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
Topic: Can I predict the value of BTC/USD? - page 3. (Read 12932 times)
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.
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.
Great thread...
Necro. Just b/c following. Sorry 
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!
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!
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.
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!
alright cool lets get filthy. (rich)
shit should be published
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
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
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.
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!
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.
See what I mean? I'm so glad they give that display.
Hmmm... interesting concept! Do you have evindence that this might actually work?
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!
http://bitcoinwisdom.com/markets/btcchina/btccny
Hmmm... it's the same here!
Hmmm... interesting concept! Do you have evindence that this might actually work?
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
Hmmm... interesting concept! Do you have evindence that this might actually work?
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.
Hmmm... interesting concept! Do you have evindence that this might actually work?
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.
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.
Its a strong feeling say. As a trader I have felt the harmonic presence you know. Like tides dude.
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 .....
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']Σnansin[ωn t + kn]
look at the linear impulse response holy moly!!
Well of course I have but only from my bad ass NMR data.
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 .....
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']Σnansin[ωn t + kn]
look at the linear impulse response holy moly!!
Well of course I have but only from my bad ass NMR data.
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!
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.
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.
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.
Thanks for this!!! It's a great program! I used to use Origin for such calculations... but this is REALLY nice!
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.
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.
It's cool I have winders 7, much thanx
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.
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.
cool story tell it again
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.
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.
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