Date   7/22/18
VWAP   $7,451.05
x   2927
y   8.916110536
a (slope) historical   0.003291732
b (intercept) historical   -0.094083644
Rsq historical   0.862594
BETI historical   -0.624
Expected Price historical   $13,901.02
Actual price / expected price historical   53.60%
Expected Date historical   1/13/18
# of Days ahead historical   -189.45
Daily VWAP Rank historical   187
Next expected price historical   $13,946.85
   
   
-2.25   $1,465.16
-2.00   $1,881.30
-1.75   $2,415.63
-1.50   $3,101.74
-1.25   $3,982.71
-1.14   $4,450.26
-1.00   $5,113.90
-0.75   $6,566.38
-0.50   $8,431.39
-0.25   $10,826.12
0.00   $13,901.02
0.25   $17,849.26
0.50   $22,918.90
0.75   $29,428.45
1.00   $37,786.88
1.25   $48,519.32
1.50   $62,300.04
1.75   $79,994.83
2.00   $102,715.40

Date   7/5/18
VWAP   $6,581.19
x   2910
y   8.791971424
a (slope) historical   0.003300186
b (intercept) historical   -0.102321079
Rsq historical   0.861406
BETI historical   -0.708
Expected Price historical   $13,361.35
Actual price / expected price historical   49.26%
Expected Date historical   12/2/17
# of Days ahead historical   -214.58
Daily VWAP Rank historical   225
Next expected price historical   $13,405.51
   
   
-2.25   $1,408.28
-2.00   $1,808.26
-1.75   $2,321.85
-1.50   $2,981.32
-1.25   $3,828.09
-1.14   $4,277.49
-1.00   $4,915.36
-0.75   $6,311.45
-0.50   $8,104.07
-0.25   $10,405.83
0.00   $13,361.35
0.25   $17,156.31
0.50   $22,029.14
0.75   $28,285.97
1.00   $36,319.91
1.25   $46,635.68
1.50   $59,881.40
1.75   $76,889.24
2.00   $98,727.74

Date   7/4/18
VWAP   $6,576.17
x   2909
y   8.791207536
a (slope) historical   0.003300690
b (intercept) historical   -0.102810479
Rsq historical   0.861336
BETI historical   -0.707
Expected Price historical   $13,330.33
Actual price / expected price historical   49.33%
Expected Date historical   12/1/17
# of Days ahead historical   -214.07
Daily VWAP Rank historical   225
Next expected price historical   $13,374.40
   
   
-2.25   $1,405.01
-2.00   $1,804.06
-1.75   $2,316.46
-1.50   $2,974.40
-1.25   $3,819.20
-1.14   $4,267.56
-1.00   $4,903.95
-0.75   $6,296.80
-0.50   $8,085.25
-0.25   $10,381.67
0.00   $13,330.33
0.25   $17,116.48
0.50   $21,978.00
0.75   $28,220.31
1.00   $36,235.59
1.25   $46,527.42
1.50   $59,742.39
1.75   $76,710.75
2.00   $98,498.55

Date   7/3/18
VWAP   $6,583.66
x   2908
y   8.792346845
a (slope) historical   0.003301193
b (intercept) historical   -0.103298972
Rsq historical   0.861266
BETI historical   -0.703
Expected Price historical   $13,299.35
Actual price / expected price historical   49.50%
Expected Date historical   12/2/17
# of Days ahead historical   -212.99
Daily VWAP Rank historical   224
Next expected price historical   $13,343.33
   
   
-2.25   $1,401.74
-2.00   $1,799.87
-1.75   $2,311.08
-1.50   $2,967.49
-1.25   $3,810.33
-1.14   $4,257.64
-1.00   $4,892.56
-0.75   $6,282.17
-0.50   $8,066.47
-0.25   $10,357.55
0.00   $13,299.35
0.25   $17,076.71
0.50   $21,926.93
0.75   $28,154.73
1.00   $36,151.39
1.25   $46,419.30
1.50   $59,603.57
1.75   $76,532.49
2.00   $98,269.67

Date   7/2/18
VWAP   $6,495.22
x   2907
y   8.778821839
a (slope) historical   0.003301694
b (intercept) historical   -0.103785239
Rsq historical   0.861195
BETI historical   -0.714
Expected Price historical   $13,268.38
Actual price / expected price historical   48.95%
Expected Date historical   11/27/17
# of Days ahead historical   -216.35
Daily VWAP Rank historical   228
Next expected price historical   $13,312.26
   
   
-2.25   $1,398.48
-2.00   $1,795.68
-1.75   $2,305.70
-1.50   $2,960.58
-1.25   $3,801.46
-1.14   $4,247.73
-1.00   $4,881.17
-0.75   $6,267.54
-0.50   $8,047.68
-0.25   $10,333.43
0.00   $13,268.38
0.25   $17,036.94
0.50   $21,875.87
0.75   $28,089.17
1.00   $36,067.21
1.25   $46,311.21
1.50   $59,464.77
1.75   $76,354.28
2.00   $98,040.83

Date   7/1/18
VWAP   $6,349.23
x   2906
y   8.756088215
a (slope) historical   0.003302203
b (intercept) historical   -0.104279407
Rsq historical   0.861126
BETI historical   -0.735
Expected Price historical   $13,237.69
Actual price / expected price historical   47.96%
Expected Date historical   11/20/17
# of Days ahead historical   -222.50
Daily VWAP Rank historical   234
Next expected price historical   $13,281.47
   
