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Author Topic: Long-Term sub-exponential, short term bubbles  (Read 1236 times)
Jutarul
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August 02, 2012, 07:20:47 PM
 #1

f(x)=0.05*exp(b*(x**c))
Final set of parameters            Asymptotic Standard Error
=======================            ==========================

b               = 0.182109         +/- 0.0119       (6.536%)
c               = 0.499584         +/- 0.01005      (2.012%)

based on that estimate we're gonna have a "base value" of $20 in a year from now. Variation due to bubbles excluded.

anyone disagreeing?


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August 02, 2012, 07:24:53 PM
 #2

You don't have enough data yet for this to have confidence above about 10%.

In other words, don't extrapolate a 3rd datapoint (year), from only two data points.

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August 02, 2012, 07:33:10 PM
 #3

So according to this chart prices would tend to infinity over time.

Bitcoin would be the very first commodity with this property.
Reasonably it would be either some probability density function or sigmoid function depending on whenever bitcoin turns out to be a lasting success.
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August 02, 2012, 07:37:47 PM
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So according to this chart prices would tend to infinity over time.

Bitcoin would be the very first commodity with this property.
Reasonably it would be either some probability density function or sigmoid function depending on whenever bitcoin turns out to be a lasting success.

You can, however approximate the first part of a sigmoid with an exponential.  We really don't have the data to tell when it will start to saturate, so an exponential is still useful for this first phase.  You just have to know it WILL start to roll over at some point.

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August 02, 2012, 07:39:17 PM
 #5

anyone disagreeing?


Have you tried fitting an e^(e^t)? Or perhaps an e^e^e^t?


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Jutarul
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August 02, 2012, 07:41:44 PM
 #6

You don't have enough data yet for this to have confidence above about 10%.

In other words, don't extrapolate a 3rd datapoint (year), from only two data points.

normally I'd agree with you. But the goal is not to get a good estimate for the trade value, but for the lower bound. For that I used periods where the bitcoin was likely not inflated due to short-term speculation.

Also, technically speaking, it's more than one data point. The green region was used for fitting.

But of course a sub-exponential fit is a relatively crude choice. Does anyone know of a more "realistic model" which includes distinct growth factors?

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August 02, 2012, 07:42:21 PM
 #7

So according to this chart prices would tend to infinity over time.

Bitcoin would be the very first commodity with this property.
Reasonably it would be either some probability density function or sigmoid function depending on whenever bitcoin turns out to be a lasting success.

Actually, w.r.t. any inflationary currency, commodities with limited supply will always tend to infinity over time.  Price != purchasing power.

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August 02, 2012, 07:42:29 PM
 #8

We really don't have the data to tell when it will start to saturate

Keep stumbling in the dark.

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From Mises's Human Action

The problems of prices and costs have been treated also with mathematical methods. There have even been economists who held that the only appropriate method of dealing with economic problems is the mathematical method and who derided the logical economists as "literary" economists.

If this antagonism between the logical and the mathematical economists were merely a disagreement concerning the most adequate procedure to be applied in the study of economics, it would be superfluous to pay attention to it. The better method would prove its preeminence by bringing about better results. It may also be that different varieties of procedure are necessary for the solution of different problems and that for some of them one method is more useful than the other.

However, this is not a dispute about heuristic questions, but a controversy concerning the foundations of economics. The mathematical method must be rejected not only on account of its barrenness. It is an entirely vicious method, starting from false assumptions and leading to fallacious inferences. Its syllogisms are not only sterile; they divert the mind from the study of the real problems and distort the relations between the various phenomena.

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August 02, 2012, 07:44:49 PM
 #9

So according to this chart prices would tend to infinity over time.

Bitcoin would be the very first commodity with this property.
Reasonably it would be either some probability density function or sigmoid function depending on whenever bitcoin turns out to be a lasting success.

You can, however approximate the first part of a sigmoid with an exponential.  We really don't have the data to tell when it will start to saturate, so an exponential is still useful for this first phase.  You just have to know it WILL start to roll over at some point.

+1
further estimate would be $3k in 8 years from now
further estimate would be $9M in 28 years from now

But that assumes that the basic growth factors don't change and we're not gonna hit saturation in the meantime.

