Learn · Part 2 of 3
The same mathematics that finds rhythms in sound, light, climate and the stars, applied to price. And how to tell a strong cycle from a passing wave.
Fig. 2 · A spectrum. Red bars stand clear of what random movement produces (grey). Black bars do not.
01
A prism splits white light into its colours. Spectral analysis does the same for any series that changes over time: it splits the series into waves of different lengths and tells you how strong each one is.
The idea goes back to Joseph Fourier, who showed in the early 1800s that almost any pattern can be written as a sum of simple waves. That is Hurst’s principle of summation, written in mathematics.
02
Spectral analysis is everyday science. It finds the notes in a recording, the rhythm in a heartbeat, the seasons and longer swings in climate records, and the pulse of distant stars.
In each field the same question comes first: is this rhythm real, or would chance produce something like it?
03
First the slow trend is set aside, because a trend is not a cycle and would swamp the result. Then the remaining movement is measured against every cycle length in a range.
For each length the spectrum gives three things: how big the wave is, how it is timed (where it is in its rise and fall today) and how consistently it has repeated.
04
A cycle has to repeat several times in the data before it can be measured with any confidence. One or two swings are just a shape, not a rhythm.
The shortest cycle you can see is two bars long. And a strong cycle can blur into lengths close to it, so two cycles very close in length are often one rhythm counted twice.
05
Feed random numbers into a spectrum and you still get peaks. Markets add a twist: price has memory, so random price paths drift in long, wave-like swings that look convincing on a chart.
Serious science handles this by comparing every peak with what a random series of the same character would produce. Only peaks that stand clearly above that background count. Climate scientists and astronomers do this as a matter of course. Most cycle tools for traders do not.
Applied to price, only the clearest cycles make the grade, and a good tool shows you which ones they are.
06
Real cycles do not keep perfect time. Their length and size drift, exactly as Hurst’s principle of variation says. So the spectrum is measured on a recent window of data and measured again as new bars arrive.
07
Hurst gives the practical tools: troughs, nesting, the FLD and its targets. Spectral analysis gives the measurement: which cycles are really in this market now, how strong they are, and whether they beat chance.
Put together, Hurst’s tools stop running on textbook averages and start running on measured, tested cycles.
Next: why measured beats average.
Part 3: Why settle for average? →