLFN_detrend :=  priceNormal_regressParams_to_priceLogRsd(WLFN, -61.6481, 0.0325753, 0.0351671)  
//	plot(WLFN_detrend, color=color.green, title="WLFN Fed Liabilities, Capital", linewidth=2)
//	rsdMinWLFN			=   10.  
//	rsdMaxWLFN			=  -10.  
//	rsdMinWLFN			:=  smalest(WLFN_detrend, n_bars)  
//	rsdMaxWLFN			:=  biggest(WLFN_detrend, n_bars)  



// Overall priceRsd[Min, Max] over full length of t_timelength
//		adjust the symbolList according to selections above
priceRsdMin			=   10.0  
priceRsdMax			=  -10.0  
priceRsdMin			:=  rsdMinSPX500Lo  
priceRsdMax			:=  rsdMaxSPX500Hi  

priceRsdMin			:=  math.min(rsdMinDAX40, rsdMinINDIA50, rsdMinNI225, rsdMinSPX500Lo, rsdMinSPX500Hi, rsdMinUKX100)		// later rsdMinTNX, 
priceRsdMax			:=  math.max(rsdMaxDAX40, rsdMaxINDIA50, rsdMaxNI225, rsdMaxSPX500Lo, rsdMaxSPX500Hi, rsdMaxUKX100)		// later rsdMaxTNX, 





#08********08
#] 17Apr2023 fix priceFrac horizontal lines (they aren't plotted)

AGAIN, I give up on PineScript - not made for any complexity

Change : 
DAX40_detrend :=  priceNormal_regressParams_to_priceLogRsd(DAX40, -61.6481, 0.0325753, 0.0351671)  
To : 
DAX40_detrend :=  priceNormal_regressParams_to_priceLogRsd(DAX40, -61.6481, 0.0325753, 0.0351671, rsdMinDAX40, rsdMaxDAX40)  

+-----+
olde code

// 03Jun2022 new "table" functions are not very good yet!  
//    better this simple approach
mat_write(string matTitle, matrix<float> matSymbol, int n_bars, int barRightShift, float serPrice, float txtLineHeight) =>  
	rows		= matrix.rows(matSymbol)
	cols		= matrix.columns(matSymbol)
	rowStr	= ""
	num		= 10.0
	y_offset	= 0.0
	y_offset := -6*txtLineHeight 
	// barFirst_label(float barFractionFrmRight, float serPrice, float priceOffset, string txt) => 
	barFirst_label(0.75, serPrice, y_offset, matTitle)
	for iRow = 0 to (rows - 1)
		rowStr  := ""
		for iCol = 0 to (cols - 1)
			num := matrix.get(matSymbol, iRow, iCol)
			rowStr :=  rowStr + str.tostring(num, '#.000') + " " 
		y_offset :=  float(-(iRow + 7)*txtLineHeight)
	barFirst_label(0.75, serPrice, y_offset, rowStr)

//	INDIA50_detrend  =  0.  
//	INDIA50_detrend :=  priceNormal_regressParams_to_priceLogRsd(INDIA50, 0.070385)
//	plot(INDIA50_detrend, color=color.rgb(200, 100, 100, 0), title="", linewidth=2)
//	rsdMinINDIA50		=   10.    
//	rsdMaxINDIA50		=  -10.  
//	rsdMinINDIA50		:=  smalest(INDIA50_detrend, n_bars)  
//	rsdMaxINDIA50		:=  biggest(INDIA50_detrend, n_bars)  

rsdMinINDIA50		:=  smalest(INDIA50, n_bars)  
rsdMaxINDIA50		:=  biggest(INDIA50, n_bars)  
rsdDelINDIA50		:=  rsdMaxINDIA50 - rsdMinINDIA50  
INDIA50_detrend :=  priceNormal_regressParams_to_priceLogRsd(INDIA50, -96.3589, 0.0497382, rsdDelINDIA50)  
plot(INDIA50_detrend, color=color.rgb(200, 100, 100, 0), title="INDIA50 nifty fifty stkIdx", linewidth=2)

