Bitcoin Forum

This is a long post and I beg you to bear with me. I have one question for you:

Can I predict the value of BTC/USD?

Lets please talk about a bit of theory here:
Is there a mathematical model to describe a chaotic system? Don't force it. The question is a trap. We must first define what IS a chaotic system. In science, a simple chaotic system can be described by a double pendulum. If one sets it in motion from an unknown angle, the trajectory will be totally different than when you start it from another one. The complexity of the system is enormous even after a few seconds; you can take your peek here (If it isn't visible click below to start it - at the time this was written forum wouldn't let gifs animate):
https://upload.wikimedia.org/wikipedia/commons/4/45/Double-compound-pendulum.gif
http://en.wikipedia.org/wiki/File:Double-compound-pendulum.gif

Now; lets make things simpler. Say we can set with a very good precision the initial conditions. We're now talking about a SIMPLE dynamic system here with fully determined initial conditions. Now pay attention: Even if you can set the initial conditions on such a system, small differences have a totally different outcome; so as the time goes by; your predictions are getting enormously difficult to be true, thus rendering the predictions useless. This system's behaviour is called "deterministic chaos" and was first observed by Edward Lorenz who defined it like this:

Chaos: When the present determines the future, but the approximate present does not approximately determine the future. ¹

Now; I need to get your attention a bit more:

Imagine an (easy) prediction of the USD/BTC trade value on MtGox within the next 5 minutes. This is a bit tricky as well. Can this model be defined as a "deterministic chaos" model? Do I see hands raising?

-Yes miss tell us:
-No it can't.
-Why do you believe so?
-Because I can read my MACD and RSI and EMAs and can predict the value.

OK. The above is a total BS and I can scientifically certify this. This is simply NOT happening. All the above BS are ways to eliminate errors (read: normalization) of an abnormal value trajectory. As much as you can read those and take the proper decision whether to buy or sell, there's also a great possibility of an average monkey can beat your odds and win more than you by randomly pushing buttons. ²

Do I see another hand raising?

-Yes sir, tell us:
-Yes it can.
-Why do you believe so?
-Because I know certain individuals that can control the market and at a specific timeframe I can control the initial conditions. THEN AND ONLY THEN I can predict the value for the next 5 mins without looking at anything and make a move on selling or buying.

True story. A deterministic chaos system (DCS for short) can be "settled" only under the above conditions. This means you have your pendulum and you have the ability to move it at will WHENEVER you feel comfortable. Then your system can be predictable. After that you can make money and be glad about you, be in a beautiful position of knowing such great movement "factors" of the "system".

The above are my scientific conclusions. I'm not claiming the non-false. If you think otherwise, please tell me your thoughts. I initially wanted to post it on the Wall Observer BTC/USD - Bitcoin price movement tracking & discussion (https://bitcointalk.org/index.php?topic=178336.64820;topicseen) but I thought it was a nice topic to start and maybe, it'll give people the chance to gather their odds before blindly jumping into trading.

Cheers.

¹Danforth, Christopher M. (April 2013). "Chaos in an Atmosphere Hanging on a Wall". Mathematics of Planet Earth 2013. Retrieved 4 April 2013.
²Article: http://www.ft.com/cms/s/0/abd15744-9793-11e2-b7ef-00144feabdc0.html

This should be a compulsory reading for any wanna-be trader who knows what the future holds. Would save them a lot of money.

The lowest points the double pendulum can reach is the same as a single pendulum of the same length.
The highest point is at the origin of the pendulum plus the length of the lower part of the arm.
The upper part of the arm always swings back and forth and can not flip over.

So while the overall system may be chaotic it can be predicted with specific constraints.

Great and erudite analysis of why all TA is utterly useless, unless you have inside knowledge of what the big movers are about to do or know news before others do.

Which is why financial markets have a preponderance of insider knowledge cheats and market manipulators, it's the only thing that gives you an edge.

Perhaps it is possible to learn about sentiments, meaning sometimes it is possible to have a good idea of how others are likely to react - but this is again at best marginal and can of course go horribly wrong.

Markets always bust after they boom.

What you're saying can be simplified to this:

The lowest value of USD/BTC is zero
The highest value of USD/BTC is the total capitalization/BTCs produced
The value can only go up and down (well, it can also be static for a while)

Again; the timeframe is of the essence. You lose any chance of prediction within a very short timeframe. Let me explain. Say you are an observer of a tiny piece of steam flowing into a sealed box. If you observe the trajectory for 2 sec you can predict with a relatively low possibility of being wrong where the H2O steam particle will be the next fraction of the second... After 2-3 seconds you may forget it.

Who said you'd have to predict the price with absolute certainty? It would be enough to predict it often enough s.t., given the amounts you chose to trade with, you are in total profitable.

I believe predicting price (with a substantial error rate, true) is possible because it is mainly a function of human (group) behavior, and there is nothing in principle that makes predicting such a system impossible, difficult as it may be.

You on the other hand seem to think it is inherently impossible to model markets, did I get that right? I hope you don't take your linked to article as evidence for that, because it's not about modeling markets, but that a random stock selection beats a capitalization weighted index (couldn't find the actual paper either, I'm going to guess it's not peer reviewed, but feel free to correct me if I'm wrong about that).

And your little Platonic dialogue about chaotic systems is rather useless in its generality: you could equally well ask "Can I predict the weather conditions 5 minutes from now". And we know the answer to that one: not perfectly, but given enough information to run the best models we have, with high probability you will be able to do so.

LOL!  ;D

1. There's no prediction with absolute certainty. That's what I wrote the article for.
2. We're saying the same thing, only in a different manner; as it may suit you best. :)
3. No you didn't get that right. Read again the 1st & last paragraph and come back.
4. I like Plato; he was my favorite Philosopher, so please accept my sincere apologies.

Interesting point of view though; thank you kindly for your comments.

The bust defines the boom.
tautology

As the pendulum has high and lows. The same thing.

