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...

Chinese Slumber Method prediction for Sunday April 27

Prediction valid for: Sunday 2014-04-27, 19:00--19:59 UTC (not before, not after)
Huobi's predicted price: 2876 CNY
Bitstamp's predicted price: 471 USD





[ Plot legend ]

Today's data point was even weaker than yesterday's (S = 0.0076 W = 0.311), but we must use it anyway to define the new straight-line trend.  Namely, A + B*(d-d0), where d-d0 is the number of days since Apr/25, A = 2814 and B = +31.

The Bitstamp prediction, as usual, is the Huobi prediction divided by the currency conversion factor R, which was assumed to be 6.11 CNY/USD. It was 6.09 today and 6.05 yesterday; althhough those points had low weight, it seems best to use a value near them rather than the values observed before the crash (6.30, 6.28, 6.34, 6.27, 6.25, 6.26).
 
Checking the previous prediction

Prediction was posted on: Saturday 2014-04-26, 04:04 UTC
Prediction was valid for: Saturday 2014-04-26, 19:00--19:59 UTC (~15 hours later)

The Huobi's "same as yesterday" prediction was rather good:

Huobi's predicted price: 2814 CNY
Huobi's actual price (L+H)/2: 2845 CNY
Error: 31 CNY (~5 USD)

The Bitstamp prediction was way too low:

Bitstamp's predicted price: 447 USD
Bitstamp's actual price (L+H)/2: 467 USD
Error: 20 USD

That last prediction used the pre-crash value of R (6.29) instead of the post-crash one (6.05) to transfer from Huobi to Bitstamp.  Had we used R = 6.05, or the "same as yesterday" estimate for Bitstamp too, the prediction would have been 465 USD, only 2 USD off.
 
NOTE: "Be not simply good; be good for something." -- Thoreau

Huobi has not updated the "red lamp" notice on their home page since Apr/17.

Did BTC-China say anything about the PBoC's "clarification to the clarification"?

It would be interesting to know how and when the conversion was made.  (Presumably that happened after November/2013, so it would be about 3'000 -- 6'000 bitcoins.)
 
Posters in other threads who seem to be well-informed claim that Ulrich's bitcoins will surely be sold through public auctions, which is what the government must do with seized goods.  But it seems unlikely that they auctioned Stomp's coins, that would have been noted and widely reported.

Perhaps the federal agents considered bitcoin a currency, not goods, at the time?  Perhaps the coins had already been converted to cash by Stomp or "J" when they were arrested?

SecondMarket will not lose any money, no matter what the price does.  When an investor gives them money for N shares, they buy N/10 bitcoins at the current market price.  When the investor liquidates those N shares, they sell the N/10 bitcoins at current market price and give him that money.

If the price went down in the meantime, the investor takes the loss; if it went up, he takes the profit.  In any case, SecondMarket skims off the entry, maintenance, and exit fees.

SecondMarket could make even more money if they had a private source that would sell them bitcoins below market price. That difference in price would be their extra profit.

I did not "accuse" you, I thought you were connected to them, rather than just their customer. And I apologized immediately for the mistake.  So what?

This is insane.  What the media wrote about Neo & Bee has been confirmed beyond any reasonable doubt.  You insulted me because I believed those reports, insulted me because I asked about the background of a person being sought by the police -- and now you accuse me of a crime?  I am the bad guy in this story?

What is happening? Why are you so obsessed about me?  Is it strange for someone to be interested in knowing the details of an attempt to swindle an entire country?

I must ask again, are you a relative or close friend of Danny? I can't make sense of your posts otherwise...

(By the way, I am not interested on Danny's  current whereabouts - that is the police's job. I never asked where is his daughter; Danny himself said he left her in Cyprus.  And I am still interested in what he did before going to Cyprus.)

The Chinese are asking too, it seems.  from OKCoin's blog: https://www.okcoin.com/t-1008520.html

Found this in OKCoin's blog:

https://www.okcoin.com/t-1008522.html

That will not save the exchanges, but it may allow arbitrage to continue until the exchanges close.

I imagine that there are only a handful of professional traders doing arbitrage between China and the West. If so, they should have lots of money and would not need to deposit money very often, so they won't mind the inconvenience as long as there is a way to do it.

If the courier had a frequent schedule and served many clients, it would be essentially an unregistered money service.  I doubt that it would be tolerated, even if it were not serving a bitcoin exchange.

