rpietila Wall Observer - the Quality TA Thread ;)

[Wary]

What IS important is if the growth trend is slowing or not.

Agree. For example, it is reasonable to suggest that "pregnancy" is shorter for early adopters and longer for general population. Then it would be steep curve in the very beginning, then less and less steep later on. Something like this:

[IMG size=200]https://i.imgur.com/6iN9ZSA.png[/img]

EDIT: It's real data

This has probably already been mentioned at some point, but have you given any thought to 'the chasm' that is inevitably encountered during adoption of a disruptive technology?

This feature (unique to disruptive innovations, in contrast with sustaining innovations) occurs after the innovators and early adopters (who, in total, account for the first 16% of total adopters) and before the early majority jump in. It appears while the innovators and early adopters revel in the adoption of a change agent, the early majority are much more comfortable using existing tools/methods and hesitate before adopting something that requires a fundamental change to their current operations. This hesitation forms 'the chasm'.

Using 2.1 million as the value of current adoption (taken from My Wallet), and assuming we have reached the chasm, that puts the future total number of Bitcoin adopters at approximately 13 million. (Granted, this value does seem a little low, especially considering it is only 9% of PayPal's current users.)

Anyway, it would be interesting to hear your thoughts on this...

I don't know much about chasms. Usually new technology adoption is drawn just like smooth S-curve. Are there real-life adoption curves where the chasm is visible? Would be interesting to compare with our graphs.

[1714482961]

1714482961

[1714482961]

1714482961

[solex]

Wary.
Don't forget that SatoshiDice started in April 2012 and kept growing until it was doing about 70% of the volume a year later. Each bet was a transaction pair in the blockchain, and some people were even using bots! Fee increases and SD internalization got rid of most of its volume by about July 2013. So the growth since then is much more of a "real world" business flow. Still, some spam-like volume coming from betting sites.

I can't see traces of this in the chart. Maybe because it's "excluding popular addresses"?

Yes, that's probably why that option is available.  

However, other business is missing, like btc purchases on Overstock from Coinbase account holders.

This is NOT decentralised though - problem is that we need micropayments in a networked economy and BTC is hostile for this.

Micropayments need to be off-chain until they reach a threshold which would be time or value based, then a summary transaction gets done on the blockchain.
Trace Mayer was on Keiser Report yesterday describing how this would work for oil sales, by charging per-barrel as it flows through a pipeline.
https://www.youtube.com/watch?v=Fyr8l9TPcLw (2nd half)

[AnonyMint]

I don't know much about chasms. Usually new technology adoption is drawn just like smooth S-curve. Are there real-life adoption curves where the chasm is visible? Would be interesting to compare with our graphs.

Chasms are apparently a speculative investment phenomenon applicable to a company or market, not a decentralized adoption of technology, which rather tends to be a logistic S curve.

[AnonyMint]

Micropayments need to be off-chain until they reach a threshold which would be time or value based, then a summary transaction gets done on the blockchain.

Then you can't pay anyone from the same account. Sorry that doesn't scale the same.

[Majormax]

What IS important is if the growth trend is slowing or not.

Agree. For example, it is reasonable to suggest that "pregnancy" is shorter for early adopters and longer for general population. Then it would be steep curve in the very beginning, then less and less steep later on. Something like this:

[IMG size=200]https://i.imgur.com/6iN9ZSA.png[/img]

EDIT: It's real data

This has probably already been mentioned at some point, but have you given any thought to 'the chasm' that is inevitably encountered during adoption of a disruptive technology?

This feature (unique to disruptive innovations, in contrast with sustaining innovations) occurs after the innovators and early adopters (who, in total, account for the first 16% of total adopters) and before the early majority jump in. It appears while the innovators and early adopters revel in the adoption of a change agent, the early majority are much more comfortable using existing tools/methods and hesitate before adopting something that requires a fundamental change to their current operations. This hesitation forms 'the chasm'.

