Logarithmic (non-linear) regression - Bitcoin estimated value

[solex]

Great work Trolololo.

Can't see it mentioned yet, maybe it is elsewhere, but do you have a version which utilizes the "market capitalization" (monetary base), instead of the price? For the first decade this may produce a somewhat different curve.

[mmortal03]

In this OP I will always post the last updated charts:

Calculate today's trendline price HERE

So, the trend line is currently just above $600. In terms of accuracy, it's at least closer than Stephen Reed's Million Dollar Logistic Model: https://bitcointalk.org/index.php?topic=366214.0

[Igluenza]

Awesome work Trolololo! I actually came across this thread last week & with this recent movement in price, I figured it deserved a bump.

[Trolololo]

Thanks for your acknowledgments!
I truly appreciate all your comments (and tips  )

Great work Trolololo.

Can't see it mentioned yet, maybe it is elsewhere, but do you have a version which utilizes the "market capitalization" (monetary base), instead of the price? For the first decade this may produce a somewhat different curve.

No, Risto also suggested that, but I don't have any "market capitalization" version yet.

Actually working on calculating the "real" R^2 value for the logarithmic regression, and in other curve shapes...

[keystroke]

Thanks for your acknowledgments!
I truly appreciate all your comments (and tips  )

Great work Trolololo.

Can't see it mentioned yet, maybe it is elsewhere, but do you have a version which utilizes the "market capitalization" (monetary base), instead of the price? For the first decade this may produce a somewhat different curve.

No, Risto also suggested that, but I don't have any "market capitalization" version yet.

Actually working on calculating the "real" R^2 value for the logarithmic regression, and in other curve shapes...

Agreed, a market cap version would be awesome as we are still experiencing high inflation.

[dinofelis]

I'm not sure about the exact type of growth of your function. What you seem to be mapping is logarithmic growth (slow) on a log chart (fast). Stripped of its minor constants, your formula is of the form 10^ln(t) for time = t. ln(t) grows extremely slow over time, but the result is used as a positive, growing exponent.

10^ln(x) = x^ln(10)

Thanks. Feel like an idiot for missing that.

Which would make it about quadratic growth. Interesting.

Yes I thought so too. If you buy the Metcalf's Law valuation argument (I don't entirely), that corresponds roughly with linear growth of usage. Which interestingly is what Chris Dixon has said they are seeing in his businesses (mostly Coinbase I think).

Hello everybody,

I'm pretty new to bitcoin, looked first at it this summer.  I also did some curve fitting to the historical data in log scale.  Of course, one has to be extremely cautious when extrapolating from early price movements, but intuitively the idea that the bitcoin price should "do something" is pretty clear.  I'm cautiously also buying modest amounts of bitcoin... for my retirement in a few decades, based upon similar extrapolations.

When looking at the long term (and not doing day trading), one must always look at the fundamentals.  Now, bitcoin is supposed to be a monetary asset, in the same way as fiat, or as physical gold: it doesn't serve any other purpose but as "money", that is, intermediate vector of value.  A monetary asset is in a certain way a "frozen Ponzi scheme" or a "frozen bubble" to some extend in my opinion: the only reason why you give it value today (why you want to spend real effort and other monetary assets on it) is that you believe that someone else will estimate it has value tomorrow, and that you will get something for it in return.
Shares, houses, and other investments also have a part of "monetary asset", but they usually also have another cash flow associated to them, like dividends, rent or usage (you can *live* in a house), so there is a "floor" to their price, which is their cash flow or usage.  Gold has a very limited "usage" in jewels and so on, but is essentially a nearly purely monetary asset.

Now, for a purely monetary asset, its "value" is solely determined by the "quantity theory of money", which states that in steady state:
P x Q = M x V

where P is the price of goods, Q is the quantity of goods bought with the monetary asset, M is the amount of monetary asset, and V is the average velocity of the monetary asset.