This thread is burning a straw man.

Having a p value of less than 100% is different from being useless.
TA is less about being always right, and more about how much confidence you put in being right at any particular point.
How much you make when you are right, vs how much you lose when you aren't is what makes it valuable or not.
For example:
RP gave himself an 80% p value for that prediction.  He may be right or not, but either way it isn't going to be indicative of whether TA is useful of not, just whether that application of it worked well or didn't.

What you have here is an analogy and a theory.  Science uses data, so from that point RP's TA is more scientific than your criticism of it.
Markets aren't pendulums.

In any efficient market TA should yield zero edge over random chance.

That said, Bitcoin markets have demonstrated, time and again, startling examples of inefficiency.

The scientific way to settle this argument is to create 30 TA algos that backtest well, simulate them them for a year, and find out if there's statistical significance.

Thanks for your criticism. Let me please answer:

This is not a game of words and surely has no intention of being an informal fallacy based on misrepresentation of an opponent's position. If that's what you made out of it I'm truly very sorry. This was not my intention.

This article is based on a chaotic system modeling in order to define the possibilities to predict WITH CERTAINTY what will happen after a specific time frame. This thing cannot be happened and it's proven. It's a theory with scientific proof and thus (until someone presents something different that kills its validity) still valid.

Markets are looking a lot like pendulums. In fact, I'd add, a lot like triple or quadruple pendulums which in their very essence can be A LOT more chaotic than a double pendulum which I above mentioned. Therefore there cannot be a certain prediction about their next timeframe of existence.

If you can provide me with scientific data that defies what I wrote; I will be glad to rephrase and/or change my thesis. Until then... me and mr. Edward Lorenz here we stand.

I'd indulge you to take a look here:
http://en.wikipedia.org/wiki/Chaos_theory

Hint: You're aware of the urban myth that physicists are one of the most wanted jobs in Wall Street... aren't you?

Exactly! Statistically, this would offer a much better model, in order to make valid predictions. It's like narrowing down the specific movement factors of the pendulum and predicting timeframe by timeframe what will  happen. But this NEEDS HISTORICAL DATA (with certain similarities to the current conditions)! I do have a couple of ideas about it, but are a bit too crazy to be honest for me to start posting them on a public forum on the net... ;D

While chaotic systems are, well, chaotic, their trajectories often tend to evolve toward one of a number of attractors, at least temporarily.

While it is not in principle feasible to determine a trajectory of some dynamical variable p (say, price) as a function of time p(t) as you can for simpler systems, the case of chaos and attractors is unique in that the phase space is of a dimension that is non-integer.

A double pendulum for example:  You might not be able to get the position q(t) or momentum q'(t) as a function of time, but plotting the set of points {q(t),q'(t)} measured when a damped, driven double pendulum is set in motion will yield fractals.  The plot is known as a pioncare section.  The 2-D plot may have dimension 1.578887 - the trajectory is drawn on the 2-D plane, but the curves with mathematical certainty do not live in a 2-D space.  They have less room than all of R² to move.

pioncare section pic:
http://piet.jonas.com/Gyroskop/GyroChaos100pl.gif

The fractal nature of the trajectories suggests that despite inability to reliably produce a trajectory, there are always pairs of values ( q(t), q'(t) } which are never allowed!  That lends predictive power, albeit in a different sense than what we're used to.

https://pbs.twimg.com/media/BaPWHCLCIAAivV0.png:large


And we have a tulip fractal:

https://i.imgur.com/1wNmChg.png

Just the fact that other traders use TA makes it viable as a predictive indicator.

A fellow Physicist!!! WE ARE MANY!!! ;D

Thanks for the comments - you've wrote some of the crazy ideas I wanted to post, mentioned on the above comment... BTW: It's Poincare section.
http://www.mwit.ac.th/~physicslab/applet_04/fun@learning/JAVA/pendchao/pendchao.html

Coolness, I need help developing the bitcoin RF idea.  :-P  I sounded like a loon describing it but its real!

Excellent thread.  My compliments Mac.   8)

I'm a sucker for these kind of games... ::)


Thanks KFR :)

Not quite, the lower arm of the pendulum can flip over.
The analogy to that would be the market can't be static after going in one direction for a longer time, but it can on shorter timescales. This is why TA, well some TA works.

Of course they are not, but they share dynamical behavior.  See large pictures above.

this thread is well beyond my level of understanding, well done, you earned my respect.

The attractors.

Crazy mac is correct.  There are FOREX traders that stare at fractals all the time to study.  They do this because markets have chaotic dynamics.  My favorite is @EdMatts, I use twitter only to speak with him.  He is brilliant.

Are they strange?

http://en.wikipedia.org/wiki/Attractor

http://upload.wikimedia.org/wikipedia/commons/thumb/5/52/Atractor_Poisson_Saturne.jpg/333px-Atractor_Poisson_Saturne.jpg

They really are.

That was not my intention; really. I really hoped to keep it simple for the masses. Thanks for the kind words though. :)

So apparently, I'm not able to make a reasoned guess that buy and hold has a much greater than average chance of working out for me.  Once I retire next year, I'll have more time to ponder my errors.

FWIW: I'm all BTC and holding... (To infinity and beyooooooond!!!!) :D

Just look at the self similar price curve of bitcoin so far.  What can you conclude would be likely to happen next?  We don't know, but if nothing externally changes much, bitcoin would, I suppose, see another big run up followed by a "crash."

But there's no guarantee that the system will remain in this state!  So the answer to "what will bitcoin price do" is precisely [?].  But at the same time, I was able to take advantage of the last run up, just by looking at pictures of April, and the big $11 spike before it...

The efficient market is like doing physics in space and discounting all variables.  

Yes, the experimentation is needed to settle it.
Its been done with the stock market extensively across backtested trade data from databases reaching back decades for every trade recorded.
This was most famously done by William O'Neil and condensed in the CANSLIM methods (which just scratches the surface now).
Having worked for O'Neil and done some programming for him a few decades ago, I developed some respect for both the scientific methods used and the effectiveness of their rigorous application.