Using 2.1 million as the value of current adoption (taken from My Wallet), and assuming we have reached the chasm, that puts the future total number of Bitcoin adopters at approximately 13 million. (Granted, this value does seem a little low, especially considering it is only 9% of PayPal's current users.)

Anyway, it would be interesting to hear your thoughts on this...

I don't know much about chasms. Usually new technology adoption is drawn just like smooth S-curve. Are there real-life adoption curves where the chasm is visible? Would be interesting to compare with our graphs.

Bitcoin is not just a new technology being adopted : It is fundamentally money, and the reflexive dynamics of profit apply. When you start looking at assets which trade in a profit pursuing environment, standard relationships and theories are not helpful (they are likely to be 'proven' wrong as soon as they are recognised)

[AnonyMint]

Bitcoin is not just a new technology being adopted : It is fundamentally money, and the reflexive dynamics of profit apply. When you start looking at assets which trade in a profit pursuing environment, standard relationships and theories are not helpful (they are likely to be 'proven' wrong as soon as they are recognised)

That is precisely my point that Bitcoin is too investor-only centric, and not enough utility-adoption-centric.

[aminorex]

Quants always fail eventually because as Armstrong points out their data sets do not encompass the long-tail events from a plurality of completed case histories going back 1000s of years.

Everything fails eventually.  You can often generate a good distribution on that pretty trivially.  All the reliability models for quant models are quant models, ultimately.

As for long tails, that makes modeling harder, not impossible.  Harder is good because it means less competition.  (Bad because it takes longer.)
I have data back to Sumerian grain markets.  One of the wealthiest people in the world spent a lot of money collecting such data for my convenient use.  (He charges an arm & a leg for it.)
Data is too sparse to be of much use by my minimal confidence threshold before Alexander the Great.

[aminorex]

How can you assert that a fit with one model is lesser fit than a fit with another model? Define 'lesser'?

The best fit is when you have a better R-squared value than any other fits. Excel calculates the best fits for every model automatically, so you can just conclude that a log-linear model has a better fit (0.94) than log-logistic (0.73).

If I am not mistaken, the best R-squared (least error from the data points) would be an N-degree polynomial for N data points such that the curve passes through every point.

Thus 'best fit' may have no correlation to predictive power.

Surely you of all people understand the concept of overfit, as it is deeply connected to ergodicity, which seems to be central to much of your thinking.
If you want a pragmatically useful and statistically rigorous treatment of overfit in predictive financial models, I suggest recent works of Marcos Lopez de Prado.
For my purposes trivial heuristics in the number of parameters are often more practical, since I need to do calculations for very large ensembles of diverse models,
but Lopez de Prado's stuff is on much firmer epistemic ground and very suitable to systems involving relatively small numbers of models (perhaps millions).

[aminorex]

If that were true, doesn't it support my thesis even more— the distribution is abnormally inequitable and thus the coin's market cap can't rise to lofty levels.

I'm not really opposed to your views, but it should be said that the Bitcoin economy works perfectly well with only a small fraction of the coins in float.  It just doesn't matter what the price is.  Volatility is more important, but it is declining with increasing price, and there are work-arounds for it.  It is technically feasible to make volatility effectively irrelevant to transactional applications.   Much wealth depends on this, so it will become pervasive.

If you're saying that bitcoin can't become valuable because it is too scarce, then I definitely have to disagree. 
If you're saying that bitcoin can't become highly utile because it is too scarce, I also disagree because of infinite divisibility.
It would be a categorical error to blindly apply models developed and tested exclusively in an environment of finite divisibility to an environment of infinite divisibility.

[Biodom]

Did you ever calculate the market cap of bitcoin with a 2000 dollar value?
That would be a current market cap of 24 billion dollars.
Such a small market cap cannot sustain any real economic transaction value, where banks, businesses and consumers use bitcoin for all kinds of offline and online financial transactions.

The $2000 is probably too low. I think $3000 is nearly assured, and $5000 - $10,000 is somewhat likely.

$10,000 x 15 million coins in 2015 = $150 billion.

