Quadratic Regression Slope [DW]

// This source code is subject to the terms of the Mozilla Public License 2.0 at https://mozilla.org/MPL/2.0/
// © DonovanWall

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// ------------------------------------------------------------------------------------------------
// Original author:  DonovanWall
// Original title:   Quadratic Regression Slope [DW]
// Licence:          MPL-2.0 (the header above is the original notice, kept verbatim)
// Pine version:     4
// Fetched:          2026-10-12
// Ported to FloScript by FloSignals; modifications under MPL-2.0.
// Converter:        @flosignals/floscript 0.1.0, strict mode, score 100/100
// ------------------------------------------------------------------------------------------------
//@floscript=1
//@version=5
// Converted by the FloScript converter from a Pine-compatible v4 source.

indicator(title="Quadratic Regression Slope [DW]", shorttitle="QRS [DW]", overlay=false)
//by Donovan Wall

//This is a study geared toward identifying price trends using Quadratic regression.

//Quadratic regression is the process of finding the equation of a parabola that best fits the set of data being analyzed.

//In this study, first a quadratic regression curve is calculated, then the slope of the curve is calculated and plotted.

//Custom bar colors are included. The color scheme is based on whether the slope is positive or negative, and whether it is increasing or decreasing.

//-----------------------------------------------------------------------------------------------------------------------------------------------------------------
//Updates:

// -> Migrated to v4.
// -> Updated QRS function for improved performance.
// -> Added an offset parameter to the script, which will base current value on offset values of the extrapolated QR curve.
// -> Included some experimental signal processing procedures:
//    - Added an option to normalize the oscillator scale using RMS.
//    - Added an optional compression algorithm to the script. This can be used to reduce transients (short duration, high amplitude values) by a specified level of intensity.
// -> Updated color scheme.

//-----------------------------------------------------------------------------------------------------------------------------------------------------------------
//Functions
//-----------------------------------------------------------------------------------------------------------------------------------------------------------------

//Quadratic Regression Slope
QRS(y, t, o) =>
    var x = 1
    x := x + 1
    b0 = math.sum(x, t)
    b1 = math.sum(math.pow(x, 2), t)
    b2 = math.sum(math.pow(x, 3), t)
    b3 = math.sum(math.pow(x, 4), t)
    c0 = math.sum(y, t)
    c1 = math.sum(x * y, t)
    c2 = math.sum(math.pow(x, 2) * y, t)
    a0 = ((b1 * b3 - math.pow(b2, 2)) * (c0 * b2 - c1 * b1) - (b0 * b2 - math.pow(b1, 2)) * (c1 * b3 - c2 * b2)) / ((b1 * b3 - math.pow(b2, 2)) * (t * b2 - b0 * b1) - (b0 * b2 - math.pow(b1, 2)) * (b0 * b3 - b1 * b2))
    a1 = (c0 * b2 - c1 * b1 - (t * b2 - b0 * b1) * a0) / (b0 * b2 - math.pow(b1, 2))
    a2 = (c0 - t * a0 - b0 * a1) / b1
    qr = a0 + a1 * (x + o) + a2 * math.pow(x + o, 2)
    QRS = qr - (na(qr[1]) ? qr : nz(qr[1]))
    QRS

//Highest High Function
hi(x, reset) =>
    var hi = 0.0
    hi := reset or x > hi ? x : hi
    hi

//Cumulative Mean Function
c_mean(y) =>
    var x = 0
    x := x + 1
    var y_sum = 0.0
    y_sum := y_sum + y
    c_mean = y_sum / x
    c_mean

//RMS Function
RMS(x, t) =>
    math.sqrt(ta.sma(math.pow(x, 2), t))

//-----------------------------------------------------------------------------------------------------------------------------------------------------------------
//Inputs
//-----------------------------------------------------------------------------------------------------------------------------------------------------------------

//Source
src = input(defval=close, title="Source")

//Sampling Period
per = input.int(defval=89, minval=1, title="Sampling Period")

//Offset
off = input(defval=0, title="Offset")

//Smoothing Period
smper = input.int(defval=2, minval=1, title="Smoothing Period")

//Normalization Toggle
norm = input(defval=false, title="Normalize Output Scale")

//Signal Compression Inputs
use_comp = input(defval=false, title="Use Compression")
comp_intensity = input.float(defval=90.0, minval=0, maxval=100, title="Compression Intensity (%)")
comp_thresh_type = input.string(defval="Auto", options=["Auto", "Custom"], title="Compression Threshold Type")
comp_ht_custom = input.float(defval=0.0, minval=0, title="Custom High Compression Threshold")
comp_lt_custom = input.float(defval=0.0, maxval=0, title="Custom Low Compression Threshold")

//-----------------------------------------------------------------------------------------------------------------------------------------------------------------
//Definitions
//-----------------------------------------------------------------------------------------------------------------------------------------------------------------

//QRS
qrs1 = QRS(src, per, off)

//RMS Normalization
rms = RMS(qrs1, per)
norm_qrs = qrs1 > 0 ? qrs1 / rms : qrs1 < 0 ? -math.abs(qrs1) / rms : 0

//Oscillator Selection
qrs2 = norm ? norm_qrs : qrs1

//Dichotomized QRS Values
qrs_pos = qrs2 > 0 ? qrs2 : 0
qrs_neg = qrs2 < 0 ? qrs2 : 0

//Compressor Thresholds
hi_qrs = hi(qrs_pos, ta.crossover(qrs2, 0))
lo_qrs = -hi(math.abs(qrs_neg), ta.crossunder(qrs2, 0))
comp_ht = comp_thresh_type == "Auto" ? c_mean(hi_qrs) : comp_ht_custom
comp_lt = comp_thresh_type == "Auto" ? c_mean(lo_qrs) : comp_lt_custom

//Transient Reduction
qrs = use_comp ? (qrs2 > comp_ht ? qrs2 - comp_intensity * (qrs2 - comp_ht) / 100 : qrs2 < comp_lt ? qrs2 + comp_intensity * (comp_lt - qrs2) / 100 : qrs2) : qrs2

//Colors
qcolor = qrs > 0 and qrs > qrs[1] ? #05ffa6 : qrs > 0 and qrs <= qrs[1] ? #00945f : qrs < 0 and qrs < qrs[1] ? #ff0a70 : qrs < 0 and qrs >= qrs[1] ? #990040 : #cccccc

//-----------------------------------------------------------------------------------------------------------------------------------------------------------------
//Outputs
//-----------------------------------------------------------------------------------------------------------------------------------------------------------------

//QRS
plot(qrs, color=qcolor, style=plot.style_columns, title="QRS")

//Thresholds
plot(use_comp ? comp_ht : na, color=color.new(#cccccc, 80), style=plot.style_circles, title="High Compression Threshold")
plot(use_comp ? comp_lt : na, color=color.new(#cccccc, 80), style=plot.style_circles, title="Low Compression Threshold")

//Bar Color
barcolor(qcolor)

This file is under the Mozilla Public License 2.0; it is a port of the original by DonovanWall, with the original licence header kept and the changes made for FloScript noted in the file.

• v22026-10-14

  Library refresh 2026-10-14

• v12026-10-12

  Library refresh 2026-10-12