I haven't analyzed RP's methods, but claiming that all TA is bunk based on an analogy to pendulums or any other analogy is, well...  I think you can do better.

X^. | = | sigma(Y-X)
Y^. | = | rX-Y-XZ
Z^. | = | XY-bZ.
http://paulbourke.net/fractals/lorenz/lorenz3.png
Only 3 differencial equations are able to predict the long run of a chaotic system. So yes. They're strange!

BTW for you - I have assessed the large time behavior of bitcoin before.  If you address the problem as a perfect product, the demand for which is always equal to precisely the number of people who have recognized its existence, the price would go like

http://en.wikipedia.org/wiki/Sigmoid_function

So for small times, the growth is approximately exponential.  So I tend to take price data into excel, take the logarithm and try this:

http://altoidnerd.files.wordpress.com/2013/11/logplot.png

The choice of your fitted price at t=0 presents a problem!  The price on the day of the IPO of BTC was, 50 or 5 cents?  Whatever it was, it was arbitrary.  I believe I ended up dividing by the IPO price normalizing that price to "1". 

http://altoidnerd.files.wordpress.com/2013/11/exp.png

This fit was done in early November, during the time when the price was rising quickly.  There is a good explanation then, why the fit so badly missed the moment when the price would hit $1k.  Left an as exercise.

This would need to be modified by the limits of communication, and population.
In the early days, the chances of someone you talk to already knowing about bitcoin were about zero
Today it is greater than zero.  as adoption increases, the rate will necessarily slow by the percentage of folks that are already in.

Yes, I posed this question in a heavy math sub as the probability of being told a secret in a room of identical people who behave a certain way e.g. tell 2 people 1 minutes after being told, then have a 20% prob of forgetting after 5 minutes...etc... the results weren't that satisfying.  Here it is:

http://www.reddit.com/r/puremathematics/comments/1q7rfa/to_quantify_the_process_of_diffusion_of_a_secret/

Yes; I've figured out that far myself. I do have several other things to attend to during my days (and nights recently...) that really leaves me with minimal time to go as deep as I wanted to. This thing is definitely huge. IMHO, there's no need someone to risk his holdings in order to make them more. Especially people who don't know what they're doing.


1. I'd say you're right (that's why several times they're wrong - they should ACCOUNTING all variables)
2. It's like Risto Pietila's method of selling your bitcoins gradually (and vice versa if you're not sure if they go down or up respectively). As I previously wrote I'm a bit hostile at economic "scientists". They're no scientists at all to me. I may begin a big flame war here (which I will miss because I will have to go to sleep soon) but that's my opinion and I've no intention to change it.
3. I did not claim that ALL TA is bunk. I wrote (I'm not copy pasting) - did you ever read what I wrote on the 5th-6th paragraph?
4. I may be able to do better; but that's who I am, and I will probably wont!  ;D

You mean you don't have infinite time to play with bitcoinz?  My girlfriend hates me.

Also...
Question: What the hell is "TA"?

YES! MY PRECIOUS!!!  ;D


Technical Analysis

I once had Eureqa find a function that seemed to predict the price within about 2% accuracy, using data with 6 hours resolution; unfortunately i never tested how it would hold against new data.

I need to figure out a way to get a finer resolution set covering the whole history; and need to get a better PC to process that without having to worry about overheating the CPU and trashing the HDD with too much use of the swap file.


Obviously, i would expect the model would only be good for doing very short term predictions, and would need to be updated as new data comes in order to retain any level of accuracy; but very short term might be enough for daytrading.

When stuff starts getting "really real" you are going to need as near to the microsecond as possible quotes.   The big boys need microsecond data in order for their bots to work.

Right now you are probably lucky to get within seconds.   Then you can do some momentum style trading.  NASDAQ level 2 here we come :).

For very short term day trading, a great start is

buy low sell high

The momentum fourier analysis type dealy would seem to work however I agree trading engine lag on GOX is too shitty for anything really awesome.

To be honest, it's been far more profitable for me to trade the alts.  They are pretty predictable.  The market is young, it's not hard to take a position in a trending altcoin on cryptsy and sell it off in 10 minutes for a profit. 

Come to www.reddit.com/r/cryptomarkets

For a school project, I once tested a bunch of machine learning algorithms on a bunch of macroeconomic data. They were surprisingly accurate at predicting even 2 years out on every time series except stock indexes and producer price indexes (I'm not sure why it was so hard to predict producer price indexes).

Btw, if anyone wanna try doing what i was talking about, you can get Eureqa from http://www.nutonian.com/ (http://www.nutonian.com/)


edit: hm, looks like it became trialware for anyone that wasn't already using the older versions... :/

I find cryptos more predictable than stocks. Probably because of my age, experience, many reasons...but I feel stock prices are subject to even more manipulation, believe it or not, than crypto prices.  Twitter seems to have an affect on (and is affected by) the altcoin markets.

But the news and stock prices.  Shit.  There is much that goes on above our heads.  People play with bitcoin market caps on the NYSE.  Shit is unpredictable as anything because you're trying to solve a game theory problem with almost no information, compared with your competitors.

This looks awesome.  If you can find the full version, I'd be down as a clown to see it and would tip you much crypto so profit.

cool story tell it again

Try https://web.archive.org/web/20121011005629/http://www.nutonian.com/download/ (https://web.archive.org/web/20121011005629/http://www.nutonian.com/download/)

That seems to be the most recent version they captured before the change that added restrictions.

Also, from their description it seems that you don't got restrictions if you use the API in conjunction with the dedicated server instead of the GUI program, i haven't tried though. Both can be found at http://www.nutonian.com/download/ (http://www.nutonian.com/download/) if you wanna give it a go.

Actually, it seems the download for the previous version is still on their current servers: http://download.nutonian.com/formulize_0_98_1_setup.exe (there was a small period when they changed the name to Formulize for some reason, it's back to Eureqa now).

