After we surpass about 5% penetration i would suggest something along the lines of a Sigmoid Function http://en.wikipedia.org/wiki/Sigmoid_function Edit With t=0 to correspond to a time in the future where one expects 50% market penetration. For t << 0 the sigmoid function approximates an exponential function
After 5% a new factor will come: Fiat's market share diminishing > fiat depreciates > everybody dumping it. Positive feedback loop, fiat run. So the jump from 5% to 100% can be very fast. 
Topic: Monthly average USD/bitcoin price & trend - page 28. (Read 118255 times)
I haven't made up my mind about how large the effect of using least squares in logarithmic space to fit a linear model vs. using least squares in linear space to fit an exponential model is. It might be negligible (or non-existant?), but it might also be large.
In the least squares method only the biggest values matter. So the shape of the curve in linear space would be defined based only on this year data. Which is not what we want. So using least squares in logarifmic space was the right way.
30 and 90 days graph on http://blockchained.com
"The fit curve is an exponential percentual to the chart least squares fit - in other words: I played around until it looked good."
The factor of increase is about 10 per year.
According to this curve Bitcoins are a little overvalued. My stash is running low and I am looking forward to a nice drop down to ~130 (with panic maybe 110) - as of now I doubt we can sustain prices above $200 for much longer....
I bet we'll not see bitcoins under 200 U$ ever !!!
Quick'n'dirty excel job:
Edit: better time scale
Edit: better time scale
+1
+1 very nice quick n dirty excel job..
Exactly what I foresee for Bitcoin future value... even more.. is this Bitcoin getting more valuable and/or Fiat U$ getting less and less valuable as more and more peoples understand the fiat ponzi ?
Welcome to the future of currency !
If we were talking about penetration, the above would hold. But now we are talking about price, and very likely the price will overshoot before finding a long-term realistic value. This has happened before with Internet stocks - userbases have grown steadily but price has behaved erratically, first growing really quickly, overshooting, collapsing, and finding stability.
Why would the new world currency "find stability"? Either the powers that be decide to let bitcoin live and take over which will lead to infinite $/Ƀ or they destroy it which leads to 0$/Ƀ. I see little in between so I also disagree with the trend flattening out at some level. Bitcoin gains utility with every business that accepts it and as soon as I can use Bitcoin for everything, I will just close my bank account and say goodbye to fiat. Why would anybody stay with fiat if bitcoin gains ultimate trust with a large percentage of the global economy?
After we surpass about 5% penetration i would suggest something along the lines of a Sigmoid Function http://en.wikipedia.org/wiki/Sigmoid_function
Edit With t=0 to correspond to a time in the future where one expects 50% market penetration. For t << 0 the sigmoid function approximates an exponential function
Edit With t=0 to correspond to a time in the future where one expects 50% market penetration. For t << 0 the sigmoid function approximates an exponential function
No. Why would that happen?
This is an excellent analysis; however there some points I wish to make:
1) The data for the BTC/USD exchange rate for 2009, and early 2010. I have managed to research this and found data for November / December 2009 and posted the results in this post https://bitcointalksearch.org/topic/m.3309071 The valuation of .005 BTC /USD is way to high. The values ranged from 0.000614866 to 0.00130719 BTC/USD. Also the "pizza valuation" would place the BTC/USD rate at around 0.0028 in May 2010. https://bitcointalksearch.org/topic/pizza-for-bitcoins-137. The net result of this is to significantly underestimate the current trend and future value.
1) The data for the BTC/USD exchange rate for 2009, and early 2010. I have managed to research this and found data for November / December 2009 and posted the results in this post https://bitcointalksearch.org/topic/m.3309071 The valuation of .005 BTC /USD is way to high. The values ranged from 0.000614866 to 0.00130719 BTC/USD. Also the "pizza valuation" would place the BTC/USD rate at around 0.0028 in May 2010. https://bitcointalksearch.org/topic/pizza-for-bitcoins-137. The net result of this is to significantly underestimate the current trend and future value.