//	NI225_detrend  =  0.
//	NI225_detrend :=  priceNormal_regressParams_to_priceLogRsd(NI225, -1.66838, 0.00291729, 0.0341034) 
//	plot(NI225_detrend, color=color.rgb(250, 200, 30, 0), title="NI225 Japan stkIdx", linewidth=2)
//	rsdMinNI225			=   10.  
//	rsdMaxNI225			=  -10.  
//	rsdMinNI225			:=  smalest(NI225_detrend, n_bars)  
//	rsdMaxNI225			:=  biggest(NI225_detrend, n_bars)  

rsdMinNI225		:=  smalest(NI225, n_bars)  
rsdMaxNI225		:=  biggest(NI225, n_bars)  
rsdDelNI225		:=  rsdMaxNI225 - rsdMinNI225  
NI225_detrend :=  priceNormal_regressParams_to_priceLogRsd(NI225, -1.66838, 0.00291729, rsdDelNI225)  
plot(NI225_detrend, color=color.rgb(250, 200, 30, 0), title="NI225 Japan stkIdx", linewidth=2)

rsdMinSPX500Lo		:=  smalest(SPX500, n_bars)  
rsdMaxSPX500Lo		:=  biggest(SPX500, n_bars)  
rsdDelSPX500Lo		:=  rsdMaxSPX500Lo - rsdMinSPX500Lo  
if  year_fraction  <=  1940.06   // yrFrac regressions [1872-1940] 
	SPX500Lo_detrend :=  priceNormal_regressParams_to_priceLogRsd(SPX500, -14.9701, 0.00830613, rsdDelSPX500Lo) 
plot(SPX500Lo_detrend, color=color.blue, title="SPX500Lo stkIdx 1871-1940", linewidth=2)

rsdMinSPX500Hi		:=  smalest(SPX500, n_bars)  
rsdMaxSPX500Hi		:=  biggest(SPX500, n_bars)  
rsdDelSPX500Hi		:=  rsdMaxSPX500Hi - rsdMinSPX500Hi  
if  year_fraction  >=  1940.06	// yrFrac regressions [1926-2022, 1938-2022] 
	SPX500Hi_detrend :=  priceNormal_regressParams_to_priceLogRsd(SPX500, -56.7736, 0.0298315, rsdDelSPX500Hi) 
plot(SPX500Hi_detrend, color=color.blue, title="SPX500 USA stkIdx 1926-2022", linewidth=2)


UKX100_detrend  =  0.  
UKX100_detrend :=  priceNormal_regressParams_to_priceLogRsd(UKX100, -25.517, 0.0145591, 0.0245999) 
plot(UKX100_detrend, color=color.rgb(200, 150, 250, 0), title="", linewidth=2)
rsdMinUKX100		=   10.  
rsdMaxUKX100		=  -10.  
rsdMinUKX100		:=  smalest(UKX100_detrend, n_bars)  
rsdMaxUKX100		:=  biggest(UKX100_detrend, n_bars)  

rsdMinUKX100		:=  smalest(UKX100, n_bars)  
rsdMaxUKX100		:=  biggest(UKX100, n_bars)  
rsdDelUKX100		:=  rsdMaxUKX100 - rsdMinUKX100  
UKX100_detrend :=  priceNormal_regressParams_to_priceLogRsd(UKX100, -1.66838, 0.00291729, rsdDelUKX100)  
plot(UKX100, color=color.rgb(200, 150, 250, 0), title="UKX100 long term stkIdx", linewidth=2)






#08********08
#] 17Apr2023 try old version of PuetzUWS IntlStkIdxs multi-fractals

"$d_web"'CompLangs/PineScript/z_Archive/220614 13h00m10s Howell - PuetzUWS [time, price] multiFractal mirrors, SPX 1872-2020.txt'
indicator(title="PuetzUWS [time, price] multiFractal mirrors, SPX 1872-2020", shorttitle="PuetzUWS 1872-2020 fractal mirrors", overlay=true)
>> works well, but horizontal lines : 
	missing lower bound 
	not produced for priceFrac < 0

use [early version, diff] to fix current version
renamed : 
$ path2="$d_web"'CompLangs/PineScript/PuetzUWS IntlStkIdxs multi-fractals.txt' 
$ pDif2="$d_temp"'PuetzUWS IntlStkIdxs diff2.txt'

$ diff "$path2" "$path1"  --suppress-common-lines | grep --invert-match  "[,cd-]" | sed 's/< //;s/> //' >"$pDif2"
>> reverse view

NUTS - both diffs essentially the same, nothing substantial in diffs
diff is almost useless (or the way that I am using it)

