By transforming the bitcoin price history into log-log space and performing quantile
regressions, we obtain a family of regression lines ("quantiles" or "percentiles").
Each line in log-log space corresponds to a power law curve when transformed back to
lin-lin space.
For example, the "50 percentile" (or "median") curve lies above the bitcoin price half
of the time. Similarly, the "0.1 percentile" curve lies above the bitcoin price only
0.1 percent of the time, and below it 99.9 percent of the time. This curve represents
the support level.
Note: The regression lines have slightly different slopes. If extrapolated too
far into the future, they will eventually intersect! This is a limitation of the Quantile
Model, as it does not fully capture the underlying nature of the bitcoin price.
For the previous 4-year cycles, the price data is first transformed into "quantile
level" data. We obtain values ranging from 0 to 1, depending on which quantile curve each
price point corresponds to. Typically the values are above 0.9 near the cycle top, and
0–0.7 when 1–2 years away from the top.
The transformed cycles are then shifted forward by 12, 8 or 4 years, so that they
coincide with the current cycle, from the beginning of 2024 to the beginning of 2028.
Finally, the "quantile level" data is transformed back into dollar prices, by
interpolating between the closest quantile curves. This yields price estimates for the
current 4-year cycle, based on previous cycles.
The "Decay Channel" is defined by an upper and a lower bound. The price at the cycle
tops is approximately equal to the upper bound curve, and the price rarely drops below
the lower bound curve.
The lower bound is the 1 percentile, and the upper bound is the 66 percentile multiplied
by an exponential decay function that converges to 1.
For the previous 4-year cycles, the price data is first transformed into normalized
values ranging from 0 to 1, depending on the relative level within the "Decay Channel".
The transformed cycles are then shifted forward by 12, 8 or 4 years, so that they
coincide with the current cycle, from the beginning of 2024 to the beginning of 2028.
Finally, the normalized values are transformed back into dollar prices, by interpolating
between the upper and lower bound curves. This yields price estimates for the current
4-year cycle, based on previous cycles.
This is a simplified power law formula. It uses round numbers that are easy to
remember, yet it remains remarkably precise:
price = 0.01 × age 5.7
...where age is in years since 2009-01-03 (now 16.32 years),
and price is in dollars. The current value is
$82k, and the change is
+78 per day.
Note that in the current cycle, this curve closely resembles the "50 percentile" (or
"median"). Their slopes are only slightly different.
Dr. Giovanni Santostasi's trend curve is a power law. The formula appears to be:
price ≈ 0.01185 × age 5.693808
...where age is in years since 2009-01-03 (now 16.32 years),
and price is in dollars. The current value is
$95k, and the change is
+91 per day.
bitcoin.powerlaw.live
The curve from Dr. Giovanni Santostasi's "full model" is based on an underlying power
law. But it is multiplied by a function that is approximately 1 half of the time and >1
the remaining half of the time. This multiplicative function mimics the cycle tops that
occur every 4 years with diminishing relative magnitude.
The current value is $99k, and the change is
+646 per day.
bitcoin.powerlaw.live