I am aware of that pricelist, but I discarded it because it is purely theoretical - no actual trade has occurred at those prices (afaik). I have based my estimate on the following nuggests of information that I consider reliable:
- I heard that "Theymos has purchased bitcoins at an all-time Bitcoin-OTC low of 0.003"
- I heard that the pizza incident (at about ~0.0025) was for a significantly cheaper price than commonly prevailing, to induce someone to make the effort
- The Norwegian guy bought BTC5,000 for $27 (0.0054)
- The price 10-doubled when Mt.Gox opened (to 0.08, i.e. from 0.008)
Since I do not have a reliable OTC price history at my disposal, I estimated the whole time to be a flat 0.005. But if someone wants to add to the information, please do!
Quote
2) The exponential model works well only when the market penetration is very low say below 5% since it neglects the probability of a newbie attempting to introduce Bticoin to a veteran. Based upon the value of the world M1 money supply approximately 20 trillion USD and the world gold supply approximately 8.2 trillion USD I would say this model will start to break down between 50,000 and 100,000 BTC/USD.
If we were talking about penetration, the above would hold. But now we are talking about price, and very likely the price will overshoot before finding a long-term realistic value. This has happened before with Internet stocks - userbases have grown steadily but price has behaved erratically, first growing really quickly, overshooting, collapsing, and finding stability.
I could not resist:
http://xkcd.com/605/
http://xkcd.com/605/
30 and 90 days graph on http://blockchained.com
"The fit curve is an exponential percentual to the chart least squares fit - in other words: I played around until it looked good."
The factor of increase is about 10 per year.
According to this curve Bitcoins are a little overvalued. My stash is running low and I am looking forward to a nice drop down to ~130 (with panic maybe 110) - as of now I doubt we can sustain prices above $200 for much longer....
I agree on your points about the exponential model. What would be another model you would suggest for after we surpass ~5% penetration?
After we surpass about 5% penetration i would suggest something along the lines of a Sigmoid Function http://en.wikipedia.org/wiki/Sigmoid_function
Edit With t=0 to correspond to a time in the future where one expects 50% market penetration. For t << 0 the sigmoid function approximates an exponential function
(I was using natural logrithm (base e) before for rpietilas function, so I got it wrong... now using hopefully correct function with base 10)
If these graphs are correct, or even close, it really puts things into perspective. $200 per coin is still so low. And some people are saying we are already into the late adoption phase? With these graphs it shows how we are still early adopters for sure and even the small amount of coin some of us are holding is still great in the big scheme of things.
This is an excellent analysis; however there some points I wish to make:
1) The data for the BTC/USD exchange rate for 2009, and early 2010. I have managed to research this and found data for November / December 2009 and posted the results in this post https://bitcointalksearch.org/topic/m.3309071 The valuation of .005 BTC /USD is way to high. The values ranged from 0.000614866 to 0.00130719 BTC/USD. Also the "pizza valuation" would place the BTC/USD rate at around 0.0028 in May 2010. https://bitcointalksearch.org/topic/pizza-for-bitcoins-137. The net result of this is to significantly underestimate the current trend and future value.
2) The exponential model works well only when the market penetration is very low say below 5% since it neglects the probability of a newbie attempting to introduce Bticoin to a veteran. Based upon the value of the world M1 money supply approximately 20 trillion USD and the world gold supply approximately 8.2 trillion USD I would say this model will start to break down between 50,000 and 100,000 BTC/USD.
3) I am not concerned about the use of a least squares fit in logarithmic space.
1) The data for the BTC/USD exchange rate for 2009, and early 2010. I have managed to research this and found data for November / December 2009 and posted the results in this post https://bitcointalksearch.org/topic/m.3309071 The valuation of .005 BTC /USD is way to high. The values ranged from 0.000614866 to 0.00130719 BTC/USD. Also the "pizza valuation" would place the BTC/USD rate at around 0.0028 in May 2010. https://bitcointalksearch.org/topic/pizza-for-bitcoins-137. The net result of this is to significantly underestimate the current trend and future value.
2) The exponential model works well only when the market penetration is very low say below 5% since it neglects the probability of a newbie attempting to introduce Bticoin to a veteran. Based upon the value of the world M1 money supply approximately 20 trillion USD and the world gold supply approximately 8.2 trillion USD I would say this model will start to break down between 50,000 and 100,000 BTC/USD.