Here is some justification, but apparently the Bitcoin velocity of money abnormally low for a currency and thus won't reach Paypal's scale at least not on-chain (i.e. off chain fractional reserves and debt won't be limited to Bitcoin's money supply):

https://www.paypal-media.com/about

PayPal’s net Total Payment Volume for 2013, the total value of transactions, was $180 billion, up 24% year over year on an FX neutral basis.

bitcoin value is an enigma; the values you quoted are arbitrary. Why? The transactional value (including exchange) is 2.9% for credit cards & paypal vs 2% (coinbase round trip). A lot of businesses can exist in this slice (2-2.9), but it is not a gigantic value proposition (if you ONLY consider transactions).
In fact, I would think that since the lower bound (2%) will have a natural trend to go down (to less than 1%), there is even less monetary reward in transactions.
I think that the store of value is much more interesting proposition for the increase of price of bitcoin (eventually-as it is failing right now, contrary to my expectations).

[keystroke]

My best estimate of a desirable target date for the issuers (assuming SEC does not seek to delay it unreasonably) is November 8th, 2014, which is the 10th anniversary of the issuance of GLD.   I do not have expert data required to form a mechanism-based timing estimate.

Just for fun...

EQUITY GOLD TRUST filed their S-1 on 13 May 2003. 1 year, 5 months, 3 weeks, 5 days later GLD was issued.

The S-1 for COIN was 1 July 2013. So that would put us on the 27th of December 2014.

[Peter R]

Hmm - do you say that the line you are watching is not 'USD/BTC = exp(-2.869800 + 0.003012 * D), D being the number of days' anymore? Have you changed the coefficients or have you changed it altogether so some other function?

It is always, every day, the line (or other construct) that gives the highest R^2 fit with the USD/BTC price data between 2009-1-3 and present_day. For all the time it has been an exponential function, which is linear when plotted in logarithmic space as I do.

Your comment about only one best fitting trendline only makes sense if you constrain your search space - for example by choosing only exponential functions.

A side note - if you for example allow for trendlines to be polynomials of unrestricted degree - then you'd be able to fit the trendline to the price chart exactly (with no divergencies at all).

1. Not really. Others just don't come close. 2. That's quite theoretical, since I cannot convince myself that a model with more than 2nd degree term is anything but noise with no predictive power, and Excel allows construction to 6th degree, with no improvement in R^2.

What IS important is if the growth trend is slowing or not. I currently hold the opinion that the trend is pretty much intact and price is about to increase 10x in a year. AnonyMint thinks it has slowed.

How about trigonometric functions? Have you tried them? Or polynomials with trigonometric functions? I am sure Excel have many many functions and you can combine them in many many ways - I am sure you have not tried them all. So my question is how do you chose your functions - why are you sure that exp is good and cos is not?

Exponential growth is not some "arbitrary function."  It is the solution to a very simple--and very meaningful--differential equation.  It occurs whenever the growth rate of something is proportional to the size of the thing that's growing: e.g., the population of bunny rabbits in a park, bacteria in a petri dish, or users of a social networks.      

Here's a simple model for bitcoin adoption:

============
Let N by the number of bitcoin users.  Assume that on average each user converts k non-users every year.  Each year (Δt) the change in the number of users (ΔN) is then clearly k N.  This allows us to write the differential equation¹:

  ΔN/Δt = k N

The solution to this equation is:
  
   N(t) = N₀ e^{k t}

Where N₀ is the initial number of users and N(t) is the number of users at a later time t (which clearly grows exponentially with time).  
============

Note that this is exactly the same rationale that we'd use to explain the growth of an intially-small population of bunny rabbits introduced into a park with abundant food:

Let N by the number of bitcoin users bunnies.  Assume that on average each user converts bunny creates k non-users new bunnies every year.  Each year (Δt) the change in the number of users bunnies (ΔN) is then clearly k N.  This allows us to write the differential equation:

  ΔN/Δt = k N

The solution to this equation is:
  
   N(t) = N₀ e^{k t}

Where N₀ is the initial number of users bunnies and N(t) is the number of users bunnies at a later time t (which clearly grows exponentially with time).  