The "price of a bitcoin" B is then 1/P, and we have:

B = 1/P = Q / (M x V)

So you can expect the price of a bitcoin to be the amount of stuff (expressed in dollars) divided by the amount of bitcoin in circulation M, and divided by the velocity V.

Now, 1/V is given by the "(harmonic) average holding time" of a bitcoin between two buys, which we can call T.

We hence have:

B = Q x T / M

Or: the market capitalisation is B x M = Q x T

In other words, the market capitalisation is grossly given by the value of all stuff bought with bitcoin, times the (harmonic) average hold time of a bitcoin.

Many expectations of "too the moon" are based upon a similar "holding time" T for fiat and for bitcoin: in that case, the market capitalisation is then comparable to the fraction of the fiat market capitalisation that is done in bitcoin.

If bitcoin becomes a success, in the sense that, world wide, people buy and sell stuff in bitcoin, then this market capitalisation can be potentially huge.  Only in dollars, there are 2 - 10 trillion dollars in circulation.  World wide, the estimate (M2 money) is of the order of 55 trillion.
If bitcoin would take 1% of the world trade, its market cap would be about 550 billion dollars.  If bitcoin doesn't even buy 1% of stuff in the world, then the question can be asked whether it made sense in the first place to consider it as a monetary asset.

That is, under the assumptions of similar average hold times.

So that's about a 100-fold increase in market cap compared to now.

Essentially, this is the "amount of value" one needs bitcoins to have in order to be able to buy all that stuff, and to hold all those coins for a time T.

The crucial point is T: if people would just buy bitcoins (with fiat) to spend them immediately, then T becomes much shorter than the average hold times.  This can pretty much lower the market cap needed to buy all that stuff.  Essentially, if bitcoins are only held "a few seconds" the time to buy them with fiat, and to spend them buying some goods, you see that the market cap of bitcoin would be extremely limited.  If 1% of goods are traded in bitcoin, but bitcoins are held 100 times less long than fiat, then market cap is not going to change !

But bitcoin has promises as a store of value too, so chances are that people will actually hold on bitcoin also as "store of value".  Even more so than to fiat which has a bad reputation as store of value.  That might actually make T *longer* than the T of fiat.

However, for the moment, I have no idea, but Q is pretty low (except maybe on black markets, which do play a role in the early phases of bitcoin).

So why is bitcoin then worth something ?  I think we are still in a hugely speculative phase, where the current price of bitcoin is more the future *expectation* of what its price will be, rather than the actual value in monetary use.  Most people (like me) speculate somehow that bitcoin is going to become a success, and that people will not only use it to buy stuff (Q), but also as a store of value (T).  

This has the potential to put the bitcoin price B pretty high.

But it won't happen overnight.  You are not going to wake up, with people buying suddenly 1% of the world economy in bitcoin.   This is going to be a slow process, and to me, *this* is the fundamental value of bitcoin.   The current prices are short-term effects of traders, and the longer term consists in the long term belief of high bitcoin value, that is, a long term speculation on the value of B, as a function of Q and of T.

It can also be that bitcoin flops.  But for the moment, I'm taking a prudent bet on "to the moon", but over a decade or more.  It would be a nice complement to my retirement.  

However, in my opinion, there's no fundamental which can support a "to the moon and staying there" in the near term: Q is too low for the moment.  For bitcoin to become money, you have to buy a significant part of the world economy with it (1% is a very "significant part").

What is dangerous with curve fitting, is that there will be a transition at some point, from the "speculative" domain where we are in now, to the "monetary domain" when it is really on its monetary fundamentals.  There's no reason why fitting laws on the speculative part should have anything to do with the monetary circumstances.

[anton000]

Hello everybody,

I'm pretty new to bitcoin, looked first at it this summer.  I also did some curve fitting to the historical data in log scale.  Of course, one has to be extremely cautious when extrapolating from early price movements, but intuitively the idea that the bitcoin price should "do something" is pretty clear.  I'm cautiously also buying modest amounts of bitcoin... for my retirement in a few decades, based upon similar extrapolations.

