Ah, distinctly I remember; it was in the bleak December,
And each dipping streak of ember brought the price through the floor;
And the sick and sad uncertain trending of that crimson curtain
Thrilled me - filled me with fantastic terrors never felt before.

I checked it and it seems really helpful.  I just learned for example that if you use a humidor, you should not stick your cigar into the same opening where you poured the water in.

(But what is a "humidor" in Quality Technical Analysis jargon?  A Fibonacci fractal type of choo choo train?)

I would further conjecture that Chinese rallying bulls are active mostly between evening and midnight 23:00, when they go to bed. Then the crashing bears take over and stay up until 02:00 01:00 am.

Unless they are all pump-and-dump werebears (bulls that turn into bears at the hour when the full moon would be at zenith if the moon was full).

EDIT: that's China's local time of course, which I believe is 9 8 hours ahead of UTC.  So 00:00 would be 15:00 16:00 UTC and 02:00 am would be 17:00 18:00 UTC, on the previous date.

EDIT: Fixed local times; China's time is UTC+08:00 not UTC+09:00

It seems that rallies and crashes and blips and blops only occur when Huobi is active, which is only when the Chinese are awake and not having New Year's dim sum with their families.

And there are many bitcoin chart/statistics sites that do not even mention them...

BTC-China currently is not a market. I can't figure out what it is.

Bitcoin may not be a Ponzi schema itself, but her is how you could run a Ponzi schema with bitcoin:

1, open an exchange.

2. Post yourself a bid at 10% over market price, say 1100$ instead of 1000$.

3. First client rushes in, sells 1 BTC. You credit his account with 1100$, warn him that withdrawal may take a couple weeks.

4. You sell that BTC at another exchange for 1000$.

5. Second client comes and sells 2 BTC. You credit him 2200$ and warn of delays.

6. You sell those two BTC for 2000$, now you have 3000$

7. You pay the first client 1100$,  still have 1900$ left.

8. Third client comes in, sells 4 BTC, ...

You guess the rest.  Like any Ponzi, it works while the clientele keeps expanding (but you may have to increase the spread, say 20%). Eventually you run pout of fresh clients and the thing collapses.  

That paper claims that Bitcoin prices must have memory because the square of the log-price increments shows medium-term autocorrelation.

My interpretation is that the trade volume has a natural time scale of a couple of hours (traders stick around for a while once they "come in").

In turn, the trade volume modulates the standard deviation (rms magnitude) of the increments.

So, there is no memory in the price per se.  Rather, the real "market clock" (that counts BTCs traded, not time) turns at variable speed, and has some inertia.

That is, if twice as many transactions as usual happened in one hour, that has the same effect on price as two hours of trade at normal levels.

Those variations in trading volume per hour may have the effect of "mandelbrotizing" the price charts, I don't know.

However I do not think that fractal analysis can produce much better predicitions that the simple log-Brownian model, unless it can somehow predict the changes in  volume.

But there are other variables that should be considered first,because theh have a larg impact on volume - like, what are the sleep hours in China, when will banks open after New Years, etc.

Thanks!  Now I got it...

But does that really encourage volume?

It seems that it encourages posting an order a penny above or below the best opposite offer, and waiting for the other guy to make the move.

Which, by the way, is what seems to be happening at BTC-China right now...

Thanks!  But I still do not understand BTC-China's reward scheme...

What is a "market maker"?  How does the new BTC-China "market maker reward" work?  Has it been tested in other markets before?

From BTC-China's English-language page: "With the most buyers and sellers, BTC China has the highest trading volumes in China, and offers the most liquidity of all exchanges." Really?

It looks like Huobi and OKCoin will see even less volume today than they did yesterday (well under 10 kBTC), so the price will probably stay where it is.  

This could be a chance for the non-Chinese exchanges to retake control of the market.  But their volume too is very low, probably still lower than the Chinese.  MtGOX has some  volume but most of of it may be fake, since it is fairly regular, does not sleep at night, and started suddenly around 13:00 UTC yesterday (Jan/31); it could be an improved version of the ping-pong robot.  

Which makes me ask again the question: volume and price changes, which is the cause and which is the effect?  Or are they like chicken and egg?

For my part, so far I have seen convincing evidence of fake trade at Mt.GOX, and now at BTC-China.

The first time I paid attention to Bitcoins was when Rick Falkvinge (founder of the first Pirate Party) tweeted a glowing endorsement, announcing that he was investing all his savings into Bitcoins.  And the first time I heard abot Mt.GOX was around Dec/01, when Rick denounced them for replaying the same transactions over and over while the price was actually falling through the floor. (If it was a bug, it was a very convenient one...)