The ASICMINER Project https://bitcointalk.org/index.php?topic=99497.0
"The way you solve things is by making it politically profitable for the wrong people to do the right thing.", Milton Friedman
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August 02, 2012, 07:48:12 PM
 #10

We really don't have the data to tell when it will start to saturate

Keep stumbling in the dark.

Quote
From Mises's Human Action

The problems of prices and costs have been treated also with mathematical methods. There have even been economists who held that the only appropriate method of dealing with economic problems is the mathematical method and who derided the logical economists as "literary" economists.

If this antagonism between the logical and the mathematical economists were merely a disagreement concerning the most adequate procedure to be applied in the study of economics, it would be superfluous to pay attention to it. The better method would prove its preeminence by bringing about better results. It may also be that different varieties of procedure are necessary for the solution of different problems and that for some of them one method is more useful than the other.

However, this is not a dispute about heuristic questions, but a controversy concerning the foundations of economics. The mathematical method must be rejected not only on account of its barrenness. It is an entirely vicious method, starting from false assumptions and leading to fallacious inferences. Its syllogisms are not only sterile; they divert the mind from the study of the real problems and distort the relations between the various phenomena.

Good quote.  Math/logic is only as good as the assumptions it is built on, and in economics you can never make accurate enough assumptions.  But, occasionally, you can can get close.  And that's why it persists.

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August 02, 2012, 07:50:47 PM
 #11

So what is x currently?
Jutarul
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August 02, 2012, 07:51:28 PM
 #12

anyone disagreeing?


Have you tried fitting an e^(e^t)? Or perhaps an e^e^e^t?



a stretched exponential is always the first choice because it roughly corresponds to a sum over individual exponentials...

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"The way you solve things is by making it politically profitable for the wrong people to do the right thing.", Milton Friedman
Jutarul
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August 02, 2012, 07:52:05 PM
 #13

So what is x currently?

742

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August 02, 2012, 07:56:16 PM
 #14

Then, according to my calculator, 8 years from now the expected price is 2942 and 28 years from now 8.9M. (Yes I was trying to deduce the current value of x from your price predictions). This is what I fed my calculator:

0.05 * e ^ (0.182109  * (x^0.499584 ))

Is that correct?
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August 02, 2012, 07:58:08 PM
 #15

anyone disagreeing?


Have you tried fitting an e^(e^t)? Or perhaps an e^e^e^t?



a stretched exponential is always the first choice because it roughly corresponds to a sum over individual exponentials...

Understood. My point was it's hard to tell what the long-term fit is from this little data. Is it an exponential? A polyomial? . The sigmoid- post above made the same point. Thus, you may fit an exponential all you like, but using it to extrapolate into the far future is futile.


 

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Jutarul
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August 02, 2012, 08:06:34 PM
 #16

Then, according to my calculator, 8 years from now the expected price is 2942 and 28 years from now 8.9M. (Yes I was trying to deduce the current value of x from your price predictions). This is what I fed my calculator:

0.05 * e ^ (0.182109  * (x^0.499584 ))

Is that correct?

The fitting parameters are accurate. The other values I reported are rough.

Your values look about right. However, as others pointed out. These values depend extremely on the growth function. Fundamental Growth functions usually don't change that fast, but 10 years or 30 years are too much Smiley But it's still fun to play around with those values...

The ASICMINER Project https://bitcointalk.org/index.php?topic=99497.0
"The way you solve things is by making it politically profitable for the wrong people to do the right thing.", Milton Friedman
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August 02, 2012, 08:10:09 PM
 #17

I know, I know, just wondering whether I typed the formula in right Wink
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August 02, 2012, 08:20:19 PM
 #18

Take random subsets of gold price, use your approach to predict where it'll go, then look back into the complete data set and see how successful you were. Ideally, do this as a blind study with a help from a friend. Let us know.

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Jutarul
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August 02, 2012, 08:26:23 PM
 #19

Take random subsets of gold price, use your approach to predict where it'll go, then look back into the complete data set and see how successful you were. Ideally, do this as a blind study with a help from a friend. Let us know.

Not random. minimum. But yes. Gold has a longer history, so that might be worth a shot Smiley

The ASICMINER Project https://bitcointalk.org/index.php?topic=99497.0
"The way you solve things is by making it politically profitable for the wrong people to do the right thing.", Milton Friedman
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