When looking at the long term (and not doing day trading), one must always look at the fundamentals.  Now, bitcoin is supposed to be a monetary asset, in the same way as fiat, or as physical gold: it doesn't serve any other purpose but as "money", that is, intermediate vector of value.  A monetary asset is in a certain way a "frozen Ponzi scheme" or a "frozen bubble" to some extend in my opinion: the only reason why you give it value today (why you want to spend real effort and other monetary assets on it) is that you believe that someone else will estimate it has value tomorrow, and that you will get something for it in return.
Shares, houses, and other investments also have a part of "monetary asset", but they usually also have another cash flow associated to them, like dividends, rent or usage (you can *live* in a house), so there is a "floor" to their price, which is their cash flow or usage.  Gold has a very limited "usage" in jewels and so on, but is essentially a nearly purely monetary asset.

Now, for a purely monetary asset, its "value" is solely determined by the "quantity theory of money", which states that in steady state:
P x Q = M x V

where P is the price of goods, Q is the quantity of goods bought with the monetary asset, M is the amount of monetary asset, and V is the average velocity of the monetary asset.

The "price of a bitcoin" B is then 1/P, and we have:

B = 1/P = Q / (M x V)

So you can expect the price of a bitcoin to be the amount of stuff (expressed in dollars) divided by the amount of bitcoin in circulation M, and divided by the velocity V.

Now, 1/V is given by the "(harmonic) average holding time" of a bitcoin between two buys, which we can call T.

We hence have:

B = Q x T / M

Or: the market capitalisation is B x M = Q x T

In other words, the market capitalisation is grossly given by the value of all stuff bought with bitcoin, times the (harmonic) average hold time of a bitcoin.

Many expectations of "too the moon" are based upon a similar "holding time" T for fiat and for bitcoin: in that case, the market capitalisation is then comparable to the fraction of the fiat market capitalisation that is done in bitcoin.

......

Awesome analysis dinofelis.  Bitcoin's full utility must be realized before its realizes it potential value. There's also quite a difference between miner's mining costs and what market is currently paying for it. So seems like even miners are speculating or rather banking on whats its future price may be.

In short we can compare this to the discovery a new important resource:  People discover Goldoilphene, and know it has great potential and promise. But no matter how much it cost to mine/make this new discovery, the realization of this new element potential, be it in part or fully, will ultimately determine the price the market will be willing to pay for it.

[BTCtrader71]

I'm not sure about the exact type of growth of your function. What you seem to be mapping is logarithmic growth (slow) on a log chart (fast). Stripped of its minor constants, your formula is of the form 10^ln(t) for time = t. ln(t) grows extremely slow over time, but the result is used as a positive, growing exponent.

10^ln(x) = x^ln(10)

Thanks. Feel like an idiot for missing that.

Which would make it about quadratic growth. Interesting.

Yes I thought so too. If you buy the Metcalf's Law valuation argument (I don't entirely), that corresponds roughly with linear growth of usage. Which interestingly is what Chris Dixon has said they are seeing in his businesses (mostly Coinbase I think).

Hello everybody,

I'm pretty new to bitcoin, looked first at it this summer.  I also did some curve fitting to the historical data in log scale.  Of course, one has to be extremely cautious when extrapolating from early price movements, but intuitively the idea that the bitcoin price should "do something" is pretty clear.  I'm cautiously also buying modest amounts of bitcoin... for my retirement in a few decades, based upon similar extrapolations.