People have claimed that most of Huobi's volume is fake, but I am not convinced yet. Note that a transaction, whether by hand or by robot, is not fake if it entails an exchange of money and bitcoins between two competing traders.

Huobi has lots of robot trade and thinly sliced orders, but I have yet to see convincing evidence of fake transactions.  For one thing, their volume is nearly zero after midnight, lower at holidays, etc. (Mt.GOX's "ping-pong" robot, in contrast, ran continuously for days at a steady rate, stopping and starting abruptly.)

(BTW, Rick later retracted his endorsement of Bitcoin, after he realized that transactions are not at all anonymous and untraceable, as bitcoiners used to claim.)

Well, considering the amount of trade they have, their order books must be huge, and must change very fast.

Since there are many sites (like bitcoinwisdom) that request that data every few seconds, their decision to truncate
the list is understndable.

EDIT: Perhaps they can be convinced to provide a coarse sampling of the full volume/price curve in real-time,
for the chart sites, and a full snapshot of the whole book every hour or so, for statisticians and such.

Is that a fact (say, deduced from analysis of the blockchain)?

When one wants to buy or sell something vauable, it is usually better to do it through a market or broker.  Otherwise one may waste a lot of time looking for the partner, and  the price may  end up being well above or below the market's price - leaving one of the sides quite frustrated.

So, who would want to trade bitcoins in private, and why?

On most of the exchanges that I monitor, the BTC trade volume for Friday Jan/31 was extremely low.

Huobi (15.26 kBTC) and BTC-China (1.17 kBTC) were the most affected; both had about 1/6 of the volume of last Tuesday's  (Jan/28).   For the non-Chinese exchanges, that ratio was around 1/3.

The decrease at Chinese exchanges is easy to understand, since Jan/31 is the Chinese new Year, and AFAIK people have several days of vacations before and/of after it.  But the fall at the non-Chinese sites is puzzling, since they are usually very active on Fridays. 

This "experiment" may show how much China infuences other exchanges.   Except for MtGOX, the prices in all exchanges are obviously tied by arbitrage.  So perhaps (less volume in China) --> (less price variation) --> (less volume at all exchanges).  Or perhaps arbitrage trading is a large part of the volume; then (less volume in China) --> (less price variation in China) --> (less arbitrage trade).

OKCoin fell "only" to 1/3 compared to Tuesday.  That is another hint that its clientele includes a significant non-Chinese component (the people who keeep trading while the Chinese are all asleep).

We all know about BTC-China's rogue robot that traded ~40,000 BTC in 2.5 hours, 40 BTC at a time, around Jan/30 18:00 UTC (Jan/31 02:00am in China) .  But there are other weird things going on at that site.  For example, its order book now has an offer to sell ~100 BTC @ 4872.38 CNY, and a bid for ~175 BTC @ 4872.37 CNY -- and those two guys just sit there, nose-to-nose, without moving a penny. 

Like some other exchanges, BTC-China also has a stream of small trades within that narrow spread, moslty below 40 BTC. I suspect that it is a robot trading with itself, to cover up the lack of real transactions and/or to inflate their volume.

Once in a while, there is a transaction that changes the price: arbitrage, perhaps?

The crypto-coin community urgently needs to define professional ethics standards for exchanges, and set up an international entity that will audit them and rate them for compliance.

Daily volumes of BTC trade to/from USD and other national currencies (in kBTC):


               !   Wed !   Thu !    Fri !    Sat !    Sun !    Mon !    Tue !   Wed !   Thu !   Fri !                     
  EXCHANGE     ! 01/22 ! 01/23 !  01/24 !  01/25 !  01/26 !  01/27 !  01/28 ! 01/29 ! 01/30 ! 01/31 ! Currencies considered

  Bitstamp     |  8.31 |  7.40 |  15.78 |   8.70 |   9.70 |  25.19 |  20.04 |  7.04 | 13.13 |  7.73 | USD                 
  BTC-e        | 22.32 |  8.53 |  15.27 |   9.34 |  10.38 |  21.02 |  16.82 |  6.53 | 12.54 |  4.65 | USD,EUR,RUR         
  BitFinEx     |  2.97 |  2.83 |  10.99 |   4.62 |   7.88 |  15.63 |  13.62 |  3.87 |  8.18 |  3.91 | USD                 
  MtGOX        |  5.51 |  2.23 |   7.38 |   9.52 |  16.11 |  10.02 |  11.82 |  7.21 |  6.60 |  4.45 | USD,EUR,GBP,AUD,JPY 
  Bitcoin.DE   |  0.69 |  0.42 |   0.52 |   0.30 |   0.34 |   0.60 |   0.49 |  0.33 |  0.47 |  0.35 | EUR                 
  Kraken       |  0.25 |  0.19 |   0.46 |   0.19 |   0.24 |   0.63 |   0.54 |  0.24 |  0.37 |  0.20 | EUR                 
  CaVirtEx     |  0.15 |  0.17 |   0.41 |   0.33 |   0.10 |   0.40 |   0.22 |  0.21 |  0.25 |  0.24 | CAD                 
  CampBX       |  0.05 |  0.08 |   0.13 |   0.04 |   0.05 |   0.13 |   0.20 |  0.07 |  0.06 |  0.05 | USD                 
  Crypto-Trade |   .   |  0.01 |   0.01 |    .   |    .   |    .   |   0.01 |   .   |  0.01 |   .   | USD                 