If you need the download for something other than Windows, let me know if you can't figure out the download link and i'll try to find it too.

I'm not very good at doing things all the way, and this was demanding too much of my hardware even before i could be sure it would be worth it. So i never got to the point of taking screenshots and doing other stuff people do when they're proud of what they achieved, much less of having any proof i was even on the right track. I believe i made clear on my post it looked promising but i hadn't managed to go all the way with it yet; what more do you want?

It's cool I have winders 7, much thanx

OK. Let's all remember a bit of calculus here. For a given f(x)=ax⁴−bx³−cx²+d, continuous on an interval I and differentiable on the interior of I, we remember from school that:

If f'(x)>0 for all x in I, then f is increasing on I.
If f'(x)<0 for all x in I, then f is decreasing on I.

Look here for an example: http://www.math.hmc.edu/calculus/tutorials/extrema/ and to remember how to determine minimal/maxima from first derivative of f(x).

Now imagine this to be done for a tiny fraction of time interval with a (FAST) link to an exchange API. This is what I'd call perfect control. Coders?
I'm willing to fund such a program. ;)


Thanks for this!!! It's a great program! I used to use Origin for such calculations... but this is REALLY nice!  :D

If you look at gox movement, I'm way more inclined to represent it with orthogonal functions.  I've never seen such a fine example of

exp[-t/t']Σ_na_nsin[ω_n t + k_n]

look at the linear impulse response holy moly!!

https://i.imgur.com/2h3kLI7.png

Well of course I have but only from my bad ass NMR data.

Hmmm... interesting concept! Do you have evindence that this might actually work?

Well look at it!  Nuff said?

Its a strong feeling say.  As a trader I have felt the harmonic presence you know.  Like tides dude.

I mean I often would base trades on those momentum waves you see below.  I would check the 1 minute, 3 minute, 5 minute, 10, minute...all components.  When they were moreso green you;d see gains...superposition of the frequencies results and if you are like us you can sort of add that up in your head by scanning.

It's an interesting concept. I will stare at it and look what it becomes through time. I'm sure you're right though. I'm not so sceptic about it. ;)

Seriously, go on gox and just look at the momenta on various time scales.  You'll see it.

I mean as physicists we tend to know that its a wave right.  has to be... heh

#physicsjerk

LOL! ;D

http://bitcoinwisdom.com/markets/btcchina/btccny

Hmmm... it's the same here!

of of course not gox even its wisdom.  I always have mad displays while goxing.  I dont gox much but when I gox...yeah..

See what I mean?  I'm so glad they give that display.

Yep; I'm with you on this. I believe you got it right! ;D

Right now (BTC china), we have a

30 min - upswing - its recovering from min point of neg momentum
15 min - going down - past the peak of a weak rally
5 min - beginning the hellish decent
3 min - worst is almost over, about to come up could be strong hard to say
1 min - very nearly min, will rise soon

alright cool lets get filthy.   (rich)

shit should be published

So you take this data:

30 min - upswing - its recovering from min point of neg momentum
15 min - going down - past the peak of a weak rally
5 min - beginning the hellish decent
3 min - worst is almost over, about to come up could be strong hard to say
1 min - very nearly min, will rise soon

they're all weighted with intensities, summed, and you have a "state function."  If the 1 and 3 and 5 min data are all doing the same thing, you kinda know what will happen in the next 5 min, if the 15 and 30 waves are sufficiently weak of course.

if they're all coherent, well thats fantastic!

Necro. Just b/c following. Sorry  :-[

Great thread...

Nice post @macsga, but I suspect that price is worse than chaotic, it is basically "random".

A chaotic system appears random but has a more or less deterministic model that, in theory, would allow one to predict its future from its current state.  In the double pendulum example, the state is the pair of angles, at the top and at the elbow, and their derivatives with time.  The trajectory in that gif was computed starting from some arbitrary state (particular choices for those four numbers) and applying the deterministic equations of motion.

A random system has no closed deterministic model, not even in theory; its evolution depends on external inputs that cannot be predicted, and cannot be enclosed in the state because they are themselves dependent on further external causes, and so on.  In this case, the external inputs include what each trader reads and thinks, the bills he has to pay and the money that he earns, government regulations, bank delays, and lost more.  If one tries to enclose all those variables as parts of the state of a closed model, one ends up with the whole universe, or at least with good part of mankind. 

So, in the theoretical model, the price must depend on external inputs that are not modeled, and therefore unpredictable, and therefore memoryless -- their future values are independent of their past values.

The question is whether one can still have some state variables in that model, so that the future prices are not entirely random but have some dependence on that state, and therefore to past prices.

The current price is known to be such a state variable, indeed a pretty good predictor of future prices.  That is, the price P(t+d) at a future time t+d is the price P(t) at the current time t times some factor (percent change)  D(t,t+d).

As far as I know, no one has been able to demonstrate any other correlation; that is, and relation between D(t,t+d) and the prices (or price changes) before the present time t.  So, it seems that D depends entirely on those external unpredictable factors.The best we can do is observe the probability distribution of D.  (I don't know what is the shape of that distribution, only that it is not log-normal.)

In other words, the logarithm of the price is a simple Brownian process whose increments log(D) are independent but not normally distributed.  This is the "log-Brownian" or "geometric Brownian" model. 

The unpredictability of price has been blamed on "whales"  who try to "manipulate" the price and break its trends.  However the market has fish of all sizes, and once one accepts that the increments depend on unpredictable external factors, it becomes unnecessary to distinguish "whales" as a separate category of trader.

For sure, a single trade of 100 BTC will have a much bigger impact on price than 100 trades of 1 BTC each, because the latter will tend to cancel.  In log scale, perhaps the change due to the large trade will be 10 times larger than the sum of all the little changes, typically.  However, one increment will be just as unpredictable as the other, and just as unrelated to past trades. 