The exponential function comes from a very simple and very reasonable underlying dynamical model.  You can't just say "maybe bitcoin growth is a trig function" or "maybe it's a Bessel function"--you need to refine the original differential equation with new reasonable dynamics, and then solve it to determine what the "function might be."  For example, the "logistic function" arises by noting that things do not grow exponentially forever.  Instead, the growth rate often slows down and then approaches zero when N reaches some saturation value N_sat.  The simplest way to model this is by adding the following term to original differential equation:

  ΔN/Δt = k N (1 - N / N_sat)

The solution to this is the logisitic function that SlipperySlope is using.  

For bunny rabbits, the saturation level is the equilibrium population of bunnies that the park in question can support.  For bitcoin…well time will tell.
 

TL/DR: The exponential growth model is the best/simplest model that explains bitcoin adoption to date.    

¹I should use an appropriate limiting procedure here.

[Biodom]

Hmm - do you say that the line you are watching is not 'USD/BTC = exp(-2.869800 + 0.003012 * D), D being the number of days' anymore? Have you changed the coefficients or have you changed it altogether so some other function?

It is always, every day, the line (or other construct) that gives the highest R^2 fit with the USD/BTC price data between 2009-1-3 and present_day. For all the time it has been an exponential function, which is linear when plotted in logarithmic space as I do.

Your comment about only one best fitting trendline only makes sense if you constrain your search space - for example by choosing only exponential functions.

A side note - if you for example allow for trendlines to be polynomials of unrestricted degree - then you'd be able to fit the trendline to the price chart exactly (with no divergencies at all).

1. Not really. Others just don't come close. 2. That's quite theoretical, since I cannot convince myself that a model with more than 2nd degree term is anything but noise with no predictive power, and Excel allows construction to 6th degree, with no improvement in R^2.

What IS important is if the growth trend is slowing or not. I currently hold the opinion that the trend is pretty much intact and price is about to increase 10x in a year. AnonyMint thinks it has slowed.

How about trigonometric functions? Have you tried them? Or polynomials with trigonometric functions? I am sure Excel have many many functions and you can combine them in many many ways - I am sure you have not tried them all. So my question is how do you chose your functions - why are you sure that exp is good and cos is not?

Exponential growth is not some "arbitrary function."  It is the solution to a very simple--and very meaningful--differential equation.  It occurs whenever the growth rate of something is proportional to the size of the thing that's growing: e.g., the population of bunny rabbits in a park, bacteria in a petri dish, or users of a social networks.      

Here's a simple model for bitcoin adoption:

============
Let N by the number of bitcoin users.  Assume that on average each user converts k non-users every year.  Each year (Δt) the change in the number of users (ΔN) is then clearly k N.  This allows use to write the differential equation¹:

  ΔN/Δt = k N

The solution to this equation is:
  
   N(t) = N₀ e^{k t}

Where N₀ is the initial number of users and N(t) is the number of users at a later time t (which clearly grows exponentially with time).  
============

Note that this is exactly the same rationale that we'd use to explain the growth of an intially-small population of bunny rabbits introduced into a park with abundant food:

Let N by the number of bitcoin users bunnies.  Assume that on average each user converts bunny creates k non-users new bunnies every year.  Each year (Δt) the change in the number of users bunnies (ΔN) is then clearly k N.  This allows use to write the differential equation:

  ΔN/Δt = k N

The solution to this equation is:
  
   N(t) = N₀ e^{k t}

Where N₀ is the initial number of users bunnies and N(t) is the number of users bunnies at a later time t (which clearly grows exponentially with time).  

The exponential function comes from a very simple and very reasonable underlying dynamical model.  You can't just say "maybe bitcoin growth is a trig function" or "maybe it's a Bessel function"--you need to refine the original differential equation with new reasonable dynamics, and then solve it to determine what the "function might be."  For example, the "logistic function" arises by noting that things do not grow exponentially forever.  Instead, the growth rate often slows down and then approaches zero when N reaches some saturation value N_sat.  The simplest way to model this is by adding the following term to original differential equation:

  ΔN/Δt = k N (1 - N / N_sat)

The solution to this is the logisitic function that SlipperySlope is using.  