  SUBTOTAL     | 40.25 | 21.86 |  50.95 |  33.04 |  44.80 |  73.62 |  63.76 | 25.50 | 41.61 | 21.58 |                     

  Huobi        | 25.81 | 25.67 |  89.25 |  58.16 |  91.31 |  63.13 |  92.88 | 32.14 | 29.27 | 15.26 | CNY                 
  OKCoin       | 15.88 | 16.50 |  34.01 |  26.33 |  31.40 |  35.41 |  52.37 | 29.11 | 18.56 | 17.11 | CNY                 
  BTC-China    |  1.62 |  2.01 |   6.82 |   3.04 |   5.55 |   4.43 |   6.45 |  1.94 |  1.99 |  1.17 | CNY (NOTE 1)

  SUBTOTAL     | 43.31 | 44.18 | 130.08 |  87.53 | 128.26 | 102.97 | 151.70 | 63.19 | 49.82 | 33.54 |                     

  TOTAL        | 83.56 | 66.04 | 181.03 | 120.57 | 173.06 | 176.59 | 215.46 | 88.69 | 91.43 | 55.12 |                     



All numbers were collected by hand from the site http://bitcoinwisdom.com. Beware of possible errors.

For each exchange, the numbers include only the trade volume to/from the currencies listed in the rightmost column. The BTC-e volumes now include retroactively also exchanges to EUR and RUR (together about 1 kBTC/day or less).  Trade between BTC and other cryptocoins, such as LiteCoin, is NOT included.

Coinbase volume is not available, neither at Bitcoinwisdom nor at Bitcoincharts, but they are said to use Bitstamp for currency conversion.

Dates on the header line are UTC. Specifically, "01/15" means "from 01/15 00:00:00 UTC to 01/15 23:59:59 UTC". (Beware that Bitcoinwisdom uses your local time, so the date may appear to be off by 1 day.  For example, if you are 2 hours west of Greenwich, it may show "01/14 22:00" when the UTC time is "01/15 00:00".)

(NOTE 1) On 2014-01-30, BTC-China had a burst of extremely fast, regular and atypical transactions, all with similar amounts (a few tens of BTC) and prices (~4836 CNY), adding up to about 41,050 BTC.  The burst started suddenly around 17:00 UTC and and stopped suddenly around 19:30 UTC. Presumably those transactions were made by a faulty robot trading against itself or some other robot, and did not represent actual exchange of money and bitcoins between distinct individuals. Therefore those anomalous transactions were subtracted from the BTC-China volume for Jan/30.

PS. Besides the fat tails for small n, there is another conspicuous feature of the data that the log-Brownian model does not capture.

Looking at a plot of the increments Z(i+1)-Z(i) as a function of i, it seems evident that the the typical magnitude of the increments changes markedly but slowly over a time scale of several hours.   That is, there are periods when the increments are quite large, other periods when they are quite small; even though in both cases they seem to be equally random and independent.  (These slow  variations in the standard deviation may perhaps account for the long tails of the global distribution).

The periods when the increments are larger seem to correlate (not surprisingly) with the periods when the trade volume per hour is larger.   Thus the following model may be more acurate:

  Z(i+1) + Z(i) + B*V(i)*RAND(i)

where V(i) is the trade volume in the sampling interval i, and B is another constant (that measures how much the price is disturbed, in the rms average sense, whenever one BTC gets traded).  Note that if the volumes V(i) are nearly constant then this is the same as the simpler model, with C = B*V(i).

If this hunch is correct, then one should perhaps describe the price changes in terms of a "volume clock", instead of the usual time clock.

That is, let's define the "accumulated volume" as the total amount of BTC traded between some fixed reference time in the past to each subsequent time.  Let's write Q(v) for the price when the accumulated is v, and let Y(v) be log_10(Q(v)).  Then the log-Brownian model in "volume clock" predicts that

  Y(v+w) = Y(v) + E*sqrt(w)*RAND(v,w)

where E is a constant, and RAND(v,w) are random variables (not independent) with zero-mean, unit-variance Gaussian distribution.

