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Author Topic: Top 20 days for Bitcoin  (Read 71199 times)
dree12
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January 23, 2013, 01:19:04 AM
 #1

1. 2011-06-09 W. Avg: 29.58
2. 2011-06-08 W. Avg: 27.25
3. 2011-06-10 W. Avg: 24.67
4. 2011-06-13 W. Avg: 20.11
5. 2011-06-07 W. Avg: 19.90
6. 2011-06-15 W. Avg: 19.68
7. 2011-06-14 W. Avg: 19.25
8. 2011-06-16 W. Avg: 18.86
9. 2011-06-06 W. Avg: 18.46
10. 2011-06-19 W. Avg: 17.77
11. 2011-06-11 W. Avg: 17.61
12. 2011-06-05 W. Avg: 17.32
13. 2013-01-22 W. Avg: 17.15
14. 2011-06-27 W. Avg: 17.01
15. 2011-06-28 W. Avg: 16.93
16. 2011-06-29 W. Avg: 16.88
17. 2011-06-30 W. Avg: 16.51
18. 2011-06-04 W. Avg: 16.41
19. 2013-01-21 W. Avg: 16.38
20. 2011-06-12 W. Avg: 16.21

(w. avgs rounded to 5 decimal places (mBTC) or 2 decimal places (BTC), Mt. Gox USD data before June 10, 2013; Bitstamp USD data after June 10, 2013)

Every one of the entries is in June 2011 except for the two previous days, which now rank 13th and 19th. I have a feeling that we'll break top ten soon.
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dree12
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January 23, 2013, 01:51:46 AM
 #2

Going a bit more in-depth, we have the king effect clearly seen in Bitcoin prices:


The king effect means that when Bitcoin goes back up above $30, it will either continue to rise before a sizable collapse, or collapse immediately. For example, all of the following are plausible scenarios:

  • Price remains below ~$25, with stability
  • Price rises above ~$25, then quickly collapses below ~$25, with some stability
  • Price rises above ~$25, then continues rising to around $40 before returning to the $25 to $30 level, with little stability
  • Price rises above ~$25, then continues rising to far above $25 before collapsing but remaining above $25, with almost no stability

The king effect means that it is unlikely we will see both new highs and stability. One has to go.
bb113
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January 23, 2013, 02:58:24 AM
 #3

Interesting, what assumptions would you say are being made with this model? E.g., Why should price be modeled as the log of the rank?
dree12
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January 23, 2013, 03:22:33 AM
 #4

Interesting, what assumptions would you say are being made with this model? E.g., Why should price be modeled as the log of the rank?
This is the King effect. While the majority of data points fit onto the line, the top few are above it. This suggests that we are unlikely to have the top 10 days having a similar price, i.e. there will be a significant reduction after the top is reached. This has been particularly applicable to Bitcoin so far.
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January 23, 2013, 03:44:18 AM
 #5

Interesting, what assumptions would you say are being made with this model? E.g., Why should price be modeled as the log of the rank?
This is the King effect. While the majority of data points fit onto the line, the top few are above it. This suggests that we are unlikely to have the top 10 days having a similar price, i.e. there will be a significant reduction after the top is reached. This has been particularly applicable to Bitcoin so far.

They clearly don't though. The line overestimates price around 20 and underestimates around 14.
dree12
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January 23, 2013, 03:48:58 AM
 #6

Interesting, what assumptions would you say are being made with this model? E.g., Why should price be modeled as the log of the rank?
This is the King effect. While the majority of data points fit onto the line, the top few are above it. This suggests that we are unlikely to have the top 10 days having a similar price, i.e. there will be a significant reduction after the top is reached. This has been particularly applicable to Bitcoin so far.

They clearly don't though. The line overestimates price around 20 and underestimates around 14.

That's cause my line is slightly distorted by the three kings. Slightly tilting it towards the horizontal axis would illustrate it better.
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January 23, 2013, 04:49:40 AM
 #7

This make sense to me.  If you buy into this analysis, it basically says we need to fill in some more data points around $16 - $18 before moving higher with any stability.  For the price to move higher with stability, it has to happen at a measured pace...basically to give the people that want or need to sell at these lower prices a chance to sell.  If you quickly move to much higher prices (say $50), then you'll still have a lot of people that may have been willing to sell at lower prices that are still holding.  As the price bounces around at $50, they may start to sell...and continue selling as the price experiences a substantial decline.