3) I am not concerned about the use of a least squares fit in logarithmic space.
Wow, thanks for researching this early data. So the first datapoint you have researched is October 5th 2009?
I agree on your points about the exponential model. What would be another model you would suggest for after we surpass ~5% penetration?
(note: For some reason your point 3) did not show in your post, only saw it when replying, strange)
I haven't made up my mind about how large the effect of using least squares in logarithmic space to fit a linear model vs. using least squares in linear space to fit an exponential model is. It might be negligible (or non-existant?), but it might also be large.
I want to try to fit some models, but first I need at least some data for pre-gox era. Your numbers help a lot. What would you suggest I could do for the time before your first data point in October 2009. I could just use "0" or interpolate linearly from 0 (Jan 3rd 2009) to your first datapoint. Any ideas?
I added point 3) in an edit that is why it did not show up right away. My suggestion for before October 2009 is to add some points based upon the cost of electricity of a mid range CPU mining Bitcoin at a difficulty of 1. Maybe one or two. The mining valuation is appropriate for 2009 since there was not much trading then. I would not use more than say 0.0001 before June 2009. 0 is not an option because it is a logarithmic scale. Between December 2009 and May 2010 (pizza) I would simply interpolate. In my opinion it is best to not include a point that a wild guess for early 2009 because these points will skew the results.
I just saw that early data was calculated using electricity prices and this one guys mining output. So these are not trading prices. But I think we can still use them for the purposes of this thread and other attempts to model exchange rate. It's the best we've got, it seems.
This is an excellent analysis; however there some points I wish to make:
1) The data for the BTC/USD exchange rate for 2009, and early 2010. I have managed to research this and found data for November / December 2009 and posted the results in this post https://bitcointalksearch.org/topic/m.3309071 The valuation of .005 BTC /USD is way to high. The values ranged from 0.000614866 to 0.00130719 BTC/USD. Also the "pizza valuation" would place the BTC/USD rate at around 0.0028 in May 2010. https://bitcointalksearch.org/topic/pizza-for-bitcoins-137. The net result of this is to significantly underestimate the current trend and future value.
2) The exponential model works well only when the market penetration is very low say below 5% since it neglects the probability of a newbie attempting to introduce Bticoin to a veteran. Based upon the value of the world M1 money supply approximately 20 trillion USD and the world gold supply approximately 8.2 trillion USD I would say this model will start to break down between 50,000 and 100,000 BTC/USD.
3) I am not concerned about the use of a least squares fit in logarithmic space.
1) The data for the BTC/USD exchange rate for 2009, and early 2010. I have managed to research this and found data for November / December 2009 and posted the results in this post https://bitcointalksearch.org/topic/m.3309071 The valuation of .005 BTC /USD is way to high. The values ranged from 0.000614866 to 0.00130719 BTC/USD. Also the "pizza valuation" would place the BTC/USD rate at around 0.0028 in May 2010. https://bitcointalksearch.org/topic/pizza-for-bitcoins-137. The net result of this is to significantly underestimate the current trend and future value.
2) The exponential model works well only when the market penetration is very low say below 5% since it neglects the probability of a newbie attempting to introduce Bticoin to a veteran. Based upon the value of the world M1 money supply approximately 20 trillion USD and the world gold supply approximately 8.2 trillion USD I would say this model will start to break down between 50,000 and 100,000 BTC/USD.
3) I am not concerned about the use of a least squares fit in logarithmic space.
Wow, thanks for researching this early data. So the first datapoint you have researched is October 5th 2009?
I agree on your points about the exponential model. What would be another model you would suggest for after we surpass ~5% penetration?
(note: For some reason your point 3) did not show in your post, only saw it when replying, strange)
I haven't made up my mind about how large the effect of using least squares in logarithmic space to fit a linear model vs. using least squares in linear space to fit an exponential model is. It might be negligible (or non-existant?), but it might also be large.
I want to try to fit some models, but first I need at least some data for pre-gox era. Your numbers help a lot. What would you suggest I could do for the time before your first data point in October 2009. I could just use "0" or interpolate linearly from 0 (Jan 3rd 2009) to your first datapoint. Any ideas?