I suspect that the main worry of the government at this point is possible use of the CNY inut/output channels of bitcoin exchanges for money laudering, paying bribes, illegal trade, etc..  The money that they move is tiny by PBoC standards, but huge by police standards.

Chinese Slumber Method prediction for Saturday April 26

Prediction valid for: Saturday 2014-04-26, 19:00--19:59 UTC (not before, not after)
Huobi's predicted price: 2814 CNY
Bitstamp's predicted price: 447 USD





[ Plot legend ]

The fairly straight price trend that held for the last six Slumber Times was obviously broken.  Today's data point was rather weak (S = 0.0062 W = 0.469), but since it is the only point we have for the new trend (if any) we must use it as the basis of the trivial prediction, "tomorrow's price will be the same as today's".

The Bitstamp prediction, as usual, is the Huobi prediction divided by the currency conversion factor R, which was assumed to be 6.29 CNY/USD. It was 6.05 today, but the low weight W makes this value suspicious.  It was 6.30, 6.28, 6.34, 6.27, 6.25, 6.26 at the previous five Slumber Times.
 
Checking the previous prediction

Prediction was posted on: Thursday 2014-04-24, 22:03 UTC
Prediction was valid for: Friday 2014-04-25, 19:00--19:59 UTC (~21 hours later)

Huobi's predicted price: 3067 CNY
Huobi's actual price (L+H)/2: 2814 CNY
Error: 253 CNY (~40 USD)

Bitstamp's predicted price: 488 USD
Bitstamp's actual price (L+H)/2: 465 USD
Error: 23 USD
 
NOTE: "Anything that calls itself 'science' probably isn't."  -- John Searle

That is my understanding too.

Even if all "easy" deposit channels are cut off, I imagine that there will be ways to get money into the exchanges, e.g. taking cash to their offices.  Perhaps even after May 10.

Arbitrage seems to be a lucrative activity for those who have the skills and tools, so they have enough motivation and money to find a way.

There seems to be a May 10th deadline, not sure for what exactly:

Ridiculous. The only reason why most bitcoin crimes go unpunished and victims get no reparation is that bitcoin was appropriated by rabid "libertarians" who hate governments, law, regulations, and police.

The logical consequence of assuming that those things are evil is that "there are no criminals nor victims, only smart people and stupid people".

The invariable response of the "bitcoin community" to each new bitcoin scam or heist is "stupid victims, they should have blah blah blah."

Last time I looked, fiatleaks was a pretty looking animation that was quite meaningless and misleading. 

I posted my reply yesterday, look in my recent posts.

I can imagine two radical alternatives: cryptocurrencies issued and managed by (1) large private multinational companies or consortia (banks, insurance companies, retailers, google, facebook, ...)  or (2) national governments (USAcoin, BitEuro, RussiaCoin, etc.).

These cryptos would retain the idea of offline generation of address/key pairs, but junk all the other "features" of bitcoin (anonymity, decentralized management, independence from gov & banks, irrevocability, mining, limited number, deflation, ...).  Libertarians would hate them (and would hate (1) too), but for most consumers and retailers they may be even better than bitcoin.

By and large I don't believe in TA either.  But "tomorrow the weather will be like today" used to be a pretty good weather prediction method, 10-20 years ago. Meteorologists with satellites and supercomputers could barely get a few percent more accuracy than that.  (Now they may do much better, I don't know.) 

I suspect that piecewise extrapolation can do a little better than that trivial method, AT HUOBI, FOR MIDDLE-OF-NIGHT PRICES, because of very special circumstances in that exchange.  At some point I will tabulate and compare the two methods.  But I am afraid of what I might conclude then... 

Hear, hear!  Hope you are right!...

Is this interpretation confirmed by courts somewhere?

One possible complication is that bitcoins were virtually traded for dollars etc. inside MtGOX.  So if a client deposited 200$ when the BTC price was 10$, and traded traded traded until he had 50BTC and 600$ in his MtGOX's account -- are those 50BTC and 600$ his "property given to MrGOX for safekeeping", debts of MtGOX towards him, or just irrelevant numbers once displayed on a webpage?

I will ask Dilma to appoint me Minister of Bitcoin, and put the BCB (Central Blockchain of Brazil) under my authority.

If THAT news does not crash the price to zero, nothing will.