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January 23, 2013, 08:26:26 PM
 #8

i believe we have a new one
Weighted Avg:$17.19569

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January 23, 2013, 08:48:12 PM
 #9

would love to see this on a log scale, starting at zero.
dree12
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January 23, 2013, 08:59:35 PM
 #10

would love to see this on a log scale, starting at zero.

What do you mean by this?

i believe we have a new one
Weighted Avg:$17.19569
UTC day isn't over yet.
bb113
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January 24, 2013, 12:15:12 AM
 #11

would love to see this on a log scale, starting at zero.

What do you mean by this?



Another possible assumption is that the top 100 days is somehow different than the top 101,102, etc days. Why stop at 100? If you plot all the days then the log curve definitely does not fit. This is originally why I asked what assumptions were usually made with the king effect model. The outliers are only outliers in that they don't fit the proposed model (price=log(rank)). Its not clear from that wikipedia page why we should expect such a relationship between rank and price.
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January 24, 2013, 12:39:15 AM
 #12

    would love to see this on a log scale, starting at zero.

    What do you mean by this?



    Another possible assumption is that the top 100 days is somehow different than the top 101,102, etc days. Why stop at 100? If you plot all the days then the log curve definitely does not fit. This is originally why I asked what assumptions were usually made with the king effect model. The outliers are only outliers in that they don't fit the proposed model (price=log(rank)). Its not clear from that wikipedia page why we should expect such a relationship between rank and price.

    the wikipedia page has a good graph of population-ranking data behaving in a similar way. the idea is that the few very large data points represent statistical aberrations, as evidenced by that the rest of the price data correlate (with an extremely good r- value) on that scale.

    from this, one assumes: The price events at the top of the list represent behavior that is abnormal in relation to the rest of the [top 100]* trading days.

    *disclaimer: this data only regards the top 100 trading days and makes no prediction about the behavior of any other data set

    from this assumption, we can reason from history that these outlier price events all relate to an event generally regarded as a bubble (i.e. high prices, low stability). the full number of predictions extendable from this assumption was made clear in the OP:

    • Price remains below ~$25, with stability
    • Price rises above ~$25, then quickly collapses below ~$25, with some stability
    • Price rises above ~$25, then continues rising to around $40 before returning to the $25 to $30 level, with little stability
    • Price rises above ~$25, then continues rising to far above $25 before collapsing but remaining above $25, with almost no stability

    The king effect means that it is unlikely we will see both new highs and stability. One has to go.
    [/list]

    this sentence has fifteen words, seventy-four letters, four commas, one hyphen, and a period.
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    bb113
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    January 24, 2013, 12:45:11 AM
     #13

      would love to see this on a log scale, starting at zero.

      What do you mean by this?



      Another possible assumption is that the top 100 days is somehow different than the top 101,102, etc days. Why stop at 100? If you plot all the days then the log curve definitely does not fit. This is originally why I asked what assumptions were usually made with the king effect model. The outliers are only outliers in that they don't fit the proposed model (price=log(rank)). Its not clear from that wikipedia page why we should expect such a relationship between rank and price.

      the wikipedia page has a good graph of population-ranking data behaving in a similar way. the idea is that the few very large data points represent statistical aberrations, as evidenced by that the rest of the price data correlate (with an extremely good r- value) on that scale.

      from this, one assumes: The price events at the top of the list represent behavior that is abnormal in relation to the rest of the [top 100]* trading days.

      *disclaimer: this data only regards the top 100 trading days and makes no prediction about the behavior of any other data set

      from this assumption, we can reason from history that these outlier price events all relate to an event generally regarded as a bubble (i.e. high prices, low stability). the full number of predictions extendable from this assumption was made clear in the OP:

      • Price remains below ~$25, with stability
      • Price rises above ~$25, then quickly collapses below ~$25, with some stability
      • Price rises above ~$25, then continues rising to around $40 before returning to the $25 to $30 level, with little stability
      • Price rises above ~$25, then continues rising to far above $25 before collapsing but remaining above $25, with almost no stability

      The king effect means that it is unlikely we will see both new highs and stability. One has to go.
      [/list]

