Here is my prediction for the coming month:
The plot shows the Bitstamp prices from Nov/2013 to Jan/2014 (purple) and estimated lower and upper bounds for Feb/2014 (green). I claim that, in any 1-hour interval in the coming month, the Bitstamp price will be within the two green lines above, with 95% probability.
For example, I claim that on Feb/22 the price will be between 300 USD and 2200 USD with 95% probability.
(Note that this is
not the same thing as saying that the entire price plot will stay in that region for the whole month with 95% probability.)
This prediction is based on the simple "log Brownian" model that I described a while ago. Namely, it assumes that the price change from one 1-hour interval to the next, in log scale, is a normal random variable that is independent of the previous history.
More precisely let P(i) be the weighted mean transaction price in the 1-hourinterval number i. Let Z(i) be log_10(P(i)). The model assumes that
Z(i+1) = Z(i) + C*RAND(i)
where the factors RAND(i) are independent random variabls with zero mean, unit deviation, and Gaussian distribution. Therefore, for any n > 0,
Z(i+n) = Z(i) + C*sqrt(n)*RAND(i,n)
where factors RAND(i,n) are again random (but
not independent) variables with zero mean, unit deviation, and Gaussian distribution.
Analysis of the Bitstamp prices from Sep/2013 to Jan/2014 yields 0.00964 as the best fit for the parameter C.
Since 95% of the probability of the Gaussian distribution is within 2 deviations of the mean, the model implies that, n steps in the future,
the value Z(i+n) will be within the values
Zmin(i,n) = Z(i) - 2*C*sqrt(n) and
Zmax(i,n) = Z(i) + 2*C*sqrt(n)
with 95% probability, where Z(i) is the current (last known) price. The green lines are these two bounds, converted back to linear scale (Pmin(i,n) = 10**Zmin(i,n), etc.)
More specifically, according to the model, at any specific 1-hour interval i+n in the future, the log price Z(i+n) will be
below Zmin(i,n) with 2.5% probability;
between Zmin(i,n) and the current price Z(i) with 47.5% probability;
between the current price Z(i) and Zmax(i,n) with 47.5% probability;
above Zmax(i,n) with 2.5% probability.
Note that, by this model, the future prices P(i+n) may be on either side of the current price (red line) with equal probability, even though the inverse log mapping yields a much wider range above than below.
Of course this model is quite rudimentary and basically useless for traders. There may be more sophisticated models, but I doubt that they can yield better predictions.
(The Brownian model is visibly inadequate for small n, since the log price increments from one interval to the next do not have a Gaussian distribution. As a consequence, the 2*sigma interval Zmin(i,n) to Zmax(i,n) contains somewhat less than 95% of the probability. However, by the Law of Large Numbers the distribution becomes almost Gaussian after a few hours. )
(before people ask: no, a model with a linear "historical trend" term Z(i+n) = Z(i) + T*n + C*sqrt(n)*RAND(i,n) does not seem appropriate, and its predictions for the next month would not be significantly different.)
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