For bunny rabbits, the saturation level is the equilibrium population of bunnies that the park in question can support.  For bitcoin…well time will tell.
 

TL/DR: The exponential growth model is the best/simplest model that explains bitcoin adoption to date.    

¹I should use an appropriate limiting procedure here.

while I agree that number of users is increasing exponentially (so far), the number of transactions is NOT, which was posted earlier.
Possible explanation-the absence of accurate statistics, but then the whole argument is mute.

[Newbie1022]

Hmm - do you say that the line you are watching is not 'USD/BTC = exp(-2.869800 + 0.003012 * D), D being the number of days' anymore? Have you changed the coefficients or have you changed it altogether so some other function?

It is always, every day, the line (or other construct) that gives the highest R^2 fit with the USD/BTC price data between 2009-1-3 and present_day. For all the time it has been an exponential function, which is linear when plotted in logarithmic space as I do.

Your comment about only one best fitting trendline only makes sense if you constrain your search space - for example by choosing only exponential functions.

A side note - if you for example allow for trendlines to be polynomials of unrestricted degree - then you'd be able to fit the trendline to the price chart exactly (with no divergencies at all).

1. Not really. Others just don't come close. 2. That's quite theoretical, since I cannot convince myself that a model with more than 2nd degree term is anything but noise with no predictive power, and Excel allows construction to 6th degree, with no improvement in R^2.

What IS important is if the growth trend is slowing or not. I currently hold the opinion that the trend is pretty much intact and price is about to increase 10x in a year. AnonyMint thinks it has slowed.

If we ever hit $5000/BTC... I give you legal ownership of my left kidney.

I like my kidneys... so what I am saying is that will never happen. Not next year. Not ever. Merry Christmas.

I could see $1500-$2000 in a bullish scenario.

Too many new players, too much regulatory bulls---, no Willy Bot, reduced black market presence, newbies getting Wall Street raped, etc., etc. Just because new adoption has, historically, been at a certain rate does not mean that this new adoption will continue out into the future. The baseline for the forecast is off.

It's, logically speaking, not terribly far off the rationale that banksters and credit agencies used in assigning inflated ratings to what were truly junk bonds -- the price of housing had not historically gone down and there had not been such a batch of foreclosures in prior history (and that sample size was much larger). However, the situation had changed... you had different people buying homes, different underwriting standards and down payment requirements, the perverse incentives created through securitization and derivatives, and balloon payments that functioned as a ticking time bomb.

Here, the dynamic that has changed is different, but the result is similar... adoption rates increased more dramatically when the price was still psychologically affordable. Now, simply having seen so many people profit, a lot of new users know that they are late to the game and that the odds are higher, now, that they'll be left holding a bag rather than profit. Tack on the fact that we went pop (moved away from black markets and towards regulation, taxation, and Wall Street) and have, resultantly, lost our hipness and appeal. Yea, this s--- is going down man. I'm not saying your math is wrong, but the application is off base.

Wait until more people start asking for wages in bitcoin... you are looking at sky high prices.  Unlike the merchants who currently accept BTC and convert instantly to $ employers would need a stock of BTC for pay day #1.  #2 Once employee is paid he rarely will spend all BTC instantly. 

This doesn't make sense, either, though. If any statistically significant amount of employees decided to be paid in Bitcoins and then they refused to spend their Bitcoins because their coins keep appreciating in value then they'd save themselves out of a job. If nobody is buying, how can you sell your wares?

In short, the proposition is at least a tad dubious.

[Peter R]

while I agree that number of users is increasing exponentially (so far), the number of transactions is NOT, which was posted earlier.
Possible explanation-the absence of accurate statistics, but then the whole argument is mute.