      Ok, but why does the price=log(rank) (of top 100 prices) imply stability? What is the mechanism behind this? Stability is something that is assessed over time, a factor which the above graph ignores. I'm not trying to say its wrong, just that I don't know if I follow the assumptions that need to be made to draw inferences from it.
      jl2012
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      January 24, 2013, 12:47:26 AM
       #14

      It was 17.22 yesterday, still rank #13

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      dree12
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      January 24, 2013, 03:22:47 AM
       #15

      The top 100 isn't special. The top 200 demonstrates the same effect, even more pronounced if I might say:


      BTW, today's weighted average ranks #13, making the third 2013 day that ranked in the top 20 (the remainder are from June 2011):

      1. 2011-06-09 W. Avg: 29.58
      2. 2011-06-08 W. Avg: 27.25
      3. 2011-06-10 W. Avg: 24.67
      4. 2011-06-13 W. Avg: 20.11
      5. 2011-06-07 W. Avg: 19.9
      6. 2011-06-15 W. Avg: 19.68
      7. 2011-06-14 W. Avg: 19.25
      8. 2011-06-16 W. Avg: 18.86
      9. 2011-06-06 W. Avg: 18.46
      10. 2011-06-19 W. Avg: 17.77
      11. 2011-06-11 W. Avg: 17.61
      12. 2011-06-05 W. Avg: 17.32
      13. 2013-01-23 W. Avg: 17.22
      14. 2013-01-22 W. Avg: 17.15
      15. 2011-06-27 W. Avg: 17.01
      16. 2011-06-28 W. Avg: 16.93
      17. 2011-06-29 W. Avg: 16.88
      18. 2011-06-30 W. Avg: 16.51
      19. 2011-06-04 W. Avg: 16.41
      20. 2013-01-21 W. Avg: 16.38
      jl2012
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      January 24, 2013, 03:27:16 AM
       #16

      The top 100 isn't special. The top 200 demonstrates the same effect, even more pronounced if I might say:


      BTW, today's weighted average ranks #13, making the third 2013 day that ranked in the top 20 (the remainder are from June 2011):

      1. 2011-06-09 W. Avg: 29.58
      2. 2011-06-08 W. Avg: 27.25
      3. 2011-06-10 W. Avg: 24.67
      4. 2011-06-13 W. Avg: 20.11
      5. 2011-06-07 W. Avg: 19.9
      6. 2011-06-15 W. Avg: 19.68
      7. 2011-06-14 W. Avg: 19.25
      8. 2011-06-16 W. Avg: 18.86
      9. 2011-06-06 W. Avg: 18.46
      10. 2011-06-19 W. Avg: 17.77
      11. 2011-06-11 W. Avg: 17.61
      12. 2011-06-05 W. Avg: 17.32
      13. 2013-01-23 W. Avg: 17.22
      14. 2013-01-22 W. Avg: 17.15
      15. 2011-06-27 W. Avg: 17.01
      16. 2011-06-28 W. Avg: 16.93
      17. 2011-06-29 W. Avg: 16.88
      18. 2011-06-30 W. Avg: 16.51
      19. 2011-06-04 W. Avg: 16.41
      20. 2013-01-21 W. Avg: 16.38

      If the price in the following 21 hours remains the current level, we will have a #10 record

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      dree12
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      January 24, 2013, 03:44:07 AM
       #17

      For those who are curious, here are weekly weighted averages (weeks do not start on any particular day):

      1. 2011-06-04 through 2011-06-10 W. Avg: 23.38
      2. 2011-06-05 through 2011-06-11 W. Avg: 22.62
      3. 2011-06-08 through 2011-06-14 W. Avg: 21.42
      4. 2011-06-07 through 2011-06-13 W. Avg: 21.41
      5. 2011-06-06 through 2011-06-12 W. Avg: 21.31
      6. 2011-06-03 through 2011-06-09 W. Avg: 21.30
      7. 2011-06-09 through 2011-06-15 W. Avg: 20.25
      8. 2011-06-10 through 2011-06-16 W. Avg: 19.06
      9. 2011-06-02 through 2011-06-08 W. Avg: 18.83
      10. 2011-06-13 through 2011-06-19 W. Avg: 17.84
      11. 2011-06-11 through 2011-06-17 W. Avg: 17.47
      12. 2011-06-12 through 2011-06-18 W. Avg: 17.33
      13. 2011-06-26 through 2011-07-02 W. Avg: 16.40
      14. 2011-06-27 through 2011-07-03 W. Avg: 16.38
      15. 2013-01-17 through 2013-01-23 W. Avg: 16.16
      16. 2011-06-28 through 2011-07-04 W. Avg: 15.79
      17. 2013-01-16 through 2013-01-22 W. Avg: 15.79
      18. 2013-01-15 through 2013-01-21 W. Avg: 15.31
      19. 2013-01-14 through 2013-01-20 W. Avg: 15.01
      20. 2011-06-01 through 2011-06-07 W. Avg: 14.94

      Note that June 2011 is underrepresented because of the Mt. Gox hack.

