CYCLESX

Track 2 · Spectral analysis · Lesson 2.1 · 7 min

Waves and the spectrum

Any price line can be described as many simple waves added together. The spectrum is a chart of how much of each wave length is present. Its peaks are the cycles.

SHORT WAVE LONG WAVE ADDED TOGETHER: WHAT YOU SEE SHORTER LONGER THE SPECTRUM: ONE PEAK PER WAVE
Fig. 2.1 · Two waves add up to one line. The spectrum separates them again: one peak per wave.

Simple waves add up

A sine wave is the simplest repeating shape: it rises and falls smoothly with a fixed length and size. Add two of them with different lengths and you get a line that looks irregular, yet is entirely made of rhythm.

Price works the same way, with more waves, a trend and a good deal of noise on top.

The spectrum reverses the sum

Spectral analysis takes the finished line and asks: how much of each wave length went into it? The answer, plotted with length along the bottom and strength up the side, is the spectrum.

A wave length that is really present shows as a peak. Lengths that are not present stay low.

Longer waves look bigger

In markets, longer cycles usually move price further than short ones. The spectrum therefore tends to rise towards the long end even where no particular cycle stands out.

This is why a peak has to be judged against what is normal at its length, not just against its neighbours.

You need repetitions

To measure a wave reliably, the data must contain it several times. A 100-bar cycle needs several hundred bars of history; one or two repetitions are too easy to get by chance.

The window also sets how finely lengths can be told apart. A short window blurs neighbouring cycles into one broad peak.

The spectrum sees the whole window

A spectrum describes the window as a whole. A cycle that was strong early in the window and has since faded still shows a peak. A peak tells you a rhythm existed, not that it is still running today.

That is why the spectrum is the start of cycle analysis, not the end of it.

Reading a spectrum in four questions

  1. 1Where are the peaks? Each clear peak is a candidate cycle.
  2. 2How tall against their surroundings? A peak should stand well above what is normal at its length.
  3. 3How many repetitions in the window? Several, or the peak may be chance.
  4. 4Is it still active? Check recent behaviour before trusting a peak for a projection.