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Author Topic: Monthly average USD/bitcoin price & trend  (Read 117283 times)
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November 02, 2013, 07:45:10 AM
 #21

To anyone, if we could get a graph over actual prices, and then an extension of the regression line past where we are today into say, 2014, I'd greatly appreciate that Smiley

Somebody with more skills, please!! Smiley

though if you already have the data entered in... Smiley

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November 02, 2013, 08:16:08 AM
 #22

To anyone, if we could get a graph over actual prices, and then an extension of the regression line past where we are today into say, 2014, I'd greatly appreciate that Smiley

This? :

http://bitcoincharts.com/charts/mtgoxUSD#czsg2009-09-30zeg2019-04-30ztgSzm1g10zm2g25zl

Change the custom time as you prefer

with the graph of this
-2.8 + 5.2/57(number_of_months_since_Jan_2009).

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November 02, 2013, 08:28:42 AM
 #23

To anyone, if we could get a graph over actual prices, and then an extension of the regression line past where we are today into say, 2014, I'd greatly appreciate that Smiley

Somebody with more skills, please!! Smiley

I'm on it, but what exactly is the equation?

Now, by applying log-scale and drawing a trendline using the linear regression with least square error, we find that the equation of the trendline is:

-2.8 + 5.2/57(number_of_months_since_Jan_2009).

doesn't seem right. "-2.8 + 5.2 * (number_of_months_since_Jan_2009)" maybe? Doesn't seem right either.

Confused, please help.

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November 02, 2013, 08:32:56 AM
 #24

or -2.8 + 5.2/(57(mos_since_jan_2009))

Is "57" a function or should there be a "*" behind it.

If the latter then no, that can't be it since that monotonically decreasing and always < "-2.8 + 5.2"

If the former we need the definition of "57"

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November 02, 2013, 08:47:24 AM
 #25

or -2.8 + 5.2/(57(mos_since_jan_2009))

Is "57" a function or should there be a "*" behind it.

If the latter then no, that can't be it since that monotonically decreasing and always < "-2.8 + 5.2"


isn't it on a log scale

what about

-2.8 + (5.2/57)(mos since jan 2009)

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November 02, 2013, 08:54:05 AM
 #26

I might have it correct now?



or not?

(I used "0" for <months since Jan 2009> for January 2009, btw. should I use "1")

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November 02, 2013, 09:03:57 AM
 #27

I might have it correct now?



or not?

It's correct for what I asked Smiley much appreciated molecular!

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November 02, 2013, 09:05:23 AM
 #28

I might have it correct now?



or not?

It's correct for what I asked Smiley much appreciated molecular!

sure. I can mod it any which way you guys like Wink

Turns out it wasn't correct at all, see above 2 posts.

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November 02, 2013, 09:05:31 AM
 #29

I might have it correct now?


or not?

(I used "0" for <months since Jan 2009> for January 2009, btw. should I use "1")


the regression might look off because remember, he derived it from monthly averages

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November 02, 2013, 11:02:47 AM
 #30

Seems like it should be a hair more vertical, which is good news.

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November 02, 2013, 11:41:53 AM
 #31

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).
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November 02, 2013, 12:13:59 PM
 #32

Quick'n'dirty excel job:
Edit: better time scale
http://iv.pl/images/82211820657513718314.png
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November 02, 2013, 12:24:41 PM
 #33

+1!
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November 02, 2013, 12:36:24 PM
 #34

Seems like it should be a hair more vertical, which is good news.

indeed, my hair stood vertical when i saw this graph...
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November 02, 2013, 02:43:28 PM
 #35



(I was using natural logrithm (base e) before for rpietilas function, so I got it wrong... now using hopefully correct function with base 10)

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November 02, 2013, 02:49:22 PM
 #36

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

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November 02, 2013, 05:04:55 PM
 #37

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://bitcointalk.org/index.php?topic=308567.msg3309071#msg3309071 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://bitcointalk.org/index.php?topic=137.0. 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.

Concerned that blockchain bloat will lead to centralization? Storing less than 4 GB of data once required the budget of a superpower and a warehouse full of punched cards. https://upload.wikimedia.org/wikipedia/commons/8/87/IBM_card_storage.NARA.jpg https://en.wikipedia.org/wiki/Punched_card
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November 02, 2013, 05:17:10 PM
 #38

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://bitcointalk.org/index.php?topic=308567.msg3309071#msg3309071 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://bitcointalk.org/index.php?topic=137.0. 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?

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November 02, 2013, 05:22:25 PM
 #39

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.


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November 02, 2013, 05:38:09 PM
 #40

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://bitcointalk.org/index.php?topic=308567.msg3309071#msg3309071 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://bitcointalk.org/index.php?topic=137.0. 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.

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