      Unsurprisingly, 2012 has dominated the top 365-day period lists (note that the leap year may cause confusion):

      1. 2012-01-25 through 2013-01-23 W. Avg: 8.07
      2. 2012-01-24 through 2013-01-22 W. Avg: 8.04
      3. 2012-01-23 through 2013-01-21 W. Avg: 8.01
      4. 2012-01-22 through 2013-01-20 W. Avg: 7.98
      5. 2012-01-21 through 2013-01-19 W. Avg: 7.96
      6. 2012-01-20 through 2013-01-18 W. Avg: 7.94
      7. 2012-01-19 through 2013-01-17 W. Avg: 7.91
      8. 2012-01-18 through 2013-01-16 W. Avg: 7.86
      9. 2012-01-17 through 2013-01-15 W. Avg: 7.82
      10. 2012-01-16 through 2013-01-14 W. Avg: 7.80
      11. 2012-01-15 through 2013-01-13 W. Avg: 7.79
      12. 2012-01-14 through 2013-01-12 W. Avg: 7.77
      13. 2012-01-13 through 2013-01-11 W. Avg: 7.75
      14. 2012-01-12 through 2013-01-10 W. Avg: 7.73
      15. 2012-01-11 through 2013-01-09 W. Avg: 7.71
      16. 2012-01-10 through 2013-01-08 W. Avg: 7.69
      17. 2012-01-09 through 2013-01-07 W. Avg: 7.67
      18. 2012-01-07 through 2013-01-05 W. Avg: 7.66
      19. 2012-01-08 through 2013-01-06 W. Avg: 7.66

      20. 2012-01-06 through 2013-01-04 W. Avg: 7.64

      The past 17 days have consistently set all time highs for the 365-day weighted average. January 6, 2012 was the last day that did not accomplish this, ending up below January 5, 2012. In 52nd place is 2010-10-11 through 2011-10-16 (which spans longer than 365 days because of the hack) with a weighted average of 7.03 USD, the highest 365-day weighted average that does not include a single day from 2012. All periods that include at least one day from 2013 (23 of them) rank in the top 23.

      Edit: Then again, the exclusion of crucial dates from June isn't necessarily fair. Here are the top thirty weekly, allowing the hack dates as zero-trade days:

      1. 2011-06-04 through 2011-06-10 W. Avg: 23.38
      2. 2011-06-05 through 2011-06-11 W. Avg: 22.62
      3. 2011-06-08 through 2011-06-14 W. Avg: 21.42
      4. 2011-06-07 through 2011-06-13 W. Avg: 21.41
      5. 2011-06-06 through 2011-06-12 W. Avg: 21.31
      6. 2011-06-03 through 2011-06-09 W. Avg: 21.30
      7. 2011-06-09 through 2011-06-15 W. Avg: 20.25
      8. 2011-06-10 through 2011-06-16 W. Avg: 19.06
      9. 2011-06-02 through 2011-06-08 W. Avg: 18.83
      10. 2011-06-13 through 2011-06-19 W. Avg: 17.84
      11. 2011-06-19 through 2011-06-25 W. Avg: 17.77
      12. 2011-06-11 through 2011-06-17 W. Avg: 17.47
      13. 2011-06-12 through 2011-06-18 W. Avg: 17.33
      14. 2011-06-14 through 2011-06-20 W. Avg: 17.26
      15. 2011-06-15 through 2011-06-21 W. Avg: 16.97
      16. 2011-06-18 through 2011-06-24 W. Avg: 16.83
      17. 2011-06-23 through 2011-06-29 W. Avg: 16.73
      18. 2011-06-22 through 2011-06-28 W. Avg: 16.68
      19. 2011-06-24 through 2011-06-30 W. Avg: 16.67
      20. 2011-06-16 through 2011-06-22 W. Avg: 16.63
      21. 2011-06-21 through 2011-06-27 W. Avg: 16.55
      22. 2011-06-25 through 2011-07-01 W. Avg: 16.51
      23. 2011-06-26 through 2011-07-02 W. Avg: 16.40
      24. 2011-06-27 through 2011-07-03 W. Avg: 16.38
      25. 2013-01-17 through 2013-01-23 W. Avg: 16.16
      26. 2011-06-17 through 2011-06-23 W. Avg: 16.01
      27. 2011-06-28 through 2011-07-04 W. Avg: 15.79
      28. 2013-01-16 through 2013-01-22 W. Avg: 15.79
      29. 2011-06-20 through 2011-06-26 W. Avg: 15.59
      30. 2013-01-15 through 2013-01-21 W. Avg: 15.31

