I want to fit this simple curve to the bitcoin price history and forecast into the future using a mcmc script I have:
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=113725.0But 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
).