Bitcoin rainbow chart model

// This Pine Script® code is subject to the terms of the Mozilla Public License 2.0 at https://mozilla.org/MPL/2.0/
// © edgeornot
//@version=6
indicator("Bitcoin Rainbow: with vs without hindsight [Edge or Not]", shorttitle = "Rainbow hindsight test", overlay = true,
     max_polylines_count = 20, max_bars_back = 5000)

// ─── Inputs ─────────────────────────────────────────────────────────────────────────────
showHonest    = input.bool(true,  "Bands without hindsight (fit on past bars only)", group = "Show")
showHindsight = input.bool(true,  "Bands with hindsight (one fit on all bars)",      group = "Show")
minBars       = input.int(1000, "Bars before the honest fit starts", minval = 100, group = "Fit")
stepBars      = input.int(5,    "Hindsight bands: draw every N bars", minval = 1, maxval = 30, group = "Fit")
showTable     = input.bool(true, "Show current band table", group = "Show")
fitStart      = input.time(timestamp("2012-12-01T00:00:00"), "Fit start date (earlier bars ignored)", group = "Fit",
     tooltip = "Default matches the Edge or Not live chart and test (Bitstamp data from Dec 2012). Popular rainbow charts often start in 2010-2011.")

// ─── Model: log10(price) = a + b * log10(days since genesis block), 9 bands by residual z ─
GENESIS = timestamp("UTC", 2009, 1, 3, 0, 0)
var array<float> Z = array.from(-2.25, -1.75, -1.25, -0.75, -0.25, 0.25, 0.75, 1.25, 1.75, 2.25)
var array<color> COL = array.from(#2b3a98, #3570d0, #36aecb, #37c48a, #9fd24a, #f0cf3a, #f39b37, #ec6436, #d63737)
var array<string> NAMES = array.from("Fire sale", "Buy", "Accumulate", "Still cheap", "Fair", "Hold", "Is this a bubble?", "Sell", "Maximum bubble")

if not timeframe.isdaily
    runtime.error("Use a daily chart of BTCUSD (for example BITSTAMP:BTCUSD).")

days = (time - GENESIS) / 86400000.0
x = math.log10(math.max(days, 1))
y = math.log10(close)

// running sums of all bars BEFORE the current one -> the honest fit never sees the current or future bars
var float n = 0.0
var float sx = 0.0
var float sy = 0.0
var float sxx = 0.0
var float sxy = 0.0
var float syy = 0.0

fit(float _n, float _sx, float _sy, float _sxx, float _sxy, float _syy) =>
    sxxC = _sxx - _sx * _sx / _n
    sxyC = _sxy - _sx * _sy / _n
    syyC = _syy - _sy * _sy / _n
    b = sxyC / sxxC
    a = (_sy - b * _sx) / _n
    sig = math.sqrt(math.max(syyC - b * sxyC, 0) / (_n - 2))
    [a, b, sig]

bandOf(float z) =>
    int k = 1
    for i = 1 to 8
        if z > Z.get(i)
            k += 1
    k

inFit = time >= fitStart

float ha = na
float hb = na
float hs = na
if inFit and n >= minBars
    [a0, b0, s0] = fit(n, sx, sy, sxx, sxy, syy)
    ha := a0
    hb := b0
    hs := s0

honestEdge(int k) => showHonest and not na(ha) ? math.pow(10, ha + hb * x + Z.get(k) * hs) : na

p0 = plot(honestEdge(0), "Honest edge 0", color.new(COL.get(0), 60), display = display.pane)
p1 = plot(honestEdge(1), "Honest edge 1", color.new(COL.get(0), 60), display = display.pane)
p2 = plot(honestEdge(2), "Honest edge 2", color.new(COL.get(1), 60), display = display.pane)
p3 = plot(honestEdge(3), "Honest edge 3", color.new(COL.get(2), 60), display = display.pane)
p4 = plot(honestEdge(4), "Honest edge 4", color.new(COL.get(3), 60), display = display.pane)
p5 = plot(honestEdge(5), "Honest edge 5", color.new(COL.get(4), 60), display = display.pane)
p6 = plot(honestEdge(6), "Honest edge 6", color.new(COL.get(5), 60), display = display.pane)
p7 = plot(honestEdge(7), "Honest edge 7", color.new(COL.get(6), 60), display = display.pane)
p8 = plot(honestEdge(8), "Honest edge 8", color.new(COL.get(7), 60), display = display.pane)
p9 = plot(honestEdge(9), "Honest edge 9", color.new(COL.get(8), 60), display = display.pane)
fill(p0, p1, color.new(COL.get(0), 78))
fill(p1, p2, color.new(COL.get(1), 78))
fill(p2, p3, color.new(COL.get(2), 78))
fill(p3, p4, color.new(COL.get(3), 78))
fill(p4, p5, color.new(COL.get(4), 78))
fill(p5, p6, color.new(COL.get(5), 78))
fill(p6, p7, color.new(COL.get(6), 78))
fill(p7, p8, color.new(COL.get(7), 78))
fill(p8, p9, color.new(COL.get(8), 78))

// add the current bar to the sums only AFTER using them
if inFit
    n += 1
    sx += x
    sy += y
    sxx += x * x
    sxy += x * y
    syy += y * y

// keep x and time of every bar for the hindsight drawing on the last bar
var array<float> xs = array.new<float>()
var array<int> ts = array.new<int>()
if inFit
    xs.push(x)
    ts.push(time)

if barstate.islast and n > 3
    [fa, fb, fs] = fit(n, sx, sy, sxx, sxy, syy)
    if showHindsight
        for k = 0 to 8
            // sample every stepBars-th bar plus the last one, so the right edge of each band is vertical
            idx = array.new<int>()
            for i = 0 to xs.size() - 1 by stepBars
                idx.push(i)
            if idx.last() != xs.size() - 1
                idx.push(xs.size() - 1)
            pts = array.new<chart.point>()
            for j = 0 to idx.size() - 1
                i = idx.get(j)
                pts.push(chart.point.from_time(ts.get(i), math.pow(10, fa + fb * xs.get(i) + Z.get(k + 1) * fs)))
            for j = idx.size() - 1 to 0
                i = idx.get(j)
                pts.push(chart.point.from_time(ts.get(i), math.pow(10, fa + fb * xs.get(i) + Z.get(k) * fs)))
            polyline.new(pts, closed = true, xloc = xloc.bar_time, line_color = color.new(COL.get(k), 100), fill_color = color.new(COL.get(k), 88))
    if showTable
        zH = (y - (fa + fb * x)) / fs
        string honestTxt = "n/a"
        if not na(ha)
            zO = (y - (ha + hb * x)) / hs
            kO = bandOf(zO)
            honestTxt := str.tostring(kO) + " - " + NAMES.get(kO - 1)
        kH = bandOf(zH)
        tb = table.new(position.top_right, 2, 4, bgcolor = color.new(#0e1117, 10), border_color = color.new(color.gray, 70), border_width = 1)
        tb.cell(0, 0, "Band today", text_color = color.white)
        tb.cell(1, 0, "1 = cheapest, 9 = most expensive", text_color = color.gray)
        tb.cell(0, 1, "With hindsight", text_color = color.white)
        tb.cell(1, 1, str.tostring(kH) + " - " + NAMES.get(kH - 1), text_color = COL.get(kH - 1))
        tb.cell(0, 2, "Without hindsight", text_color = color.white)
        tb.cell(1, 2, honestTxt, text_color = color.white)
        tb.cell(0, 3, "Edge or Not", text_color = #ffb020)
        tb.cell(1, 3, "Hindsight bands fit past tops by construction", text_color = color.gray)