      And the yearly now has 2010-10-15 through 2011-10-14 ranking 47th.
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      January 24, 2013, 04:49:42 AM
       #18

      In order to see the King effect, you have to make the time spans non-overlapping, or it will be dominated by a short period of very high price (i.e. June 2011)

      For those who are curious, here are weekly weighted averages (weeks do not start on any particular day):

      1. 2011-06-04 through 2011-06-10 W. Avg: 23.38
      2. 2011-06-05 through 2011-06-11 W. Avg: 22.62
      3. 2011-06-08 through 2011-06-14 W. Avg: 21.42
      4. 2011-06-07 through 2011-06-13 W. Avg: 21.41
      5. 2011-06-06 through 2011-06-12 W. Avg: 21.31
      6. 2011-06-03 through 2011-06-09 W. Avg: 21.30
      7. 2011-06-09 through 2011-06-15 W. Avg: 20.25
      8. 2011-06-10 through 2011-06-16 W. Avg: 19.06
      9. 2011-06-02 through 2011-06-08 W. Avg: 18.83
      10. 2011-06-13 through 2011-06-19 W. Avg: 17.84
      11. 2011-06-11 through 2011-06-17 W. Avg: 17.47
      12. 2011-06-12 through 2011-06-18 W. Avg: 17.33
      13. 2011-06-26 through 2011-07-02 W. Avg: 16.40
      14. 2011-06-27 through 2011-07-03 W. Avg: 16.38
      15. 2013-01-17 through 2013-01-23 W. Avg: 16.16
      16. 2011-06-28 through 2011-07-04 W. Avg: 15.79
      17. 2013-01-16 through 2013-01-22 W. Avg: 15.79
      18. 2013-01-15 through 2013-01-21 W. Avg: 15.31
      19. 2013-01-14 through 2013-01-20 W. Avg: 15.01
      20. 2011-06-01 through 2011-06-07 W. Avg: 14.94

      Note that June 2011 is underrepresented because of the Mt. Gox hack.

      Unsurprisingly, 2012 has dominated the top 365-day period lists (note that the leap year may cause confusion):

      1. 2012-01-25 through 2013-01-23 W. Avg: 8.07
      2. 2012-01-24 through 2013-01-22 W. Avg: 8.04
      3. 2012-01-23 through 2013-01-21 W. Avg: 8.01
      4. 2012-01-22 through 2013-01-20 W. Avg: 7.98
      5. 2012-01-21 through 2013-01-19 W. Avg: 7.96
      6. 2012-01-20 through 2013-01-18 W. Avg: 7.94
      7. 2012-01-19 through 2013-01-17 W. Avg: 7.91
      8. 2012-01-18 through 2013-01-16 W. Avg: 7.86
      9. 2012-01-17 through 2013-01-15 W. Avg: 7.82
      10. 2012-01-16 through 2013-01-14 W. Avg: 7.80
      11. 2012-01-15 through 2013-01-13 W. Avg: 7.79
      12. 2012-01-14 through 2013-01-12 W. Avg: 7.77
      13. 2012-01-13 through 2013-01-11 W. Avg: 7.75
      14. 2012-01-12 through 2013-01-10 W. Avg: 7.73
      15. 2012-01-11 through 2013-01-09 W. Avg: 7.71
      16. 2012-01-10 through 2013-01-08 W. Avg: 7.69
      17. 2012-01-09 through 2013-01-07 W. Avg: 7.67
      18. 2012-01-07 through 2013-01-05 W. Avg: 7.66
      19. 2012-01-08 through 2013-01-06 W. Avg: 7.66

      20. 2012-01-06 through 2013-01-04 W. Avg: 7.64

      The past 17 days have consistently set all time highs for the 365-day weighted average. January 6, 2012 was the last day that did not accomplish this, ending up below January 5, 2012. In 52nd place is 2010-10-11 through 2011-10-16 (which spans longer than 365 days because of the hack) with a weighted average of 7.03 USD, the highest 365-day weighted average that does not include a single day from 2012. All periods that include at least one day from 2013 (23 of them) rank in the top 23.