We don't actually have a reliable way to measure the number of bitcoin users.  The Metcalfe Value plots I prepare assume that it's correlated with the number of TXs per day and the number of unique addresses used per day.  The plot below shows that both of these two proxies for the number of users has indeed been increasing exponentially (along with bitcoin's market cap).  Today it appears that a "concave down" function would fit better than a straight line, but late last November people were arguing for a concave up (super exponential) model.   So we must wait and see.  The ups-and-downs away from exponential growth look like noise to me and are not yet significant enough to invalidate the model.  

[iCEBREAKER]

We don't actually have a reliable way to measure the number of users.  The Metcalfe Value plots I prepare assume that it's correlated with the number of TXs per day and the number of unique addresses used per day.  

Do we guesstimate the number of users from client/wallet downloads, key site (BTCT/blockchain) traffic, and Google search trends? Or what?

[wachtwoord]

We don't actually have a reliable way to measure the number of users.  The Metcalfe Value plots I prepare assume that it's correlated with the number of TXs per day and the number of unique addresses used per day.  

Do we guesstimate the number of users from client/wallet downloads, key site (BTCT/blockchain) traffic, and Google search trends? Or what?

No we just use the number of transactions per day and the number of unique addresses used per day as proxies for the number of users. It is highly likely they are strongly correlated.

[Biodom]

while I agree that number of users is increasing exponentially (so far), the number of transactions is NOT, which was posted earlier.
Possible explanation-the absence of accurate statistics, but then the whole argument is mute.

We don't actually have a reliable way to measure adoption.  The Metcalfe Value plots I prepare assume that it's correlated with the number of TXs per day and the number of unique addresses used per day.  The plot below shows that both of these two proxies for the number of users has indeed been increasing exponentially (along with bitcoin's market cap).  Today it appears that a "concave down" function would fit better than a straight line, but late last November people were arguing for a concave up (super exponential) model.   So we must wait and see.  The ups-and-downs away from exponential growth look like noise to me and are not yet significant enough to invalidate the model.  

https://i.imgur.com/SHtly3v.png

I agree re waiting, but by December it should be clear (at least short term), don't you agree?
In addition, Steve Reed's graph shows -0.7 deviation from expectation (lowest yet).
I was basing my assertion on prior OP post:

[Peter R]

I agree re waiting, but by December it should be clear (at least short term), don't you agree?

Not at all.  There is a great deal of psychological research that shows how our human minds try to find patterns that aren't really there.  A fantastic book on this topic is "Thinking Fast and Slow" by Daniel Kahneman.

IMO, the growth rate for bitcoin would need to decline strongly (or retreat over a long period) to truly invalidate the exponential growth model.  Here's a model that fixes bitcoin's market cap at inception at $500,000.  The "rationale" is that Satoshi spent approximately 2 years building it, and the market-value for Satoshi-level talent is $250,000 / year.  



I'm not arguing for this model, just pointing out that if growth slows to a more modest (but still exponential level), arguments could still be made that we are on trend.  IMO it would take a failure to reach a new ATH by 2017, or a sustained (1 year+) fall below $250, for me to say that "bitcoin growth has halted."  

...

It's so easy to be fooled by randomness.  Here's several simulations of the same underlying exponential growth model.  But instead of solving a regular differential equation to get a smooth exponential curve, I'm solving a stochastic differential equation that adds process noise.  The people in Alternate Universe #1 who get to ride the upper purple curve will think bitcoin is the most fantastic thing!  The people riding the bottom blue curve are going to make up story after story about how it's failing.  But in all cases, the only difference was randomness.  

[aminorex]

It's so easy to be fooled by randomness.  Here's several simulations of the same underlying exponential growth model.  But instead of solving a regular differential equation to get a smooth exponential curve, I'm solving a stochastic differential equation that adds process noise.  The people in Alternate Universe #1 who get to ride the upper purple curve will think bitcoin is the most fantastic thing!  The people riding the bottom blue curve are going to make up story after story about how it's failing.  But in all cases, the only difference was randomness.  

loved your example. will steal it. thanks