Humans are genetically programmed to find patterns, even where they don't exist.  The trends and patterns that one may think of seeing in price charts may well be only illusions.  We also remember more easily our predictions that worked than those that failed, which reinforces the illusion.

Correlations between past and future price changes may exist for very short time scales d.  For example, it may happen that a trader who decides to sell (or buy) will do so in a series of successive trades; since these trades are all derived from a single decision, there will be strong dependence betwen them.  Also, presumably the general feeling of most traders will not change in a few minutes.  On the other hand, that general feeling may not influence their feeling towards the small changes that are likely to happen in that time span.  That is, one may believe that bitcoin will go to the moon this year, but nevertheless feel that it may go down in the next minute.  Also,

Correlations between past and present also may exist in common stocks.  For most traders, the main external inputs are a small set of  "fundamentals" like products and their demand. These variables tend to vary slowly and smoothly with time, so one can postulate models for them that include "momentum" --  that is, a dependence between the past and the future.

Hello people. It seems this thread is still attracting people I'm glad to see it revived...

Distinction between Chaos and Randomness

As previously stated in this thread (and elsewhere), a system can describe a [deterministic] chaos if very small differences at the initial conditions, give an outcome of enormous differences at a later time. A very common example is described by the movement of a double pendulum or at a larger scale at long term weather simulations. What we people do to form an understandable pattern, is to use rounding techniques (ie: integration) to limit possible "fallacies".

So, is our system chaotic? As it is commonly observed, we tend to describe a non chaotic system (or if you prefer a random one) easier than what it takes to describe a chaotic one. For instance when an Ordinary Differential Equation satisfies a Lipschitz continuity(1) in the Picard & Lindeloef theorem(2). In this case there's a linear correlation factor between differences in initial and final conditions and this factor is M * e^(LT). You can eliminate computations errors if L is large enough.

Summing, to state a system as non-chaotic, we need to do so for a very large L or for a non-linear correlation factor, if a global Lipschitz continuity is present. For such a "random" system we need to declare (as you very well mentioned) a probability space, which is in the essence a completely different system. Finally, there's always the possibility of mixing them and consider chaotic or unstable O.D.E.(3) with a random variable(s) as the initial conditions.  

To what category BTC/USD can be enlisted, remains as a task for the reader...

Further reading:
1. http://en.wikipedia.org/wiki/Lipschitz_continuity
2. http://en.wikipedia.org/wiki/Picard%E2%80%93Lindel%C3%B6f_theorem
3. http://en.wikipedia.org/wiki/Ordinary_differential_equation
4. http://en.wikipedia.org/wiki/Randomness
5. http://www.math.tamu.edu/~mpilant/math614/chaos_vs_random.pdf
6. http://en.wikipedia.org/wiki/Peano_existence_theorem
7. http://www.researchgate.net/post/What_is_difference_between_chaos_and_random

That only applies for "sufficiently small" displacements in the initial conditions.  If the state space is bounded (as in the double pendulum example), the initial displacement d must be less than R/(M * e^(LT)) where R is the domain radius.  Otherwise the d-neighborhood of the starting state will be not only stretched but also folded or rolled over itself, destroying the linear correlation.

Is there any evidence of any relation between future changes in price and past price history (other than the current price)?  I have tried looking for linear correlations in the case of bitcoin, but without success.  But that of course does not prove anything.

All the best, --jorge

Exactly, you have absolutely right. The thing is how small is "sufficiently small"...

Well; not one that I can recall or mathematically prove. What I could provide as a "proof" is that everything falls to a repetitive pattern that could very well be organized by "significant" participants. Maybe I got this thing wrong, but in complex problems, the best solutions are the simplest ones (Occam's Razor).

Thanks for your thoughts.
All the best
Costa, Greece

interesting thread guys, thanks

Thanks Room101, glad you like it.

I prefer to use the "watch" function for this to add it to the watchlist.

It was a "necro" thread before Risto came along (thread necromancer? WTF???). So I owed him some kind of progression. TBH, a lot have changed since I first wrote this thread though; for instance I'm not exactly sure that the "system" is certified as "pure" chaotic or random or a mix of those two. Several thoughts have demented my brain and Jorge has made things even worse with his post (thank you dearly Jorge).

Me and Altoidnerd (yeah, the other crazy physicist here) have been into a lot of google talk chats and even started a project towards a "prediction model" that could imitate the intrinsic infrastructure of similar "systems"; for instance an equation prediction via a mathematical package (ie: Mathematica) of the price and predicting the next couple of minutes by taking the 1st derivative of the projected equation (explained 10 posts above).

Another idea is to build a system that could use a "set" of given equations that could be "pretty close" to the one that projects the value of USD/BTC per minute. Say for instance, is it a damped oscillation? Then load up equation #1. Is it a log equation? take #2 etc. Unfortunately, I'm way beyond my programming skills that I used to utilize a decade ago, and frankly my dear, I don't give a damn programming such a system for me or anyone else.

This project needs fresh brains, fast coding hands and A LOT of time to do it. I could provide the science -and a couple of BTCs maybe- to see it fulfilled; but that's that. So if any of you younger chaps feel the urge, please seize the opportunity. This may turn you into filthy (rich) or (at worse) with a brand new PhD thesis. ;)

Cheers

It's almost next year.  ARE you still planning to retire?  Does your retirement depend on the price of BTC or the ability to predict the price?  If your retirement does depend on the price of BTC, what is that price, and is it realistic? 

In light of the topic of this thread, I am inclined towards buy and hold based on my thoughts that we can predict generally the upward trajectory of BTC prices, but we cannot really tell where they are going to be at any point in time.. but we seem to be able to predict with some degree of probability (and certainty) that BTC prices are going to be within a range of prices.

Accordingly, I think that i can give some tentative plans towards my being able to include bitcoin prices in my investment portfolio, but since BTC prices are so volatile (which is also within the expectations), I cannot keep too much wealth in BTC in order to rely upon its appreciation for my plan... but if it does appreciate at the high end of the range, then I can act upon that in order to preserve some of the value of the gains... and accordingly to be able to remove some of the volatility from my whole investment planning package.

