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<TITLE> Howell - [interest, exchange] rate models </TITLE>    
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<H2>[Interest, exchange] rate models</h2>


<h3>Table of Contents</h3>
<UL>
        <LI><A HREF="#Key [results, comments]">
                                          Key [results, comments]</a>
        <LI><A HREF="#Play with the [time, mind]-bending perspective yourself">
                                          Play with the [time, mind]-bending perspective yourself</a>
</ul>
<BR>


<HR>
<A id="Key [results, comments]"> </a>
        <H3>Key [results, comments]</h3>

Standard & Poor's index of stock market prices for 500 large capitalisation companies (SP500) from 1872 through 2020 is shown in the semi-log plot below.  Two "eyeballed" linear trend lines are shown for the periods [1872-1926, 1926-2020].  <BR>
<BR>
<IMG SRC="[#=; backtrack ;=#]economics, markets/SP500/multi-fractal/SP500 TradingView eyeballed trends for (1872-1926) and (1926-2020).png" WIDTH=90%  NAME="SP500 eyeballed trends"></a><BR>
<BR>
<BR>


<HR>
<A id="Play with the [time, mind]-bending perspective yourself"> </a>
        <H3>Play with the [time, mind]-bending perspective yourself</h3>
.

Download data : 

Trading View data : 
Do NOT use existing graphs - just doubles the work
https://www.tradingview.com/ ->  click on "ssearch markets here" enter desired symbol
	-> Advanced chart -> New format  -> 



//	All manually-provided constants for del[Min, Max]_<sym>10Y will become inaccurate with time!!
// ONLY time.periods [3M, 6M, 1Y, 5Y] work.  
// time.periods [1D, 5D, 1M, ALL] do NOT work - I haven't manually provided values from charts.
// there are some errors in my manually [read, record] of the 5Y time-periods
// additionally, this Pine Script was thrown together in a day, no rigorous testing

// exchange rates are shown by darker colors, interest rates lighter similar colors
// China - green, Euro - purple, Great Britain - blue,  Japan - orange   (you can see this in the4 code below!) 
// stable rates :  [JP10Y, CN10Y]
//		https://www.tradingview.com/x/OXFvIi7I/
// policy-manipulated rates :  [TNX, EU10Y, GB10Y]  
//		https://www.tradingview.com/x/V4LOppCz/

// at some future point: 
//		more factors will be added
//		a Multiple Linear Regression (Lasso) will be done for more aqccurate results



// https://www.tradingview.com/pine-script-docs/en/v4/appendix/HOWTOs.html#count-bars-in-a-dataset
// Find the highest and lowest values for the entire dataset
// 20Mar2021 Howell - adapt this for viewable data

// 20Sep2022 WARNING!!  
// PineScript fails at providing functions that work over the full length of the visible stock period.  
//		One cannot accurately determine the start time bar
//		functions like [big, small]est below give WRONG results!!  - best to hand-craft answers

biggest(series,size) =>
	max =  0.0
	for j = 0 to size
		if series[j] > max 
			max := series[j]
	max

smalest(series,size) =>
	min =  100000.  
	for j = size to 0
		if series[j] < min 
			min := series[j]
	min



//+-----+
// Setup - data specifics for this script
// 25Sep2022 "lingua franca" approach, using USA [interest, GDP] rates and [oil imports/GDP, ] as basis
// 21Sep2022 WARNING!  
// hand-crafted off chart, typed in!!  To read the values : 
//		set params like this for ?[the maximum, a given]? time.period, example CNYUSD 
//		comment out section below for specific del[Min, Max]_CN10Y  
//			now delMin_CN10Y = 0.,  delMax_CN10Y = 1.
//		enter [min, max] values shown on graph for the given time.period of : 
//			intDiff_CN10Y	= (v_TNX - v_CN10Y - delMin_CN10Y)/(delMax_CN10Y - delMin_CN10Y)
//								= (v_TNX - v_CN10Y)
//								= del_CN10Y
//		comment out line plot(x_CNYUSD, ....
//		uncomment   line plot(intDiff_CN10Y, ...
// Now, read [min, max] of intDiff_CN10Y = del[Min, Max]_CN10Y for time.periods [3M, 6M, 1Y, 5Y]  
// YES - this is STUPID work, but only if PineScript could do well...