This is an excellent analysis; however there some points I wish to make:
1) The data for the BTC/USD exchange rate for 2009, and early 2010. I have managed to research this and found data for November / December 2009 and posted the results in this post https://bitcointalksearch.org/topic/m.3309071 The valuation of .005 BTC /USD is way to high. The values ranged from 0.000614866 to 0.00130719 BTC/USD. Also the "pizza valuation" would place the BTC/USD rate at around 0.0028 in May 2010. https://bitcointalksearch.org/topic/pizza-for-bitcoins-137. The net result of this is to significantly underestimate the current trend and future value.
2) The exponential model works well only when the market penetration is very low say below 5% since it neglects the probability of a newbie attempting to introduce Bticoin to a veteran. Based upon the value of the world M1 money supply approximately 20 trillion USD and the world gold supply approximately 8.2 trillion USD I would say this model will start to break down between 50,000 and 100,000 BTC/USD.
Edit: 3) I am not concerned about the use of a least squares fit in logarithmic space.
1) The data for the BTC/USD exchange rate for 2009, and early 2010. I have managed to research this and found data for November / December 2009 and posted the results in this post https://bitcointalksearch.org/topic/m.3309071 The valuation of .005 BTC /USD is way to high. The values ranged from 0.000614866 to 0.00130719 BTC/USD. Also the "pizza valuation" would place the BTC/USD rate at around 0.0028 in May 2010. https://bitcointalksearch.org/topic/pizza-for-bitcoins-137. The net result of this is to significantly underestimate the current trend and future value.
2) The exponential model works well only when the market penetration is very low say below 5% since it neglects the probability of a newbie attempting to introduce Bticoin to a veteran. Based upon the value of the world M1 money supply approximately 20 trillion USD and the world gold supply approximately 8.2 trillion USD I would say this model will start to break down between 50,000 and 100,000 BTC/USD.
Edit: 3) I am not concerned about the use of a least squares fit in logarithmic space.
No the above chart is wrong.
I hope I got it right now (you didn't state what base the log should have, I used e instead of 10)
This is derived using not gut feeling, but the generally accepted least squares method (meaning approximately that the trendline is fitted such that there is the same area between the price above and the trendline, as there is between price below and the trendline).
There can be a criticism made regarding your methodology: while it might be generally accepted to use least square method, it probably isn't generally accepted to use it in log space.
I think you will get different results when you fit an exponential function ( price = a + 10 ^ time ) in linear space to the data using least squares.
EDIT: I think most here would agree that attributing much predictive power to this approach is questionable anyways, though.
But it sure is fun!
EDIT2: I agree with the function that $1,000/BTC by April 2014 is reasonable
(I was using natural logrithm (base e) before for rpietilas function, so I got it wrong... now using hopefully correct function with base 10)
Seems like it should be a hair more vertical, which is good news.
indeed, my hair stood vertical when i saw this graph...
+1!
No the above chart is wrong.
We have seen million regression charts using mtgox daily, this is the novel approach of having volume weighted monthly prices going all the way to January 2009. So please use the data in OP. If drawing the line is the difficult part, it goes straight between these points:
January 2009:
10^(-2.8 + 5.2/57*(0)) = 0.0016 $/BTC
November 2013:
10^(-2.8 + 5.2/57*(58)) = 310 $/BTC
This is derived using not gut feeling, but the generally accepted least squares method (meaning approximately that the trendline is fitted such that there is the same area between the price above and the trendline, as there is between price below and the trendline).
We have seen million regression charts using mtgox daily, this is the novel approach of having volume weighted monthly prices going all the way to January 2009. So please use the data in OP. If drawing the line is the difficult part, it goes straight between these points:
January 2009:
10^(-2.8 + 5.2/57*(0)) = 0.0016 $/BTC
November 2013:
10^(-2.8 + 5.2/57*(58)) = 310 $/BTC
This is derived using not gut feeling, but the generally accepted least squares method (meaning approximately that the trendline is fitted such that there is the same area between the price above and the trendline, as there is between price below and the trendline).
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