In the least squares method only the biggest values matter. So the shape of the curve in linear space would be defined based only on this year data. Which is not what we want. So using least squares in logarifmic space was the right way.
In that case
I'm probably not sure about "what we want" here. Note: I'm not arguing that we shouldn't do it like rpietila did, just that it isn't clear-cut.
We are trying to find an exponent curve that matches bitcoin growth for it's whole history. That curve will let us predict bitcoin future growth. But for it to work, some assumptions must hold:
i. Mechanics of bitcoin growth is viral: basically every 3 month each old user "infects" a new user. That causes the exponent.
ii. The rate of infection is constant, whether BTC worth 1c or 10K$, whether is it a crypto-geek infecting his friend or multi-billion hedge fund infecting it's competitor.
This is obviously a big simplification. Any model is simplification. The trick is to get complexity just right, to go between Scylla and Charybda. If the model is too simple, it's predictions will be too far off the mark. If it's too complex, we won't have enough data to setup it's parameters.
1.The simplest model: OP. IMO, it's too simple (I doubt the assumption ii) and, as result, too optimistic.
2. More complex: Zarathustra's model. Here he discards assumption ii, and draws a 4-segment line instead of 1 line. So the Scylla is better, but there is already a bit of Charybda: he lack enough data to draw the 4-th segment, since he draws by peaks and we don't know where the current peak is going to be. Maybe the better approach would be to use just 2 segments, with joint somwhere in 2011 and match them using least squares technique.
3. Even more complex: Staircase model. Discard both assumption. Instead take others.
i. Growth is viral: but it is not users that are infected, but markets. Geek market infects SR market, SR market infects amator speculators market etc. It causes "staircase" curve. Vertical part is filling up of the market, horysontal part - building of infrastructure for the next market.
ii. The rate of infection is different for each step and depends on relative size of markets, how long it takes to build infrastructure etc.
Unfortunately this model would be practically useless because of Charybda: we don't know all the required parameters.
So I would suggest improving rpietila's model: using least squares method, match (in log scale) either 2-segment line, or a log curve.
Anyone with experience of a proper math package?