Change : 
+-----+
priceNormal_regressParams_to_priceNormalRsd(priceNormal, constant, slope, relStdDev, yrStrtRegr) =>
	priceNormalTrend  =  constant + slope * (year_fraction - yrStrtRegr)
	(priceNormal / priceNormalTrend - 1) / relStdDev

priceNormal_regressParams_to_priceSemilogRsd(priceNormal, constant, slope, relStdDev, yrStrtRegr) =>
	priceLogTrend  =  constant + slope * (year_fraction - yrStrtRegr)
	(math.log(priceNormal) / priceLogTrend - 1) / relStdDev

priceNormalRsd_to_priceNormal(priceNormalRsd, constant, slope, relStdDev, yrStrtRegr) =>
	priceLogTrend  =  constant + slope * (year_fraction - yrStrtRegr)
	priceLogTrend * ((priceNormalRsd * relStdDev) + 1)

priceSemilogRsd_to_priceNormal(priceSemilogRsd, constant, slope, relStdDev, yrStrtRegr) =>
	priceLogTrend  =  constant + slope * (year_fraction - yrStrtRegr)
	math.pow(10, priceLogTrend * ((priceSemilogRsd * relStdDev) + 1))
+-----+
To : 
+-----+
priceNormal_regressParams_to_priceNormalRsd(priceNormal, constant, slope, relStdDev, yrStrtRegr) =>
	priceNormalTrend  =  math.power(10, constant + slope * (year_fraction - yrStrtRegr))
	(priceNormal / priceNormalTrend - 1) / relStdDev

priceNormalRsd_to_priceNormal(priceNormalRsd, constant, slope, relStdDev, yrStrtRegr) =>
	priceLogTrend  =  math.power(10, constant + slope * (year_fraction - yrStrtRegr))
	priceLogTrend * ((priceNormalRsd * relStdDev) + 1)

// priceSemilogRsd should NOT be used?  

priceNormal_regressParams_to_priceSemilogRsd(priceNormal, constant, slope, relStdDev, yrStrtRegr) =>
	priceLogTrend  =  math.power(10, constant + slope * (year_fraction - yrStrtRegr))
	math.log( (priceNormal / priceLogTrend - 1) / relStdDev

priceSemilogRsd_to_priceNormal(priceSemilogRsd, constant, slope, relStdDev, yrStrtRegr) =>
	priceLogTrend  =  math.power(10, constant + slope * (year_fraction - yrStrtRegr))
	math.pow(10, priceLogTrend * ((priceSemilogRsd * relStdDev) + 1))
+-----+

Oops - now output is 10^58!!!

Back to : 
priceNormal_regressParams_to_priceNormalRsd(priceNormal, constant, slope, relStdDev, yrStrtRegr) =>
	priceNormalTrend  =  constant + slope * (year_fraction - yrStrtRegr)
	(priceNormal / priceNormalTrend - 1) / relStdDev

priceNormalRsd_to_priceNormal(priceNormalRsd, constant, slope, relStdDev, yrStrtRegr) =>
	priceLogTrend  =  constant + slope * (year_fraction - yrStrtRegr)
	priceLogTrend * ((priceNormalRsd * relStdDev) + 1)

>> now back to (0  -1000), inverted graph
priceNormal_regressParams_to_priceLogRsd(priceNormal, constant, slope, relStdDev, yrStrtRegr) =>
	priceLogTrend  =  constant + slope * (year_fraction - yrStrtRegr)
	(math.log(priceNormal) / priceLogTrend - 1) / relStdDev

priceLogRsd_to_priceNormal(priceLogRsd, constant, slope, relStdDev, yrStrtRegr) =>
	priceLogTrend  =  constant + slope * (year_fraction - yrStrtRegr)
	math.pow(10, priceLogTrend * ((priceLogRsd * relStdDev) + 1))

>> now back to where I started :  SP500 at -12.25!???

What about yrStrtRegr?
SPX500Hi_detrend :=  priceNormal_regressParams_to_priceLogRsd(SPX500, -56.7736, 0.0298315, 0.0937853, 1926.06) 
>> NUTS!!! arg1 not symbol, but base year!!!
>> NYET! - SP500 - is the closing price

CRAP! PiceScriopt : 
	math.log is NATURAL logarithm
	math.log10 is log base 10

>> same problem now t -11.35 

manual calc 
see /home/bill/web/Qnial/MY_NDFS/economics, markets/230417 priceNormal_regressParams_to_priceLogRsd.ndf 

	priceNormal_regressParams_to_priceLogRsd  IS OP  priceNormal  constant  slope  relStdDev  yrStrtRegr
{  
	priceLogTrend  :=  constant + (slope * (year_fraction - yrStrtRegr))  ;  
	((log  priceNormal) / priceLogTrend) - 1) / relStdDev
}  

# priceNormal_regressParams_to_priceLogRsd  2022.0 -14.9701 0.00830613 0.122382 1871.22

constant : I was using +14.9701 instead of -14.9701!!
BUT - should have been using 1926-2022 parameters, not 1871-194!!

