Logistic Growth Curves to BTC/USD

[bb113]

I want to fit this simple curve to the bitcoin price history and forecast into the future using a mcmc script I have:

Code:

y = a/(1+exp((b - x)/c ) ) + sigma
a=asymptote
b=Time to half max
c=Rate constant (time between 37% and 63% max)
sigma= Average Residual deviation from curve (due to bubbles, etc)

So how long out should I forecast? How much will the price deviate from its "true value" on average over that time (eg $10 dollars)

I realize this is a very simple model but it is superior to the exponential curves everyone likes.

[pretendo]

Theoretically price will be immanentized at a difference, equal to the market interest rate (time value) if that is what you're asking.

[mobodick]

I want to fit this simple curve to the bitcoin price history and forecast into the future using a mcmc script I have:

Code:

y = a/(1+exp((b - x)/c ) ) + sigma
a=asymptote
b=Time to half max
c=Rate constant (time between 37% and 63% max)
sigma= Average Residual deviation from curve (due to bubbles, etc)

So how long out should I forecast? How much will the price deviate from its "true value" on average over that time (eg $10 dollars)

I realize this is a very simple model but it is superior to the exponential curves everyone likes.

Seems like i beat you to it
https://bitcointalk.org/index.php?topic=113725.0

But what i did was slightly simpler. I didn't break down the formula as much as you did.
I noticed a pattern and projected a simple y=x^1/z curve against it.
z was somewhere between 1 and 2 and if i remember correctly it was about 1.8 (but it may have been 1.3, it was very late that night ).

[mobodick]

I want to fit this simple curve to the bitcoin price history and forecast into the future using a mcmc script I have:

Code:

y = a/(1+exp((b - x)/c ) ) + sigma
a=asymptote
b=Time to half max
c=Rate constant (time between 37% and 63% max)
sigma= Average Residual deviation from curve (due to bubbles, etc)

So how long out should I forecast? How much will the price deviate from its "true value" on average over that time (eg $10 dollars)

I realize this is a very simple model but it is superior to the exponential curves everyone likes.

Also, i think that a formula like yours cannot predict the mean price.
Bitcoin seems realy weird in this respect as all the action seems to be projected on top of a curve and not around it.
Mean price and top price would require more complex formulas.