FOURIER TRANSFORM RMS ENERGY
link: http://tos.mx/1Wkl4HtDESCRIPTION
This indicator is an attempt to look at the energy present in the market's price action by looking at the RMS (root mean squared) energy shared between four harmonic fourier transformations of the CLOSE price series.
It does this by calculating the Fourier transform approximation of the 1st harmonic (the length parameter defines half a wavelength, so that the default value of 64 is actually looking at a wave 128 bars in length) along with the 3rd, 5th, and 7th harmonics. The RMS energy in these waves is then calculated for lengths of L, L/2, L/4, and L/6. These lengths are shown as vertical dashed lines on the chart for ease of reference. The RMS energy of the four waves is summed, and the portion of that energy possessed by each of the waves is plotted.
In keeping with my love of physics, the longest wavelengths are red, followed by orange, green, and the shortest is blue. This is really the only way the colors make any sense to my poor head.
USAGE
when reading this indicator, note when the red line has the highest position. That indicates that the long-term wave (1st harmonic) has the bulk of the energy in the Fourier decomposition. Conversely if the blue line has the greatest value, the price movements have generally been short term but dramatic. If either of the other lines, orange or green are showing energy, fluctuations in the middle are more likely.
I use this to determine whether I should expect to be in a trade for a short time (measured in bars) or a long time.
Code:
####################################################
#
# FOURIER TRANSFORM DECOMPOSITION
# RMS ENERGY FOR 1st, 3rd, 5th, and 7th Harmonics
#
# A guage of market instability and flutter
#
# by mashume for the usethinkscript.com community
#
# 2022.03.28
#
# Released the MIT License as open source
# (c) mashume 2022
#
####################################################
declare lower;
declare once_per_bar;
def pi = Double.Pi;
input n = 64;
script ReX_k {
input k = 0;
input n = 64;
def return_value = fold i = 0 to n - 1 with value = 0 do value + close[i] * Cos(2 * Double.Pi * k * i / n);
plot ReX_k = return_value;
};
script ImX_k {
input k = 0;
input n = 64;
def return_value = fold j = 0 to n - 1 with value = 0 do value + close[j] * Sin(2 * Double.Pi * k * j / n);
plot ImX_k = -return_value;
};
script ReX {
input k = 0;
input n = 64;
def return_value =
if (k != 0 and k != (n / 2))
then 2 * ReX_k(k, n) / n
else if k == 0
then ReX_k(k, n) / n
else if k == n / 2
then ReX_k(k, n) / n
else 0;
plot ReX = return_value;
};
script ImX {
input k = 0;
input n = 64;
plot ImX_value = -2 * ImX_k(k, n) / n;
};
script x {
input i = 1;
input k = 0;
input n = 64;
def sum1 = fold a = 0 to n / 2 with value = 0.0 do value + ReX(k, n) * Cos(2 * Double.Pi * k * (n - a) / n);
def sum2 = fold b = 0 to n / 2 with value2 = 0.0 do value2 + ImX(k, n) * Sin(2 * Double.Pi * k * (n - b)/ n);
plot x = sum1;
};
def curve_1 = x(i = 0, k = 1, n = n);
def curve_2 = x(i = 0, k = 3, n = n);
def curve_3 = x(i = 0, k = 5, n = n);
def curve_4 = x(i = 0, k = 7, n = n);
def d = 2 * n;
def c1_mean = Average(curve_1, d);
def c1_rms = sqrt(fold i1 = 0 to d with ms1 = 0 do ms1 + sqr(curve_1[i1] - c1_mean));
def c2_mean = Average(curve_2, floor(d / 2));
def c2_rms = sqrt(fold i2 = 0 to floor(d / 2) with ms2 = 0 do ms2 + sqr(curve_2[i2] - c2_mean));
def c3_mean = Average(curve_3, floor(d / 4));
def c3_rms = sqrt(fold i3 = 0 to floor(d / 4) with ms3 = 0 do ms3 + sqr(curve_3[i3] - c3_mean));
def c4_mean = Average(curve_4, floor(d / 6));
def c4_rms = sqrt(fold i4 = 0 to floor(d / 6) with ms4 = 0 do ms4 + sqr(curve_4[i4] - c4_mean));
def bar = barNumber();
AddVerticalLine(visible = bar == highestAll(bar) - d, "2n", color.red);
AddVerticalLine(visible = bar == round(highestAll(bar) - (d / 2), 0), "2n / 3", color.orange);
AddVerticalLine(visible = bar == round(highestAll(bar) - (d / 4), 0), "2n / 4", color.green);
AddVerticalLine(visible = bar == round(highestAll(bar) - (d / 6), 0), "2n / 6", color.cyan);
def dist_sum = c1_rms + c2_rms * 4 + c3_rms * 8 + c4_rms * 16;
plot FirstHarmonicPercent = c1_rms / dist_sum;
plot ThirdHarmonicPercent = (c2_rms / dist_sum) * 4;
plot FifthHarmonicPercent = (c3_rms / dist_sum) * 8;
plot SeventhHarmonicPercent = (c4_rms / dist_sum) * 16;
FirstHarmonicPercent.setDefaultColor(color.red);
ThirdHarmonicPercent.setDefaultColor(color.orange);
FifthHarmonicPercent.setDefaultColor(color.green);
SeventhHarmonicPercent.setDefaultColor(color.cyan);EYE CANDY AND DESCRIPTION
This is not investment advice.Several new indicators are included in this screen shot. But I'm lazy and only did one write up. You can find the other threads somewhere on usethinkscript.com
A
The LINEAR REGRESSION CENTERLINE EXCURSION indicator shows a clear enter signal which lasts nicely through the bulk of the upward movement.
B
The PRICE ACTION within LINEAR REGRESSION CHANNEL indicator shows a squeeze and a bounce off the lower line which corresponds nicely with a move upward in the price chart.
C
The LINEAR REGRESSION CENTERLINE EXCURSION indicator shows a good short signal, though the signal does not last as long as the downward trend.
D
Fourier RMS shows an increase in short term energy as a proportion of the total energy (the blue line rises and the red falls).
E
Fourier RMS shows a dramatic decrease in the short term (blue) line and a distinct rise in the long term (red).
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The signals look pretty good so far, and the trade targets are getting solid, but I've been thinking about a way to make them more generalizable. They are best on tick charts for futures so far.