Change to : 
priceNormal_regressParams_to_priceLogRsd(priceNormal, constant, slope, relStdDev, yrStrtRegr) =>
	expnt    =  constant + slope * (year_fraction - yrStrtRegr)
	priceTrend  =  math.pow(10, expnt)  
	(priceNormal / priceTrend - 1) / relStdDev

"$d_Qmkts"'market symbol [regressSL, detrend].ndf'  
'market tblWhole.dat' : 
>> yTrn are "log



"$d_web"'CompLangs/PineScript/z_Archive/220614 13h00m10s Howell - PuetzUWS [time, price] multiFractal mirrors, SPX 1872-2020.txt'
// for 1871-1926 =10^( 0.784617 +  (0.000140925*(x - 1871.08)))
calc_SP500Trend(y_fraction) =>  
    expnt = 0.792392+0.0289587*(y_fraction - 1926.25)  
    SP500base = math.pow(10,expnt)

but now are : 
if  year_fraction  <=  1940.06   // yrFrac regressions [1872-1940] 
	SPX500Lo_detrend :=  priceNormal_regressParams_to_priceLogRsd(-14.9701, 0.00830613, 0.122382, 1871.22) 
if  year_fraction  >=  1926.06	// yrFrac regressions [1926-2022, 1938-2022] 
	SPX500Hi_detrend :=  priceNormal_regressParams_to_priceLogRsd(SPX500, -56.7736, 0.0298315, 0.0937853, 1926.06) 

Mistake? - double log maybe?
	priceNormal_regressParams_to_priceLogRsd_fix  IS OP  year_fraction  priceNormal  constant  slope  relStdDev  yrStrtRegr
{  
%	priceLogTrend  :=  power 10  (constant + (slope * (year_fraction - yrStrtRegr)))  ;  
	priceLogTrend  :=  				constant + (slope * (year_fraction - yrStrtRegr))   ;  
		write  priceLogTrend  ;  
	((priceNormal / priceLogTrend) - 1) / relStdDev
}  


	priceHiFix  IS OP  year_fraction  priceNormal  
{  
	priceNormal_regressParams_to_priceLogRsd_fix  year_fraction  priceNormal  -56.7736 0.0298315 0.0937853 1926.06  
}  


#
qnial> EACH  priceHiFix  (2022.079  4795.490)  (2000.721  1430.830)  (1988.721   272.020)  (1980.308   112.950)  (1956.389    48.700)   (1933.470     8.870)   
-11.3907 -11.2795 -11.1355 -11.0595 -10.9847 -10.8414


qnial> loaddefs link  d_Qndfs 'economics, markets/230417 priceNormal_regressParams_to_priceLogRsd.ndf' 
qnial> 00.721  1430.830)  (1988.721   272.020)  (1980.308   112.950)  (1956.389    48.700)   (1933.470     8.870)   
-53.9092
-54.5464
-54.9043
-55.1553
-55.8688
-56.5525
-959.158 -290.359 -63.4901 -32.4982 -19.9571 -12.335
>> OK, so my regressions put out LINEAR (normal) priceTrend
>> sign is WRONG!!!

Change : priceNormal_regressParams_to_priceLogRsd(priceNormal, constant, slope, relStdDev, yrStrtRegr) =>
	expnt    =  constant + slope * (year_fraction - yrStrtRegr)
	priceTrend  =  math.pow(10, expnt)  
	(priceNormal / priceTrend - 1) / relStdDev
To : 
priceNormal_regressParams_to_priceLogRsd(priceNormal, constant, slope, relStdDev, yrStrtRegr) =>
	priceTrend   =  constant + slope * (year_fraction - yrStrtRegr)
	(priceNormal / priceTrend - 1) / relStdDev

But chart back to -1000 pricing instead of -1 to 1 or something like that, inverted
must have double-correcvtion somewhere?
>> I was plotting 1871-1940 by left-over mixup : 
plot(SPX500Lo_detrend, color=color.rgb(100, 100, 255, 0), title="SPX500 USA stkIdx 1871-1940")


Change : 
	priceLogTrend  :=  				constant + (slope * (year_fraction - yrStrtRegr))   ;  
To : 
	priceLogTrend  :=  				constant + (slope * (year_fraction - yrStrtRegr))   ;  


"$d_Qndfs" 'fit_linearRegress.ndf'  : 
+--+
	yTrn_paramL_SLRgress_xyTrnEstL  IS OP  yTrn  
paramLabelStr  xTrnPhr  xUnTrnPhr  yTrnPhr  yUnTrnPhr  slope  constant  
>> slope first, then constant?