This model may yield tighter confidence intervals for the future price Q(v+w).  However, it does not predict the price range after n hours in the future, but rather after an additional w bitcoins will have been traded.   

Basically, that is it, yes.

My number hacking so far is telling me that the market does not care for the past history of the price, not even over the past hour; it only considers the current price and increases or decreases it by a random percentage amount.   If that is true, no analysis, no matter how sophisticated, will be able to provide substantially better forecasts than those stupid green lines derived from the log-Brownian model.

You say that an experienced bitcoin trader would have guessed "300-2200 in 20 days" without doing any math.  Possibly.  It may be that, after staring at the charts for years, those traders developed a subconscious "calculator" to make such predictions.  If they got the right intuition, their guesses should roughly match my green lines.

I am sure that there exist better prediction methods (say, that provide "X% confidence" intervals that are narrower than those of the Brownian model but still  contain the predicted value at least X% of the time in the long run).  I am a complete amateur in this field.

Indeed, as you say, a fat tail is evident in the distribution of the one-step increments Z(i+1) - Z(i).  However, both theory and data tell me that a Gaussian distribution, with linearly increasing variance,  works well for larger steps Z(i+n) - Z(i) when n is ~20 hours or more.  See this plot:



This is a series of crude histograms of the quantity R(i,n) = (Z(i+n) - Z(i))/sqrt(n), sampled from the reference datafile (Bitstamp 2013-09-01 to 2014-01-30, 1 hour intervals) with various values of i,  tallied separately for each stride n.  The "n" axis runs across the middle of the plot, with n=1 at the upper left edge and increasing down to the right. The "R" axis is perpendicular to it, with R=0 in the middle.  The histogram for each n is normalized to unit sum.

The long fat tails and narrower peak of the distribution for small n is quite evident.  However, as n increases, the tails and sharp peak seem to disappear, as one would expect from the Law of Large Numbers.

Actually, I am not really sure about the tails because the number of samples in each histogram also gets smaller when n increases.  Perhaps the following plot is more convincing:



In this plot, the horizontal axis is the stride n (hours), and the vertical axis is the log increment D(i,n) = Z(i+n) - Z(i)  (not divided by sqrt(n)).

The light brown crosses on each vertical line are a sample of differences D(i,n) with same value of n and various values of i.  Each green dot is the mean of the sample increments D(i,n) with same n.  Each red dot is the standard deviation of those increments, computed assuming that their expected value is 0 (rather than the empirical mean shown by the green dot).  The histogram-like lines are the 2.5% and 97.5% percentiles of those samples. 

The orange curve is the deviation sigma(n) = C*sqrt(n) of D(i,n) predicted by the log-Brownian model.  The purple curves are the ±2*sigma(n) bounds above and below D=0.

According to this plot, for n ~15 hours or more, the empirical deviation (red dots) is very close to the model C*sqrt(n) (orange line).  For n ~30 hours or more, the curves ± 2*C*sqrt(n) folow the empirical 2.5%-97.5% percentiles as accurately as one could expect. 

The model clearly fails for smaller n; in particular, over the span of 5 hours, large swings occur more often than would be expected in a log-Brownian model.   Therefore, I  was too confident in my prediction for tomorrow; but with a bit of luck, I should be safe for the rest of the month. 

The slightly ascending green line means that there is a consistent increasing trend in that sample.  That trend also manifests itself in the growing gap between the empirical 2.5% percentile and the -2*sigma(n) curve.  However, if I had used only the last 2 months of data for the analysis, instead of the last 5, the trend would have been decreasing - and stronger.  That is one of the reasons why I did not include a trend term.

I have looked for correlations between successive increments (Z(i) - Z(i-1)  and Z(i+1)-Z(i)), but did not see anything clearly significant.  If there is such a correlation, it must be very subtle, and should be quickly "forgotten" after a few time steps.

Note that real stock prices are influenced by "real world" factors such as demand for the product, raw material prices, etc.  Those factors vary according to their own nature in various time scales, that range from decades to hours.  Maybe it is those factors that provide the long-term correlations characteristic of fractal signals?

In contrast, Bitcoin's price is almost entirely set by speculation; while external news may trigger changes, they do not directly determine the magnitude of those changes. ("How many billion dollars were subtracted from Bitcoin's future usage in e-commerce payments because of Shrem's arrest?")

So perhaps Bitcoin's price is indeed better described by a log-Brownian model than by a fractal process...