Topic: Wall Observer BTC/USD - Bitcoin price movement tracking & discussion - page 27996. (Read 26710240 times)

Explanation

its turning around now really...

The only thing that makes me doubt $7k bubble this summer/autumn is that this is the big one

this is gonna be the one who makes or break bitcoin

The feeling of a price explosion has almost slipped my mind. Much has changed since the last one. I'm guessing it'll take a big dollop of US inspiration to get the next one rolling.

It's very very very long overdue

I just wanna feel the moment of the next bull run

lol!

i banking on the youngsters doing a good job

i'm getting old guys....

 

Posting will surely accomplish that, right?

That's what all my models do, except I never use gaussians unless I need consistency with closed form options.  Can't tell you if it's standard.

Regarding EMH, for every Rijksbank prize winner who advocates some formulation, I can name 2 who will repudiate that formulation as obviously inconsistent with basic observations.  Use it every day, in order to do principled valuations, but give it no credence.

poeple we need to forget about 1 billion chinese poeple making us all rich beyond belief

and fouces on what really matters

making us all rich beyond belief

there comes a point where the market rises unexplained regardless of news. historically, the best time to buy is during genuine tragedy, even (especially) during serious wars. the day will come, when this market will rise regardless of china. something to do with offshore exchanges opening in USA and Europe, I suspect.

Happy days are here again why exactly? I really want to know. What has changed?

I think it's improbable that China is done fucking the world markets until it shoots its wad right in Bitstamp's butthole. We have at least 3 potential goxxings on our hands because Huobi, BTC China and OK Coin are all sketchy volume-faking exchanges with very limited and diminishing sources of deposits. It doesn't matter if it's their fault or the PBoC or someone else. These exchanges are likely going to wither and die, crash out or go offshore.  Markets will be rattled and you can either be in a position to profit, ride out the storm or get caught with your pants down.

China is a 50 ton battleship anchor on BTC price and will continue to be until the chain is broken. That doesn't make me happy, but pretending significant negative factors don't exist makes for poor investment strategy. So if there is something good that outweighs this Chinese clusterfuck, I'd love to hear about it, but don't tell me it isn't real or it's irrelevant.

Explanation

Thinking about this always makes me excited.

Atlas, Circle, Coinsetter, SecondMarket Exchange, Xapo, Buttercoin, and some others have raised more than $100 million + combined in investments.

When these companies launch, they are going to have to do some serious marketing to bring volume to their exchanges so they can start earning to break even on their investments.

I think when these guys start their marketing campaigns, the price and volume is going to skyrocket.

It will never conclude. Good thing it doesn't really matter. Hopefully, at some point, people will figure this out.

hehe, totally agree
We needed some very needed bullish posts

Same chart, just linear:



 

free the market free the world

bitcoin is gana be the money in the future

we all know this....

the network is perfect, and perfection is constantly being improved upon.

programmers know murphy's law "everything that can go wrong..." and they have programed that into the fucking code man


you know whatn i'm saying.


welcome to hollywood 2012 when the bits where free

for me china is done...

there banning it, srota wtv the F that means.....

idk why they let that 2 hour bitcoin documentary run on there tv b4 they SORTA banned it.

but wtv

the rest of the world is cheering for freedom and so am I!

Agreed with dnaleor & Adam, but not until the long-running ChinaFUD soap opera concludes.
This may be during May, but only when the global price has adjusted to reflect that CNY transfers to/from the China exchanges are severely and permanently crippled.

OK, it seems that I was using a definition of "log Brownian" that is not the standard one used in finance.

Indeed I was assuming that the increments D(i) = Z(i+1)-Z(i)  = log(P(i+1)/P(i)) were normal variables with zero mean, so that Z(i) would be a Brownian variable as it is usually defined in other areas - with no trend.  (Note that I am a prof of computer science, not economics!)

However, as you point out, by that definition the expected price E(P(i0+n)) would grow exponentially with n; which does not make sense in the trading context, where the "efficient market hypothesis" demands E(P(i0+n)) = P(i0).  (Or does it? See below.)

We agree at least that in a log-Brownian model the increments D(i) = Z(i+1)-Z(i)  = log(P(i+1)/P(i)) should be assumed to be independent random variables, yes?

The standard way to achieve E(P(i0+n)) = P(i0), in finance, seems to be: assume that the increments D(i) are Gaussian variables with slightly negative mean, mu = -sigma^2/2.  That is, one assumes a slight negative trend in the log-price Z(i) so that the broadening of the log-normal distribution of P(i0+n) as n increases preserves the mean P(i0).   Is that correct?

That assumption satisfies the "efficient market hypothesis", but implies (as you pointed out) that the price is slightly more likely to go down than to go up at each step.  Then Prob(P(i0+n) < P(i0)) increases with with the stride n.  Which seems weird too.

We can get rid of this weidness by assuming a probability distribution for D(i) such that E(D(i)) = 0, E(exp(D(i))) = 1.  It seems that these two conditions cannot be obtained with a Gaussian distribution, except in the limit when sigma → 0.  However, they can be achieved with other distributions that are symmetric about zero, especially if they have fatter tails than the Gaussian.  And, indeed, the most obvious deficiency of the log-Brownian model seems to be that, in real data, the distribution of the increments is not Gaussian.

If my math is correct, the distribution of the n-step increments too would satisfy both conditions: E(Z(i0+n)) = Z(i0), and E(P(i0+n)) = P(i0).  Moreover the distribution of Z(i0+n), being the convolution of n symmetric distributions, would be symmetric about Z(i0), implying that Prob(Z(i0+n) < Z(i0)) = 1/2, and hence Prob(P(i0+n) < P(i0)) = 1/2.

With these assumptions, even though the distribution of P(i0+n)/P(i0) approaches a log-normal distribution as n increases (by the central limit theorem), it remains sufficiently "log-abnormal" to satisfy those conditions (which a true log-normal distribution cannot achieve, it seems).

Perhaps you can tell me what would be a convenient "fat-tailed" symmetric distribution to assume for the increments D(i) that would satisfy both conditions.  (Perhaps a mixture of Gaussians with zero mean whose variance has log-normal distribution?  I would have a justification for that choice...)

Finally, about the "efficient market hypothesis": shouldn't it say that E(P(i0 + n)) = P(i0)*Q^n, where Q > 1 is the typical ROI factor of a generic investment per time step?  That is, if E(P(i0+n)) = X, then P(i0) should be less than X, otherwise other investments would be more profitable.

With that modification to the "efficient market hypothesis", the distribution of D(i) must satisfy E(exp(D(i)) = Q, not 1; and one can achieve that even with a zero-mean Gaussian if desired.  In that case one would have a legitimate log-Browninan model (with Gaussian increments) such that that E(Z(i0+n)) = Z(i0), E(P(i0+n)) = P(i0)*Q^n, and Prob(P(i0+n) < P(i0)) = 1/2.  Does this make sense?

EDIT: not sure whether the distribution must/may have fatter tails than a Gaussian.  Too sleepy to think now...