+--+
	fit_SLRgress  IS OP  symName  xObs  yObs  xTrnPhr  yTrnPhr  povr    
returns
	constant  slope  relStdDevObs  relStdDevTrn  xObsMin  xObsMax  yObsMin  yObsMax  yDetrendMin  yDetrendMax     
# qnial> fit_SLRgress  xObs  yObs  "pass     "log   (link d_temp  'fit_SLRgress quick test.txt')  
-56.7736 0.0298315 0.333903 0.0937853 1926.06 2022.13 4.77 4804.51 0.910925 1.29852
>> OK -56.7736 0.0298315 are constant  slope  

priceNormal_regressParams_to_priceLogRsd(priceNormal, constant, slope, relStdDev, yrStrtRegr) =>
	priceTrend   =  power 10  (constant + slope * year_fraction)  
	(priceNormal / priceTrend - 1) / relStdDev
>> OK PineScript chart looks OK, but missing fracGrid < 0

NOW, add plots of other stock indices
>> similar scaling problem for others?


+-----+
olde code

//    over a "segment" of time for symbols with multiple segments

//	priceNormal_regressParams_to_priceLogRsd(priceNormal, constant, slope, relStdDev, yrStrtRegr) =>
//		expnt    =  constant + slope * (year_fraction - yrStrtRegr)
//		priceTrend  =  math.pow(10, expnt)  
//		(priceNormal / priceTrend - 1) / relStdDev

//	priceLogRsd_to_priceNormal(priceLogRsd, constant, slope, relStdDev, yrStrtRegr) =>
//		expnt    =  constant + slope * (year_fraction - yrStrtRegr)
//		priceTrend  =  math.pow(10, expnt)  
//		math.pow(10, priceLogTrend * ((priceLogRsd * relStdDev) + 1))

// price[Min, Max] over full length of t_timelength, txtLineHeight
//		only used for placing labels on chart 
// 23May2022 do NOT declare with 'var'!!! :

priceMin	 =  smalest(close, n_bars) 
priceMax	 =  biggest(close, n_bars) 

	//  
	priceLabel := priceRsdMax - 2*txtLineHeight
	simple_label(bar_2_3rds, priceLabel, "priceMin = " + str.tostring(priceMin))
	simple_label(bar_1_half, priceLabel, "priceMax = " + str.tostring(priceMax))
	simple_label(bar_1_qrtr, priceLabel, "midIdx   = " + str.tostring(midIdx))

>> it's working fairly well right now.  I should stop after fixing priceFrac horizontal lines

//	priceRsdMin			:=  math.min(rsdMinDAX40, rsdMinINDIA50, rsdMinNI225, rsdMinSPX500Lo, rsdMinSPX500Hi, rsdMinUKX100)		// later rsdMinTNX, 
//	priceRsdMax			:=  math.max(rsdMaxDAX40, rsdMaxINDIA50, rsdMaxNI225, rsdMaxSPX500Lo, rsdMaxSPX500Hi, rsdMaxUKX100)		// later rsdMaxTNX, 


#08********08
#] 16Apr2023 what has changed in the code? 'PuetzUWS IntlStkIdxs multi-fractals (version 2).txt' 
"$d_web"'CompLangs/PineScript/230414 10h57m PuetzUWS IntlStkIdxs multi-fractals (version 2).txt' 

$ path1="$d_web"'CompLangs/PineScript/230414 10h57m PuetzUWS IntlStkIdxs multi-fractals (version 2).txt' 
$ path2="$d_web"'CompLangs/PineScript/PuetzUWS IntlStkIdxs multi-fractals (version 2).txt' 
$ pDif="$d_temp"'PuetzUWS IntlStkIdxs diff.txt'

$ diff "$path1" "$path2"  --suppress-common-lines | grep --invert-match  "[,cd-]" | sed 's/< //;s/> //' >"$pDif"
>> no real diff

$ path1="$d_web"'CompLangs/PineScript/220721 07h08m Howell - PuetzUWS [time, price] multiFractal mirrors, SPX 1872-2020.txt' 
>> no diff? 