When looking at the long term (and not doing day trading), one must always look at the fundamentals.  Now, bitcoin is supposed to be a monetary asset, in the same way as fiat, or as physical gold: it doesn't serve any other purpose but as "money", that is, intermediate vector of value.  A monetary asset is in a certain way a "frozen Ponzi scheme" or a "frozen bubble" to some extend in my opinion: the only reason why you give it value today (why you want to spend real effort and other monetary assets on it) is that you believe that someone else will estimate it has value tomorrow, and that you will get something for it in return.
Shares, houses, and other investments also have a part of "monetary asset", but they usually also have another cash flow associated to them, like dividends, rent or usage (you can *live* in a house), so there is a "floor" to their price, which is their cash flow or usage.  Gold has a very limited "usage" in jewels and so on, but is essentially a nearly purely monetary asset.

Now, for a purely monetary asset, its "value" is solely determined by the "quantity theory of money", which states that in steady state:
P x Q = M x V

where P is the price of goods, Q is the quantity of goods bought with the monetary asset, M is the amount of monetary asset, and V is the average velocity of the monetary asset.

The "price of a bitcoin" B is then 1/P, and we have:

B = 1/P = Q / (M x V)

So you can expect the price of a bitcoin to be the amount of stuff (expressed in dollars) divided by the amount of bitcoin in circulation M, and divided by the velocity V.

Now, 1/V is given by the "(harmonic) average holding time" of a bitcoin between two buys, which we can call T.

We hence have:

B = Q x T / M

Or: the market capitalisation is B x M = Q x T

In other words, the market capitalisation is grossly given by the value of all stuff bought with bitcoin, times the (harmonic) average hold time of a bitcoin.

Many expectations of "too the moon" are based upon a similar "holding time" T for fiat and for bitcoin: in that case, the market capitalisation is then comparable to the fraction of the fiat market capitalisation that is done in bitcoin.

If bitcoin becomes a success, in the sense that, world wide, people buy and sell stuff in bitcoin, then this market capitalisation can be potentially huge.  Only in dollars, there are 2 - 10 trillion dollars in circulation.  World wide, the estimate (M2 money) is of the order of 55 trillion.
If bitcoin would take 1% of the world trade, its market cap would be about 550 billion dollars.  If bitcoin doesn't even buy 1% of stuff in the world, then the question can be asked whether it made sense in the first place to consider it as a monetary asset.

That is, under the assumptions of similar average hold times.

So that's about a 100-fold increase in market cap compared to now.

Essentially, this is the "amount of value" one needs bitcoins to have in order to be able to buy all that stuff, and to hold all those coins for a time T.

The crucial point is T: if people would just buy bitcoins (with fiat) to spend them immediately, then T becomes much shorter than the average hold times.  This can pretty much lower the market cap needed to buy all that stuff.  Essentially, if bitcoins are only held "a few seconds" the time to buy them with fiat, and to spend them buying some goods, you see that the market cap of bitcoin would be extremely limited.  If 1% of goods are traded in bitcoin, but bitcoins are held 100 times less long than fiat, then market cap is not going to change !

But bitcoin has promises as a store of value too, so chances are that people will actually hold on bitcoin also as "store of value".  Even more so than to fiat which has a bad reputation as store of value.  That might actually make T *longer* than the T of fiat.

However, for the moment, I have no idea, but Q is pretty low (except maybe on black markets, which do play a role in the early phases of bitcoin).

So why is bitcoin then worth something ?  I think we are still in a hugely speculative phase, where the current price of bitcoin is more the future *expectation* of what its price will be, rather than the actual value in monetary use.  Most people (like me) speculate somehow that bitcoin is going to become a success, and that people will not only use it to buy stuff (Q), but also as a store of value (T). 

This has the potential to put the bitcoin price B pretty high.

But it won't happen overnight.  You are not going to wake up, with people buying suddenly 1% of the world economy in bitcoin.   This is going to be a slow process, and to me, *this* is the fundamental value of bitcoin.   The current prices are short-term effects of traders, and the longer term consists in the long term belief of high bitcoin value, that is, a long term speculation on the value of B, as a function of Q and of T.

It can also be that bitcoin flops.  But for the moment, I'm taking a prudent bet on "to the moon", but over a decade or more.  It would be a nice complement to my retirement. 

