Bitcoin midterm slump and log linear price prediction model

Perhaps you have noticed bitcoin has taken a dive in recent weeks.  The question on everybody’s mind must then be “gosh, is this normal? From a historical context, is bitcoin OK?”

If we disregard all real world facts (which show the bitcoin network IS healthy, and the transaction malleability doesn’t represent any fundamental failure, much less a new risk to the network) and if we just stick to data, and math… my humble opinion would be “this behavior is nothing out of the ordinary for bitcoin;  we are seeing a price fluctuation very typical of historical data.”

I have constructed a log plot and fitted to two parameters, as I have done before, just to demonstrate that since bitcoin grows in powers of 10, (seemingly large) contemporary fluctuations may look alarming. This rests on the observation I and perhaps a few others have made, that the bitcoin price follows a log linear growth model, on average, according to what we may expect from the diffusion equation.

In the following chart, the blue dots represent base 10 logarithm of the price data since September 13, 2011. The orange line is the best fit line, allowing the price on day (1) to float and be fitted.  The vertical axis is the base ten log of the price, so you can get the price meant for vertical value “3” by computing 10^3 = 1,000 (all in USD).

fit PNG

You might compare this plot with the one I made months ago.

You can use my sheets to perform other types of fits if you wish to choose a particular value for the price on a particular day, or if feeling frisky, try to extract periodic trends.  

By taking the exponential of the log fit, we can “predict the bitcoin price into the future.”  Note: This does not really work.  But it’s interesting.  I decided to take the fit out to 1 year from today – what does the log linear fit say the price will be then, on February 20, 2015? For this we must look to day 1258 (that’s 893 + 365)…and the result is about 5 grand (the prediction is $4,943.89

future white

Just for fun, here is the log of the price with all axes blacked out and no trendline so you can see the raw (log) data for what it is.


Here is the raw price data in similar fashion, without compression via the logarithm:


I grabbed the daily weighted price from for selections “all data” and “auto” for resolution.  That resulted in a vector of 893 numbers – the bitcoin average price in dollars each day since September 13, 2011.   I had to erase a handful of “infinities” that came out of the raw data at bitcoincharts; there were perhaps ten such cells for which I manually put in reasonable values.  All of the infinities happened within the first 100 days of the series.

In general, these plots cannot be taken too seriously, although they have given me insight in the past.  If you have any questions, please feel free to contact me.  Cheerio.

Sheet and raw data:

data, pastebin

Note: the following link is to directly download my excel workbook. This link is not for the paranoid.  

future predict

Use solver; on sheet 2, minimize cell I4 by changing cells G2 and H2

Here is a github repo for doing stuff with discrete lists in mathematica Here’s the github repository:


You can follow my guide here also on how to extract frequencies from the data.  I use the more powerful Mathematica software for fourier analysis, but Excel can take fourier transforms as long as the length of the vector is a power of two.  So add zeros at the end.

Donations: 13xdMqkaVKkHKT3ZZx5ikAvQUEkzqpDkDb



The Bitcoin Price Model – Large Time Calculations of the Bitcoin Price



Just for a toy model, to start us off, I used excel to insist the log data is strictly linear, implying the price follows a perfect exponential curve.  We observe bitcoin hits $1000 on precisely….ok lets not get carried away.  The Price cannot be a pure exponential function of time – that seems to violate some economic conservation laws.  But these are still fun plots.  The source is an excel sheet which you can find here

A somewhat sophistocated model for the price of bitcoin based on diffusion

In a previous post I suggested that the log linear behavior of bitcoin was a trend that will continue and proposed a model by which this would operate.  Here is a gogle drive containing the mathematica code I wrote to investigate the matter.  These equations do support the long term log linear behavior and produce price curves which seem to match the behavior we have seen from bitcoin.

You will be able to manipulate a parameter controlling the effective bitcoin supply.

The rules I used to derive the formulas were:

1) the Bitcoin demand D(t) is proportional to the probability that somebody on earth has learned of Bitcoins existence.  This function is an exponential in t for small times

D(t) ~ exp[-t / to]

However the probability question has vastly distinct long time behavior.  The function that really represents the long term demand of bitcoin over time is closely related to the hyperbolic tangent 


This family of functions has the form

D(t) = 1 / ( 1 + exp[- t / t0] )

2) The Bitcoin supply is known in the short term to be proportional to t, but since the number of bitcoins generated per unit time halves every fixed amount of years, dictated by the protocol, I said we should model the supply as

S(t) = t * 2^(-t / t’)

Where t’ is in general a parameter that can be adjusted to dictate the effective supply of bitcoin as a function of time.

This incredibly simplistic model was in fact successful at generating the family of curves that the bitcoin price and its log seem to belong to.

Perhaps in the future more sophisticated models for the supply curve can be employed, since it seems clear the supply curve is responsible for the volatility.  See tables beneath:

Anyone who has mathematica ready to can run this code.  An animation can be generated as well as a dynamic plot you may manipulate.  A simple table of outputs for the price and log of the price is given in the above google drive as the supply parameter is swept.  You can observe the supply in the model has a strong influence on the price – many orders of magnitude in fact.  Below are some excerpts from the PDF and interactive mathematica program provided in the google drive, as well as the source code.






Demand[t_] := 1/(1 + Exp[-t/tp])
 Supply[t_] := t*2^(-t/th)
Slider[Dynamic[tp], {0, 29, .1}, ImageSize -> 1300], Dynamic[tp],
 "= propogation time tp" ,
 Slider[Dynamic[th], {0, 4, .1}], ImageSize -> 1300, Dynamic[th],
 "= effective bitcoin supply"}
 Plot[Demand[t]/Supply[t], {t, .0000001, 5}, ImageSize -> 500]]
 Plot[Log[Demand[t]/Supply[t]], {t, .0000001, 5}, ImageSize -> 500]]
 {Slider[Dynamic[tp], {0, 29, .1}, ImageSize -> 1300], Dynamic[tp],
 "= propogation time tp", Slider[Dynamic[th], {0, 2, .001}],
 ImageSize -> 1300, Dynamic[th], "= effective bitcoin supply"}
 Plot[Demand[t]/Supply[t], {t, .0000001, 5}, ImageSize -> 500]],
 Dynamic[Plot[Log[Demand[t]/Supply[t]], {t, .0000001, 5},
 ImageSize -> 500]]}*)

Donate Bitcoins
Want more of this?  I have a donate button.    Invest wisely and safely!
Donate Bitcoins