$ path1="$d_web"'CompLangs/PineScript/z_Archive/220614 13h00m10s Howell - PuetzUWS [time, price] multiFractal mirrors, SPX 1872-2020.txt'  
>> OK, many differences, look at next day I work on this

// priceSemilogRsd should NOT be used?  
// calculate priceNormal from [priceNormalRsd, priceSemilogRsd] 
// derivation of  priceSemilogRsd_to_priceNormal : 
// priceLogTrend  =  constant + slope * (year_fraction - yrStrtRegr)
// priceNormalRsd =  (math.log(priceNormal) / priceLogTrend - 1) / relStdDev
// (math.log(priceNormal) / priceLogTrend - 1)  =  priceNormalRsd * relStdDev
// math.log(priceNormal) / priceLogTrend )  =  (priceNormalRsd * relStdDev) + 1
// math.log(priceNormal)  =  priceLogTrend * ((priceNormalRsd * relStdDev) + 1)
// priceNormal  =  math.pow(10, priceLogTrend * ((priceNormalRsd * relStdDev) + 1))
//	
//	priceNormal_regressParams_to_priceSemilogRsd(priceNormal, constant, slope, relStdDev, yrStrtRegr) =>
//		priceLogTrend  =  constant + slope * (year_fraction - yrStrtRegr)
//		(math.log(priceNormal) / priceLogTrend - 1) / relStdDev
//	
//	
//	priceSemilogRsd_to_priceNormal(priceSemilogRsd, constant, slope, relStdDev, yrStrtRegr) =>
//		priceLogTrend  =  constant + slope * (year_fraction - yrStrtRegr)
//		math.pow(10, priceLogTrend * ((priceSemilogRsd * relStdDev) + 1))




#08********08
#] 15Apr2023 why doesn't PineScript work?: 'PuetzUWS IntlStkIdxs multi-fractals (version 2).txt' 
"$d_web"'CompLangs/PineScript/PuetzUWS IntlStkIdxs multi-fractals (version 2).txt'  

+-----+
ln instead of log? myet - log is specified as "yTrnPhrL in : 
	"$d_web"'Qnial/MY_NDFS/economics, markets/' : 
		market symbol header.ods
		market tblWhole.dat

+-----+
what now?

#08********08
#] 15Apr2023 revamp symbol names: "$d_web"'economics, markets'  

'CADUSD Jun1987-Sep2022 TradingView'
'CAEXP Jan1971-Jul2022 TradingView'
'CAGDP Dec1960-Sep2022 TradingView'
... etc

geany regexpr search :  ^(['a-zA-Z0-9]* )[a-zA-Z0-9\-]* ([a-zA-Z0-9,']*) 
	replace  \1\2
'CADUSD TradingView'
'CAEXP TradingView'
'CAGDP TradingView'
... etc

geany regexpr search :  ^(['a-zA-Z0-9]*) (.*) 
	replace  \1\'
'CADUSD'
'CAEXP'
... etc

geany regexpr search :  ^(['a-zA-Z0-9]*) (.*) 
	replace  \'\2
'TradingView'
... etc

geany regexpr search :  ^(['a-zA-Z0-9]* )([a-zA-Z0-9\-]*) ([a-zA-Z0-9,']*) 
	replace  \'\2\'
	doesn't quite work, manual corrections
'Jun1987-Sep2022'
'Jan1971-Jul2022'
... etc


#08********08
#] 14Apr2023 Background tables for SP500 detrended Puetz [time, price] multifractals

SP500 semiLog trendline 1926-2022 :  10 power (-56.7736 + (0.029831 * year)) 
year fraction  2000.0  2005.0  2010.0  2015.0  2022.0  2022.5  2022.75  2023.0  2025  2030    2040   2050
SP500 price     773    1090    1537    2167    3505    3627    3690     3754    4307  6071  12,068 23,985

Fibonacci               [0.000  0.236  0.382  0.500  0.618  0.786  1.000] 
Puetz 1st level    [0.000               0.333               0.666              1.000]
Puetz mix              [0.000  0.222  0.333  0.500  0.666  0.777  1.000]
Puetz half-wave  [0.000  0.167  0.333  0.500  0.666  0.833  1.000]





# enddoc