However, in my opinion, there's no fundamental which can support a "to the moon and staying there" in the near term: Q is too low for the moment.  For bitcoin to become money, you have to buy a significant part of the world economy with it (1% is a very "significant part").

What is dangerous with curve fitting, is that there will be a transition at some point, from the "speculative" domain where we are in now, to the "monetary domain" when it is really on its monetary fundamentals.  There's no reason why fitting laws on the speculative part should have anything to do with the monetary circumstances.

This is an excellent analysis dinofelis and I think your thought process is spot on. I see so many people making estimates that fail to take into account velocity and are therefore fundamentally flawed. If you were to write this as an op-ed or article and get it published somewhere (coindesk perhaps), I think you would be doing the community a good service.

[nakaone]

person talking sense

thanks for the great insight.

I always thought that the quantity theory of money would fail to deal with the store of value function of money (or hodling) assuming that money is always neutral.

You seem to have a deeper understanding of that - so I have a few questions:

1.) I think that bitcoins function as a store value will for quite a long time be more important than its usage (even though being interdependent). Can you give more insight regarding factor T? Or provide a good (academic) article regarding that factor in this particular kind of analysis in QTM?

2.) It is obvious that the price is hugely driven by speculation - but given todays market capitalization (~5 Billion) we could say that it shows (no one knows if this is really possible on methodological level) that we give it a 1 % chance to get 1 % of the trade and store of value of the world economy (500 Billion). or do I misunderstand that?

3.) I always have the assumption that we as economist fail when time comes into play . But you tried to give some insight regarding that, when you say that you do not think that it will be an overnight ride to the moon and assume that it takes a decade. But let us simply assume that perception regarding bitcoin changes due to some factors. At question 2 we had a 1% chance at todays prices to reach 1% of the world market. for simplification let us assume we change to a 10% chance. Don't you think that prices would climb much faster, even given the same or nearly the same velocity?

4.) given your formula. Do you think it is possible to fill it with numbers, to give us a speculation free price of bitcoin - I think I do not completely get your factor t and how to use it.

[dinofelis]

person talking sense

thanks for the great insight.

I always thought that the quantity theory of money would fail to deal with the store of value function of money (or hodling) assuming that money is always neutral.

You seem to have a deeper understanding of that - so I have a few questions:

1.) I think that bitcoins function as a store value will for quite a long time be more important than its usage (even though being interdependent). Can you give more insight regarding factor T? Or provide a good (academic) article regarding that factor in this particular kind of analysis in QTM?

Yes, that is a good question.  My opinion (but only my personal opinion) is that for something to be a long term store of value, it needs more trust than to be a means of payment.  Both are monetary assets of course, but with different functions and time scales.  I'm strongly influenced by the Austrian school and by von Mises and Rothbard's thinking.  Of course, these people didn't know about computers and internet and so on, and they are highly tied to the gold standard, which I'm personally not.
But there's something to say for gold, which bitcoin hasn't: "historical proof of trust".
There's a difference between taking a high-risk, high potential return speculation (like I do too with bitcoin) with a small part of one's savings, and to need something to build your retirement on.  There you need trust, or (and!) diversification, to hedge the breach of trust.

So my personal opinion is that a long term store of value needs trust, and trust takes time to build.  This is why I don't believe that bitcoin, as of yet, can take a large part in the market share of the aggregate demand for "store of value" in the long term.  Of course, lots of people are holding on bitcoin, but that is *speculative*.  They think they are first adopters of a monetary asset that hasn't yet reached, by far, its full potential.  As such, the tradeoff between the lack of trust (it is too new) and the potential benefit (it will "go to the moon") turns it into nevertheless an attractive asset.  But a high-risk/high gain asset.  That's not "a store of value".

Stores of value are things that need trust.  Real estate, gold, "trust-worthy" (haha) pension funds, and a diversified portfolio.  State bonds (haha).  

