// This source code is subject to the terms of the Mozilla Public License 2.0
// © Yaseen Khalil
// @version=5
// Defining as indicator, overlay on chart, assigning maximum line count // to 500
indicator("Multinomial Retrogression Projection (MRP)", overlay = true, max_lines_count = 500)
// SETTINGS
// User inputs to define the length or period, the projection, and the // degree of the multinomial retrogression.
length = input.int(100, minval = 0)
extrapolate = input.int(10, minval = 0)
degree = input.int(3, 'Polynomial Degree', minval = 0, maxval = 8)
src = input(close)
lock = input(false, 'Lock Forecast')
// Style to define the color and width of the MRP line
up_css = input.color(#0cb51a, 'Upward Color', group = 'Style')
dn_css = input.color(#ff1100, 'Downward Color', group = 'Style')
ex_css = input.color(#ff5d00, 'Extrapolation Color', group = 'Style')
width = input(1, 'Width', group = 'Style')
// Fill lines array
// Creating a new array, type line
var lines = array.new_line(0)
// Checking if current bar is first bar in the barset. Repeating as new // bar is set.
if barstate.isfirst
for i = -extrapolate to length-1
array.push(lines, line.new(na, na, na, na))
//Designing the matrix & partially solving the system
// Setting n to the current bar index
n = bar_index
// Assigning variables to new matrix object, type float
var design = matrix.new<float>(0, 0)
var response = matrix.new<float>(0, 0)
// Checking if current bar is first bar in barset. Developing loop that // iterates through each degree, starting from 0 up to the specified // degree. // Initializing a new array named 'column' to store floating-point // values that will be initially empty.
// Creating a loop through each element in the range from 0 to the // length //of the array minus 1.
if barstate.isfirst
for i = 0 to degree
column = array.new_float(0)
//Pushing the result of raising j to the power of i.
for j = 0 to length-1
array.push(column, math.pow(j,i))
//Adding the column array as a new column to the design matrix.
matrix.add_col(design, i, column)
// calculating the inverse of the product of the changed position of the // 'design' matrix and the 'design' matrix itself and assigning it to // variable 'a'. // Then calculating the product of 'a' and the changed position of the // 'design' matrix and assigning it to variable 'b
var a = matrix.inv(matrix.mult(matrix.transpose(design), design))
var b = matrix.mult(a, matrix.transpose(design))
//Getting response matrix and computing rolling polynomial retrogression
// Now we initialize the variables 'pass', 'coefficients', 'x', and // 'forecast' with default values
var pass = 1
var matrix<float> coefficients = na
var x = -extrapolate
var float forecast = na
// Checking if the current bar state is the last one. Checking if 'pass' // is true. If yes, we will initialize an array 'price' to store float // values.
if barstate.islast
if pass
prices = array.new_float(0)
// Looping through each element in the 'src' array and adding each
// element of 'src' array to the 'prices' array.
for i = 0 to length-1
array.push(prices, src[i])
// Adding the 'prices' array as a new column to the 'response' matrix at // index 0 and calculating coefficients by multiplying matrix 'b' with // matrix 'response'
matrix.add_col(response, 0, prices)
coefficients := matrix.mult(b, response)
// Initializing 'y1' variable as 'na' and 'idx' as 0
float y1 = na
idx = 0
// Looping through -extrapolate to length-1.
for i = -extrapolate to length-1
y2 = 0.
// Calculating 'y2' using multinomial retrogression based on 'i' and
// 'coefficients'
for j = 0 to degree
y2 += math.pow(i, j)*matrix.get(coefficients, j, 0)
if idx == 0
forecast := y2
// Here we set the line attributes.
// Set 'css' variable based on the comparison of 'y2' and 'y1'.
// Then Update line positions, colors, and width.
css = y2 < y1 ? up_css : dn_css
get_line = array.get(lines, idx)
line.set_xy1(get_line, n - i + 1, y1)
line.set_xy2(get_line, n - i, y2)
line.set_color(get_line, i <= 0 ? ex_css : css)
line.set_width(get_line, width)
// Updating 'y1' with 'y2' value and increment 'idx' by 1
y1 := y2
idx += 1
// Setting 'pass' to 0 if 'lock' is true
if lock
pass := 0
// Resetting 'y2' and reducing 'x' if 'pass' is false
else
y2 = 0.
x -= 1
// Now, we calculate the forecast for extrapolation - 'y2' for // projection based on 'x' and 'coefficients'
for j = 0 to degree
y2 += math.pow(x, j)*matrix.get(coefficients, j, 0)
forecast := y2
// Finally, we plot the forecasted values if 'pass' is 0, else plot 'na'
plot(pass == 0 ? forecast : na, 'Extrapolation'
, color = ex_css
, offset = extrapolate
, linewidth = width)
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Now, let’s check out how well it back tests!