      Edit: Then again, the exclusion of crucial dates from June isn't necessarily fair. Here are the top thirty weekly, allowing the hack dates as zero-trade days:

      1. 2011-06-04 through 2011-06-10 W. Avg: 23.38
      2. 2011-06-05 through 2011-06-11 W. Avg: 22.62
      3. 2011-06-08 through 2011-06-14 W. Avg: 21.42
      4. 2011-06-07 through 2011-06-13 W. Avg: 21.41
      5. 2011-06-06 through 2011-06-12 W. Avg: 21.31
      6. 2011-06-03 through 2011-06-09 W. Avg: 21.30
      7. 2011-06-09 through 2011-06-15 W. Avg: 20.25
      8. 2011-06-10 through 2011-06-16 W. Avg: 19.06
      9. 2011-06-02 through 2011-06-08 W. Avg: 18.83
      10. 2011-06-13 through 2011-06-19 W. Avg: 17.84
      11. 2011-06-19 through 2011-06-25 W. Avg: 17.77
      12. 2011-06-11 through 2011-06-17 W. Avg: 17.47
      13. 2011-06-12 through 2011-06-18 W. Avg: 17.33
      14. 2011-06-14 through 2011-06-20 W. Avg: 17.26
      15. 2011-06-15 through 2011-06-21 W. Avg: 16.97
      16. 2011-06-18 through 2011-06-24 W. Avg: 16.83
      17. 2011-06-23 through 2011-06-29 W. Avg: 16.73
      18. 2011-06-22 through 2011-06-28 W. Avg: 16.68
      19. 2011-06-24 through 2011-06-30 W. Avg: 16.67
      20. 2011-06-16 through 2011-06-22 W. Avg: 16.63
      21. 2011-06-21 through 2011-06-27 W. Avg: 16.55
      22. 2011-06-25 through 2011-07-01 W. Avg: 16.51
      23. 2011-06-26 through 2011-07-02 W. Avg: 16.40
      24. 2011-06-27 through 2011-07-03 W. Avg: 16.38
      25. 2013-01-17 through 2013-01-23 W. Avg: 16.16
      26. 2011-06-17 through 2011-06-23 W. Avg: 16.01
      27. 2011-06-28 through 2011-07-04 W. Avg: 15.79
      28. 2013-01-16 through 2013-01-22 W. Avg: 15.79
      29. 2011-06-20 through 2011-06-26 W. Avg: 15.59
      30. 2013-01-15 through 2013-01-21 W. Avg: 15.31

      And the yearly now has 2010-10-15 through 2011-10-14 ranking 47th.

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      January 24, 2013, 07:36:30 AM
       #19

      wow if we jump $8 in one day again that's for sure da big bubble

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      this statement is false


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      January 24, 2013, 10:01:44 AM
       #20

      Ok, but why does the price=log(rank) (of top 100 prices) imply stability? What is the mechanism behind this? Stability is something that is assessed over time, a factor which the above graph ignores. I'm not trying to say its wrong, just that I don't know if I follow the assumptions that need to be made to draw inferences from it.

      there is only one assumption in the model and it was included, bolded, in my post: that since these data points are outliers, they must not adhere to whatever mechanism is constraining the rest of the trading days to the log correlation.

      there is no need to assert that the log correlation implies stability, but rather that the outliers are outliers because they occurred when trading was behaving abnormally in comparison to the rest of the data. one possible explanation for this is the extreme price instability that accompanied these outlying price events.

      in other words, we're focussing on the set of outliers, and asking: what makes them different? rather than asserting anything about the rest of the data which is unified only by the observed log rule.

      this sentence has fifteen words, seventy-four letters, four commas, one hyphen, and a period.
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