Thread by @DeFi_initiate

Is there periodicity in the price of #bitcoin? I'm glad you asked. I have distilled the answer to a single chart using Fourier transform on the de-trended data (power law). Chart shows the magnitude of periodic components. Highlighted peaks: 2.11, 4.06 and 5.08 years.

The 4-year component corresponds to the halving cycle, and the 2-year one seems to be its lower harmonic. The 5-year component is intriguing and it's something I haven't seen discussed before - needs further examination.

As you can see, the annual component is insignificant.

Here is what the halving cycle looks like. The grey dots represent individual values and the red line is their average across the 4-year cycle. The cycle is normalized into 200 steps. Values are log10 of residual price (after removing the long-term power law trend).

Prices on the trendline show up as 0 on this chart (log 1 = 0). Individual values range from -0.64 to 1.21, corresponding to a range of 0.23 to 16.32 trend multipliers. Average values range from -0.39 to 0.57, corresponding to a range of 0.41 to 3.74 trend multipliers.

A trend multiplier of 3 means that the price is 3 times that of the trendline value. A trend multiplier of 0.5 means that the price is oen half of the trendline value. The logarithm of these values are shown on the chart (0.48 and -0.30 in this example).

The red (average) line shows a very strong cyclic pattern: price tends to peak 38% into the halving cycle, then drops until the 70% point. After this, it's essentially flat (against the rising trend) until shortly (6%) after the halving. This is perfectly symmetrical behaviour.

The flat price level is 0.5 (10^-0.3), and the peak is at 3.74 (10^0.57). These are average trend multipliers and there is a lot of individual variation. As described already, 0.5 means half of the trend price and 3.74 means 3.74 times the trend price.

I have just posted the latest (and most significant) update of this model:

https://twitter.com/DeFi_initiate/status/1487837760324964354