The following plots are based on historical data of bitcoin and some data analysis methods.
If we take the logarithm of the bitcoin price and the logarithm of the time, the data seems to follow a linear trend, as seen in the plot below. A linear function is fit, the parameters are shown in the plot itself.
It is possible to plot exactly the same data but in linear time. Such a plot is shown below, and the equation of the fit describing the conversion rate in linear time is
USD/BTC = [(t - 2009-Jan-03)/(1 day)]5.7e+00 × 2.9e-17 × USD/BTC
By extending the fit into the future it is possible to get an estimation of the future of bitcoin. This is shown below. This plot is commonly known as "rainbow plot".
For ease of read, it is possible to reverse the logarithm in the y axis to get the data in the units of the conersion rate. This is shown below.
Here is a detail in the years to come:
By substracting the fit to the conversion rate (in logarithmic units) it is possible to observe the deviations of bitcoin from the average evolution to study its volatility:
Ignoring the time variable and plotting this data in a histogram it looks like this:
We can show the same data in a violin plot, where it is easier to observe te differences in each halving cycle. This plot is shown below.
As seen in the previous plots, after every halving the bitcoin gets more stable, i.e. less fluctuations. For those who like to exploit the volatility for short- and mid-term trading, this is bad news. We can still expect a volatility of about a ×2 ÷2 with respect to the mean price for the current halving era nhalving=4.
We can overlay some statistics like the maximum, minimum, 25% and 75% quantiles on the price evolution of bitcoin:
Last updated 2025-Feb-23.
Source code