v_USOIL = security("TVC:USOIL", timeframe.period, close)
USOIL_detrend =  v_USOIL /  pow(10, -1.6684 + (0.00291 * yrFrac))

// 21Sep2022 eyeballed averages from TradingView charts
//		not terribly useful, as all script plots go to an un-named axis where they share the same scale
//		it is best to arrange for all script plots to have the same [range, average] 
//			that way all plots will scale [min, max] the same as each other, 
//			and the same scale (visually) as plots that are not part of the script.

avg_INRUSD    =   0.01731   
delMin_IN10Y  =  -2.49478
delMax_IN10Y  =   0.98706  
constCoeff    =   0.0004  


// avg_<ctry>USD - note that time.periods [1D, 5D, 1M, All] are NOT included and those timescales don't work
//      time.periods [3M, 6M, 1Y, 5Y] do work
// current estimates eyeballed from graph 24Sep2022 (no regression yet!)
// note that constCoeff  doesn't vary by much!

// doesn't even need this - except 5Y time.period, but leave it at that
//if			(timeframe.period == "60")		// 3 months  
//	avg_INRUSD    :=   0.007264   
//else if	(timeframe.period == "120")	    // 6 months 
//	avg_INRUSD    :=   0.007264  
//else if	(timeframe.period == "D")		// 1 year 
//	avg_INRUSD    :=   0.007264  
//else if	(timeframe.period == "W")		// 5 years
//	avg_INRUSD    :=   0.007264  

//+-----------------------------------------------------------------+
//+-----------------------------------------------------------------+
// Code adapted from my previous PineScript, only using one symbol!
//		simple search (same case!) replace CN with OR[CA, EU, JP] in this section ONLY  

v_TNX   = security("TVC:TNX",   timeframe.period, close)
v_IN10Y = security("TVC:CN10Y", timeframe.period, close)		// 01Jul2002-24Sep2022 

intDiff_IN10Y   =   v_TNX - v_IN10Y
intRatio_IN10Y  =  (v_TNX - v_IN10Y - delMin_IN10Y)/(delMax_IN10Y - delMin_IN10Y)

// 21Sep2022 need regression for each currency to add in oil price effect
//		for now, just guess
// 21Sep2022 eyeballed averages from TradingView charts
//		not terribly useful, as all script plots go to an un-named axis where they share the same scale
//		it is best to arrange for all script plots to have the same [range, average] 
//			that way all plots will scale [min, max] the same as each other, 
//			and the same scale (visually) as plots that are not part of the script.

// use the maximum time.period (i.e. 5Y) to visually fit the [actual, estimate] echange rate
oilCoeff    =   -0.003  
intCoeff    =   -0.003  

x_INRUSD  =  avg_INRUSD + (oilCoeff * USOIL_detrend)  +  (intCoeff * intRatio_IN10Y) + constCoeff


// standard named colors : 
// https://www.tradingview.com/pine-script-reference/v5/#var_color{dot}black
// "see also" list of named colors
// 	color.[black, silver, gray, white, red, purple, fuchsia, green, lime, olive, yellow, navy, blue, teal, aqua, orange]

// 21Sep2022 is there some way to plot against the corresponding currency exchange rate axis?

// Initially, use a separate axis for the plot(x_INRUSD), then adjust [oil, int] Coeff for incomplete "fit" 
// uncomment this line when determining del[Min, Max]_<country>10Y, comment out afterwords 

//plot(intDiff_IN10Y, color=color.purple,  linewidth=1, title="d_IN10Y")		// green

// Next, put plot(x_INRUSD) on the same axis as the exchange rate  
// AFTER determining the del[Min, Max]_<country>10Y in the step above, comment out that line
// uncomment this line to proceed : 

plot(x_INRUSD, color=color.green, linewidth=1, title="d_IN10Y")		// green






17Sep2020 initial posting<BR>
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