I *think* it's not the time just yet. Realistically speaking any person with 50 BTCs or above could be considered "retired" by the time the next "projected bubble" occurs. That won't have to involve the trading drama though. Several charts have been posted here and elsewhere predicting the inevitable:

https://i.imgur.com/cU6q7IT.png

Chances are that this will happen sooner or later for a TON of other reasons though (https://plus.google.com/+PeterHDiamandis/posts/dWQFcpcws8V) but we don't know for sure *WHEN* its going to be. We may get a good idea though if we have our eyes and ears open (which is why we hang out a significant time of our lives in places like this).

So to summarize, I think this is the season; we're getting close, but not just yet. Some of the most intelligent people I've met are probably reading this text right now. If it gets to be differently, then A VERY intelligent person, has managed to fool us all, which is perfectly fine by me. I'd seriously laugh about it. :)

The real question that arises into my head for sometime now though (provided that what we anticipate about bitcoin turns out to be true) is this: Who is going to sell last? ;)

What if we are heading under the blue line? That's my fear, I believe in bitcoin but this downswing seems that never ends.

For one, this has happened before (see September 10). Secondly, it also went above for a couple of times. What we people do is trying to "fit" random data to "non random" equations. This thread is trying to prove that since there are "enormous sized" players into the game, the game itself cannot be described perfectly by a mathematical model and thus its unpredictable. Is there a possibility the USD/BTC value goes to zero? Yes it is. Is there a possibility that goes 100,000,000? Well, that has about the same odds with the first possibility. :)

I believe, this game is not for the masses. At least not for now. It requires a) either deep understanding of very complex economic aspects of our society or b) enormous levels of stupidity to go "all in" with bitcoin. I'm into neither of those categories. Or I'm into both of them. I'd say if I was an electron I'd define myself as super-positioned between these two quantum states. I'd advise you to read and try to comprehend Risto's SSS plan here: https://bitcointalk.org/index.php?topic=345065.0 and take a leap of faith. Or don't.

Everything is a choice.

50BTC at $5000 is only a quarter mill. I wouldn't call that retired just yet.

Everything is a matter of perspective (and personal needs). Most people I know would have called it retirement at that point.  :)

I guess there are a lot of people in certain countries that would be able to more than retire form that amount of money. But when it comes to developed western countries, I guess most people tend to forget about the general inflation that's occurring. People are in danger of becoming broke when they're old.

Well $250,000 is sufficient if you can live of off $10,000 of today's earning power of US Dollars indefinitely and don't invest foolishly.

This is absolutely true for most of the US and most EU countries right now. Inflation is an inevitable decease and IMHO, that's where BTC will make the difference. The smartest people I know have a smart retirement plan that *INVOLVES* BTCs and PMs in it.

Yeah but if you had 50BTC and it went to 5000USD, are you saying you would cash out 100% of it just to retire? Could you live with the doubt of it reaching 10K and missing on legit gains?
And if you do not cash out, could you live off the doubt of it crashing after 5k?
It's a psychological game.

It's a decisional game. I, for instance, will NOT sell even one BTC until I DESPERATELY need to spend it. Some people here just live off by mining and spending; others think that selling at $1200 was a good idea... so many people, so many decisions. Everyone thinks his choice is the best of all.

The amount really depend on your lifestyle.

People like Larry Ellison probably find it insufficient as he can spend up to 250k in one day alone.

This is the most critical parameter. I strongly believe that most of us here won't be around when USD/BTC is $50,000 though; as this alone, certainly may add some extra "spice" to most of our daily "needs"... People always like to treat ourselves better when we have the chance (and the ability) to do so. Do we really need it? No. But most of us do so anyway.

That is what I was thinking, too.  And even if BTC is going to $10k soon,but then half a million is NOT really enough either... and would a person cash out or diversify part of that BTC portfolio.  My actions would depend in part about how quickly the price goes up and then for how long do I expect it to stay there and what had apparently caused the upswing.

Agreed. To live comfortably after retirement age one should have around a million. Which is why it's so important for the average person to begin saving as soon as they start earning income of any sort. Unfortunately we see the opposite more and more, at least here in the U.S.

Dude my annual rent is more than $10k  :D (and it's not like I'm living lavish or anything, it's an apartment).

Well, I guess you will have to wait a couple of years more then... ;)

Actually, we get into a few complications and speculations here; however, I also like to use $1million in liquid (or quasi-liquid) income generating assets as a decent target to aspire to. 

If you have $1million in liquid assets then with traditional investment models, you should expect at least be able to employ a 4%  per year withdrawal of the income without undermining the principle.  That would be $40k per year and $3,333 per month, gross. 

However a few things could change those variables regarding how much to draw.

1)  if you are able to achieve higher growth rates with your assets, then your withdrawal rate can be higher.

2)  Another variable can be if you are ready to start shrinking the principle, then you can start to draw into the principle and have a higher income but to expect that it will not last forever, that depends, usually on life expectancy and potentially the running into other income sources.

3) people are going to come to differing judgements concerning regarding how much they need to live, whether it is $1k per month or $3k or $10k or $20k or higher... Many times with current USA averages, $3k or more can be adequate in today's dollars (but maybe a little bit tight).

4) regarding inflation, we can probably project that inflation will continue to cause the amount needed to go up and even double by the time you need it (expect halfing of the value of the dollar every 10 years). If you think you will need it in 1 year or 5 years or 10 years or 20 years, the inflation should be accounted.  Also, If you live in another country the amount may be more or less than the american amount too, and those values are going to change over time and change relative to one another.  And, likely a world of bitcoin will affect these values, and affect decisions about where you would like to store your value... or how you would like to diversify your assets.

If you retired, you are not tied to your job anymore, so you can move to a cheaper place/city/country.