The high potential gain is in my opinion not an offset for the high risk, as a storage of value.

But indeed, if bitcoin works essentially as a storage of value, then its market cap (and hence the bitcoin price) will not so much be determined by M x V = P x Q, but rather by the fraction it will cover in the aggregate demand for "storage of value" worldwide.

That is essentially unpredictable for the moment.  You could just as well assume that bitcoin will completely replace gold (6 trillion worth or something), or will replace 1% of it.  As I said, for the moment I have a hard time believing that there is sufficient trust in bitcoin to replace the century-long trust in gold.  But I may be too conservative.

For the moment, it is hard to distinguish what part of holding bitcoin is speculative for "to the moon", and what part is just "holding value".  My personal guess is that it is 99.9% the first.  That not many people are considering bitcoin as a storage of value were it not for its large potential to increase.  But then, it is *not* a storage of value, but rather a high-risk high return asset.  Like shares in a start-up.

2.) It is obvious that the price is hugely driven by speculation - but given todays market capitalization (~5 Billion) we could say that it shows (no one knows if this is really possible on methodological level) that we give it a 1 % chance to get 1 % of the trade and store of value of the world economy (500 Billion). or do I misunderstand that?

That's also how I understand it.  You should also take into account a risk aversion factor, which is especially sensitive to long-time storage of wealth, if your pension depends on it for instance.

Between something worth 100 for sure, and something worth 1000 with a chance of 10% and worth 0 with a chance of 90% (same expectation value), most people prefer the first, by a large factor.  I don't know what the risk factor is.  

3.) I always have the assumption that we as economist fail when time comes into play . But you tried to give some insight regarding that, when you say that you do not think that it will be an overnight ride to the moon and assume that it takes a decade. But let us simply assume that perception regarding bitcoin changes due to some factors. At question 2 we had a 1% chance at todays prices to reach 1% of the world market. for simplification let us assume we change to a 10% chance. Don't you think that prices would climb much faster, even given the same or nearly the same velocity?

The market ideally (ideally, because now it is probably manipulated by traders on the rather short term with effects on the longer term) takes into account all available information.  If the probability jumped from 1% to 10%, ideally, the (speculative) price should jump by a factor of 10.  But how could this probability suddenly jump ?
It could by an improbable event like a country officially adopting bitcoin as its currency.  The day the Swiss government, after a public voting, announces that the Swiss Franc is replaced by bitcoin, yes :-)  It could by an oil country announcing that oil will now be paid in bitcoin.  Or something of the kind.  Otherwise, only a smooth evolution is thinkable, no ?

4.) given your formula. Do you think it is possible to fill it with numbers, to give us a speculation free price of bitcoin - I think I do not completely get your factor t and how to use it.

Ok,let us take just an illustration.

Let us assume (it is just for sake of having an idea and an illustration, I don't imply anything) that bitcoin is *the* money for the drugs market, and for nothing else. (again, I'm not implying anything, it is just to get some numbers for an illustration).

The world drugs market is estimated, according to wiki http://en.wikipedia.org/wiki/Illegal_drug_trade to $300 billion in 2003.  So let us estimate that now at $500 billion.  Now, if the velocity of money in that world is comparable to the M2 velocity of money in the US according to the FED, that's between a factor of 2 and 4 grossly (see wiki http://en.wikipedia.org/wiki/Velocity_of_money).

If the entire drugs economy were bitcoin and nothing else were bitcoin, and we take that the bitcoin velocity is similar to the dollar velocity in the normal economy (highly uncertain) then the estimated market cap of bitcoin would be $500 billion / 4 = $ 125 billion.

We take the velocity of bitcoin here to be 4.  That means that bitcoins are traded on average 4 times a year to buy drugs with.  Some will be held years, others will be spend ten times a year.  Like your savings account and your cash in your wallet.  But on average, it is 4.