What most people don't think is "how long will I be here"? You know, as human beings we tend to believe that this thing we call "life" will last forever. Well, it won't. Let me explain with plain 5th grade math how this "prediction" of 50BTC will be more than efficient for a "life".

I'm in my mid 40s now. That means, I have ran (with high probability) about 5/8 of my life so far. I will probably have about 30 years of "quality" life in front of me with a strong possibility this goes extremely off-track when/if a chronic disease hits me (there's a 15-25% probability for this).

The good scenario.
Where I live a person can live with about $1000 per month if he/she doesn't pay a rent (add 200-250 monthly for a small apartment). I mean not lobster for dinner, but I don't mean beans everyday either. Here you have the ability to have your chicken, goats and a small garden that you can use to feed yourself off pretty healthy. A small car, a bicycle can help me live perfectly fine, me and my wife for this lot per month.

So: 1000x12=12K per year or 30x12K= 360K for the next 30 years of my life. For this to happen, BTC must land somewhere north $7200 within the next bubble. I wouldn't laugh at this just yet, but it's not 100% sure either.

What I'd propose is to spend "as much as" every year. To simplify this, I'd propose to sell that amount of BTCs you need in order to achieve the lifestyle you want. This will have the drawback you will miss the high value some year(s) but if you're monitoring this, you'd know exactly when to liquidate a-priori. That gives you an advantage over the traders.

The bad scenario.
Well, it's this scenario where every disaster that you wish for not to happen to you, for a strange whimsey of life, lands upon your head. Well; in this unfortunate scenario you'll realize that money or assets you have at your disposal don't really matter. Whether you have money or you don't, fate will always find its victims. What matters most, is you to manage to give the most to those closer to you and let them know that you *REALLY* cared for them all these years.

In this [un]fortunate scenario you will also realize that the most precious things in life are not the ones you can buy with money, or BTCs. Actually, they're no "things" at all.

Cheers.

Either scenario, it would be good to have a financial cushion.  

In the good scenario, your cushion does NOT need to be as great, if there is some fortune in that the BTC portion of your investment out performs expectations.  So maybe you withdraw only enough to live each month, but the remaining portion continues to gain value.. and yes, if you foresee price movements (whether they are above or below what you reasonably believe to be the trendline), then you can act accordingly to sell and/or to buy back in.

We should NOT delude ourselves into any kinds of thoughts that there are times in which money does NOT matter.   There are many variations of the bad scenario, and if shit really does hit the fan and you become debilitated or disabled in some kind of way, it could be a very good thing to be able to hire someone to perform home care services for you, rather than to drain other family members with some of these sometimes exhausting and time-consuming duties.  

My point is merely that having a financial cushion can make a considerable difference no matter what the scenario that plays out... and that seems to be a fairly large justification concerning why your plan should attempt to contemplate ways to live off of the passive income and NOT touching the principle as long as you can..  (or maybe only touching the principle when you can reasonably foresee that you are likely in the last 5-10-ish years of your anticipated life).

JayJuanGee, you have absolutely right on the second point presented. Indeed there's a great difference to have a financial cushion in a case of an emergency situation. My point though, was not this. It was a rather philosophical aspect of life and its consequences as they're presented by the factor "pure luck". You see, nearly everything we do, is 50% based on luck.

I recently (last year) had a family member threatened by imminent death due to some very nasty biochemical reaction of a drug she was using. She was able to get through and outlive it "by pure luck". No doctor was able to find, what I was able to foresee from the very beginning, which was based on Michaelis Menden enzyme kinetics diagram**

I previously thought that we were able to live our lives via our decisions. That we live in a deterministic universe that we are able to control our lives via our actions, our mental abilities, our strength... and it may be right. But only for the 50%. The other 50% is pure luck. What is the definition of luck you might ask. Well, what I know for sure is that it can be described by a triple differential equation; or a double pendulum with non standard initial conditions; or a Lorentz attractor.

As a scientist, I present myself to the inner circle of mine as "a-religionist" so I will write this here only for historical reasons. What my grandmother used to say about luck was this: "My boy, luck is the will of God"

Hmm...


**Michaelis-Menten saturation curve of an enzyme reaction.
http://upload.wikimedia.org/wikipedia/commons/thumb/b/b0/Michaelis-Menten_saturation_curve_of_an_enzyme_reaction_LARGE.svg/220px-Michaelis-Menten_saturation_curve_of_an_enzyme_reaction_LARGE.svg.png
http://en.wikipedia.org/wiki/Michaelis%E2%80%93Menten_kinetics

Before i sleep, some links:

https://www.google.com/search?q=site%3Aarmstrongeconomics.com+hidden+order

https://bitcointalk.org/index.php?topic=355212.msg10890931#msg10890931

https://bitcointalk.org/index.php?topic=365141.msg9566419#msg9566419

http://i0.wp.com/armstrongeconomics.com/wp-content/uploads/2015/02/CHAOS-DJ.jpg?resize=584%2C438 (http://armstrongeconomics.com/archives/27477)

See also his entropy model for a stochastic momentum model.

Implicit in your point is that we can not specify initial conditions with exact precision due to Planck's constant (which is intimately related to that the speed-of-light is finite and also conceptually related to the Heisenberg uncertainty principle).

That is all fine and dandy, except it is irrelevant to games of chance in real world outcomes. If it were true that no order emerged from chaos, then entropy would be simultaneously infinite (internally) and 0 (externally) and nothing could exist from an internal nor external perspective. The internal perspective would fail to find any relative order (no point of reference with which to make an observation) and the external observer would observe a void.

Order exists at higher levels of conceptualization. And this is your myopia on our disagreement about Armstrong's computer model (https://bitcointalk.org/index.php?topic=68655.msg11561129#msg11561129) and your other egregious attack on knowledge (https://bitcointalk.org/index.php?topic=68655.msg11563137#msg11563137). I encourage you to delve into the links I gave you upthread (https://bitcointalk.org/index.php?topic=372346.msg11561137#msg11561137) to Armstrong's writings about his model and chaos theory wherein he explains that moving to higher dimensions can extract order that is hidden in lower dimensional conceptualizations similar to your myopia here.

P.S. you are correct that the existing stochastic models employed are one-dimensional and thus don't have the scope to pull order out-of-chaos. Armstrong developed a multi-dimensional entropy stochastic model which extracts hidden order.

But due to chaos theory we can't predict that the sun will rise tomorrow  ???

(this is satire)

Exactly. That's about it. BTW, I've read all the links you PMd me (thank you) on Armstrong Economics (BTW, most of them I've already was aware of; never dived in detail though). I think he has gone a step further than most of us (ok, at least me). The conclusive thought of his, based on "following the pattern of a Stokes diagram on 3D" truly *TRULY* amazes me. I'm sure he has his reasons for not sharing "which is the triple differential equation that rules our world"; but based on his thesis, -more or less- this is about it.


First things first. Entropy is coming from the words "Eν τρoπή" which -in essence- means "during the process". What you're presenting here is a "burning a straw man" paradigm. But you see, on the contrary, Entropy is totally different if you change the initial conditions; as a totally different chaotic model is built. The internal perspective wouldn't fail to find a relative order since you -theoretically- could pick any single moment as a "Zero Point". Thus a new Entropic order within a specifically chosen chaos. This is pretty similar with picking as accurately as possible the initial conditions.

Further reading: Cellular Automata (http://mathworld.wolfram.com/CellularAutomaton.html).


First of, it's not bad for someone to admit his myopia. I believe we have a doctor here for these kind of cases, I hope he will give me a nice price fixing my 13/13 vision (joking)... ;D

Second:
I disagree. Order DOESN'T exists ONLY at higher levels of conceptualization. There's a mathematical proof for this. To put it on another perspective; Chaos incorporates Entropy from its very beginning. Otherwise entropy would've been non existent in the first place. That's why we are here and be able to talk about it. BTW: I'm not a personal fan of Anthropocentric Model, but some times like this one, I truly struggle not to.

Third:
I must admit I gained a lot of info from your links (thank you, once more). I must also admit I'm a bit impatient to learn more (ie: how he normalizes the abnormalities, while choosing to leave aside "minor details"). Such a model is a true gem. I have more questions, but I don't think littering a place like this with an off-topic matter like "prediction of entropic morphemes within a chaotic model" is something I like to do... (This is sarcasm) ;)

PS: my other egregious attack on knowledge (https://bitcointalk.org/index.php?topic=68655.msg11563137#msg11563137) points to a link that I have not posted anything... Do you want to fix it / correct it?

It points to a quote of you and clicking the link of that quote takes the reader to your post immediately above mine and contains the context of your argument. Is that insufficient or did I misunderstand your grievance?

I will come back some other time to read and digest what you have written here. The theoretical is a lower priority for me at this moment for reasons you may be able to imagine. Thank you for your cordial reply.

Is this the one?

I suspect the disagreement is only in definitions of words. I am trying to articulate that order is relative to perspective. So if you want to find order, you need a conceptualization (a.k.a. perspective) that enables to you recognize that order. I refer to that process as higher level, but that doesn't mean higher as in macroscopic versus quantum. It means higher in the sense of applying some rules on the interpretation other than the default one that rendered only noise.

Hey WTF are you praising PnF TA nonsense (https://bitcointalk.org/index.php?topic=1064374.msg11772020#msg11772020)? Surely you know that TA does not have anything better than a 50/50 perspective on future prices moves, and worse than that if you include human emotion since one mathematical truth (of the wealth effect, i.e. mcap != capital invested) is the majority always has to lose more in the markets than the minority.

In case you need to refer to them again, I moved all the posts kLee deleted here (https://bitcointalk.org/index.php?topic=1082909.msg11771844#msg11771844).

Armstrong is predicting price moves correctly. I proved it again in the PnF thread.

Hello and welcome.

Indeed it's often a compulsion of mine to disagree in order to create a fruitful discussion (how on earth we'd have a discussion if we'd agree on everything?). As you may understand the matter we're talking about is far more complex than a "simplified physics" chat. So, yes; I agree with the first paragraph of yours in full detail. My thesis would've been the following though and I will try not to over-complex it:

1. Every data represents a x,y,t point within a diagram. Thus it will perfectly modelize a 3D diagram (2D representation by t=z).
2. After the collection of a specific amount of data (ie: enough to make a "chaos") you can recognize a pattern that represents a stokes diagram of a 3D differential equation.
3. The pattern represents the entropic trajectory of the chaos that tends to form a Lorentz Tensor [or more].
4. The pluralism of Tensors in question depends of the respective Chaos(es) that each and everyone incorporates or vice versa. If you check the diagram from DJ that Armstrong has on his website there's a strong possibility you get EXACTLY what I'm talking about.
5. Reverse engineering the equation. Well. That's easy... as long as you know EXACTLY the deterministic chaos initial conditions (aka:Zero point).

From all the above, step 5 requires A LOT of discussion, mainly on the fact that the "initial conditions" are pretty subjective to significant moves (ie:a whale sale / buy).

Your turn :)

PS: Klee is a fellow Greek and I like his way of thinking. Besides, I never turn down anything without first giving it a good chance testing it. That's the way I function. :)

I tried the PnF crap and managed to lose $70,000+ in 2012 doubling down after getting stopped out on options. After that I started reading Armstrong and have lost any money on any investment since.

kLee was profiting quite well from following my timing calls on the Bitcoin price moves and now he decides to delete my posts that disagree with him. I guess he has to learn the hard way, such as when most of his coins got stolen for failing to do basic wallet security.

You can lead a horse to water, but you can't make a stubborn Greek drink.

Hahahaha... true! :P

Watching and will try to participate! Very interesting thread!

Hehe, come here so you will drink with me, macsga and your Greek numerate fan club (I partially helped to form) tsipouro, ouzo, raki and fine red wine!