That is, if all bitcoins took part in that economy, with the same distribution of "holding times" as M2 dollar money in the US economy.

In other words, in that case, the price of bitcoin would have to rise with something like a factor of 25, to about $ 10 000,-, just to sustain the purely monetary aspect of this business.

In this case, bitcoin is not really used any more as long-term store of value than fiat dollars in the US economy.  It is the merchant usage of bitcoin that drives its price: the demand for bitcoins to be able to do all this trading sets the price.  It is what I considered with the quantity theory of money formula.

As I personally do not think that bitcoin can take a large part in the "store of value" market (without the speculative "to the moon" drive) for the moment (because of lack of trust), but I think it is merchant adoption that will be a fundamental to the bitcoin price, it is the above kind of estimation that gives an idea of what value to speculate for (multiplied with the probability of the scenario happening, and reduced with a risk aversion factor).

But I may be wrong, and it may be the "store of value" market that drives the price.  If you estimate that bitcoin will take on 1% of the gold market, that's good for $60 billion.  If you give that a 10% chance of happening, well, we are not very far from the current market cap.

[xa4]

Hey, thanks for sharing your work.

I suspect that in the very long term (reaching year 2075 i.e.) the linear price axis graph would look like an "S" curve (logistic growth). Pending task...

I'm not sure the linear price axis graph should look like an S curve. I believe this could be true for adoption or #users, network hashing power + others, their growth is bound by max resources, Bitcoin price however isn't bound by any resources in my opinion. That's why I prefer your model to Stephen Reed's logistic model, you don't have an arbitrarily $1000000 price limit.

EDIT : even #users isn't bound to max resources if you count bots, agents, DACs, machines, ... in the future.

[Joe200]

Plotting a best fitting line through a time series makes no statistical sense. It doesn't matter that you have a high R2 or that everyone else is doing it.

See here: https://bitcointalk.org/index.php?topic=600802.0

Another problem that I also discuss is that model parameters change over time. How far back should we go to estimate the current parameters going forward?

This is actually an issue now. Because if we use the past half year or a year of data to estimate model parameters -- then the trend is DOWN.

[lesni4ok]

Bitcoin logarithmic regression with inverted and scale dollar index on it.

http://www.everego.com/btc-dxy.jpg

[cbeast]

Bitcoin logarithmic regression with inverted and scale dollar index on it.

I like how the channel goes from $15 to $60k. 

[asdlolciterquit]

In this OP I will always post the last updated charts:

Calculate today's trendline price HERE

R^2 = 0,988 is not bad.

Oh, how i hope that this analysis is right, but BTC is, imho, one kind of market that can be used in this case

anywais in 4 months will see if the first prediction will be right!

[Trolololo]

As I posted time ago, R^2 is not 0'98... but quite smaller (possibly around 0'91...).
I will recalculate it in the next update.

[franckuestein]

Bitcoin logarithmic regression with inverted and scale dollar index on it.

Nice! Thanks for the update, @lesni4ok.
Could be interesting to build that charts on an online-system that updates automatically and let everyone check in real-time   Don't you think so?

I don't know if there's something similar  

[Trolololo]

Bitcoin logarithmic regression with inverted and scale dollar index on it.

Nice! Thanks for the update, @lesni4ok.
Could be interesting to build that charts on an online-system that updates automatically and let everyone check in real-time   Don't you think so?

I don't know if there's something similar  

Yes, it would be nice.

You can check today's value HERE

[79b79aa8d5047da6d3XX]

Plotting a best fitting line through a time series makes no statistical sense. [...] Another problem that I also discuss is that model parameters change over time.

Paging a statistics expert prepared to defend the use of the ordinary least squares method.

[mmortal03]

Plotting a best fitting line through a time series makes no statistical sense. [...] Another problem that I also discuss is that model parameters change over time.

Paging a statistics expert prepared to defend the use of the ordinary least squares method.

lol, did this debate fizzle before it even got started?