   
-2.25   $1,395.24
-2.00   $1,791.53
-1.75   $2,300.37
-1.50   $2,953.73
-1.25   $3,792.66
-1.14   $4,237.90
-1.00   $4,869.87
-0.75   $6,253.04
-0.50   $8,029.06
-0.25   $10,309.52
0.00   $13,237.69
0.25   $16,997.53
0.50   $21,825.26
0.75   $28,024.19
1.00   $35,983.77
1.25   $46,204.07
1.50   $59,327.20
1.75   $76,177.64
2.00   $97,814.02

Date   6/30/18
VWAP   $6,370.48
x   2905
y   8.759429974
a (slope) historical   0.003302728
b (intercept) historical   -0.104787853
Rsq historical   0.861058
BETI historical   -0.729
Expected Price historical   $13,207.43
Actual price / expected price historical   48.23%
Expected Date historical   11/21/17
# of Days ahead historical   -220.76
Daily VWAP Rank historical   233
Next expected price historical   $13,251.13
   
   
-2.25   $1,392.05
-2.00   $1,787.43
-1.75   $2,295.11
-1.50   $2,946.98
-1.25   $3,783.99
-1.14   $4,228.21
-1.00   $4,858.74
-0.75   $6,238.75
-0.50   $8,010.71
-0.25   $10,285.96
0.00   $13,207.43
0.25   $16,958.68
0.50   $21,775.38
0.75   $27,960.14
1.00   $35,901.53
1.25   $46,098.47
1.50   $59,191.61
1.75   $76,003.53
2.00   $97,590.46

Thanks, you're welcome.

Date   6/29/18
VWAP   $5,936.40
x   2904
y   8.688857985
a (slope) historical   0.003303248
b (intercept) historical   -0.105292582
Rsq historical   0.860990
BETI historical   -0.797
Expected Price historical   $13,177.14
Actual price / expected price historical   45.05%
Expected Date historical   10/30/17
# of Days ahead historical   -241.39
Daily VWAP Rank historical   245
Next expected price historical   $13,220.74
   
   
-2.25   $1,388.86
-2.00   $1,783.33
-1.75   $2,289.84
-1.50   $2,940.22
-1.25   $3,775.31
-1.14   $4,218.52
-1.00   $4,847.60
-0.75   $6,224.44
-0.50   $7,992.34
-0.25   $10,262.37
0.00   $13,177.14
0.25   $16,919.79
0.50   $21,725.43
0.75   $27,896.01
1.00   $35,819.19
1.25   $45,992.75
1.50   $59,055.86
1.75   $75,829.22
2.00   $97,366.64

Date   6/28/18
VWAP   $6,020.60
x   2903
y   8.702942127
a (slope) historical   0.003303818
b (intercept) historical   -0.105844696
Rsq historical   0.860929
BETI historical   -0.781
Expected Price historical   $13,148.16
Actual price / expected price historical   45.79%
Expected Date historical   11/3/17
# of Days ahead historical   -236.42
Daily VWAP Rank historical   242
Next expected price historical   $13,191.67
   
   
-2.25   $1,385.81
-2.00   $1,779.41
-1.75   $2,284.81
-1.50   $2,933.75
-1.25   $3,767.01
-1.14   $4,209.24
-1.00   $4,836.94
-0.75   $6,210.75
-0.50   $7,974.76
-0.25   $10,239.79
0.00   $13,148.16
0.25   $16,882.57
0.50   $21,677.65
0.75   $27,834.65
1.00   $35,740.40
1.25   $45,891.58
1.50   $58,925.95
1.75   $75,662.42
2.00   $97,152.47

Date   6/27/18
VWAP   $6,091.41
x   2902
y   8.714634951
a (slope) historical   0.003304376
b (intercept) historical   -0.106385735
Rsq historical   0.860866
BETI historical   -0.767
Expected Price historical   $13,118.94
Actual price / expected price historical   46.43%
Expected Date historical   11/6/17
# of Days ahead historical   -232.17
Daily VWAP Rank historical   239
Next expected price historical   $13,162.36
   
   
-2.25   $1,382.73
-2.00   $1,775.46
-1.75   $2,279.73
-1.50   $2,927.23
-1.25   $3,758.64
-1.14   $4,199.88
-1.00   $4,826.19
-0.75   $6,196.95
-0.50   $7,957.04
-0.25   $10,217.04
0.00   $13,118.94
0.25   $16,845.05
0.50   $21,629.47
0.75   $27,772.79
1.00   $35,660.97
1.25   $45,789.59
1.50   $58,795.00
1.75   $75,494.28
2.00   $96,936.57

Here's a bunch of new charts.

For ease of use, all my charts will have the following color coding:

Orange - refers to "Current" data, ie Current BETI, Current Expected Price, etc.

Red - refers to "Historical" data, ie Historical BETI, Historical Expected Price, etc.

Green - all trendlines



Chart 1 - Current BETI (orange)
  - This chart shows high and low of BETI value
  - This chart is fitted with all data from not only from that day and before that day, but also from all data up until today.
  - If you discount the first 6 months or so, this chart has much smaller amplitudes than Historical BETI
  - Current BETI and Historical BETI are always equal for today, thereafter, they drift apart
  - I personally think that Current BETI is more accurate than Historical BETI because uses all the data. However I am no math/stats major.  
  - Someone more qualified can argue it is more relevant or less relevant than Historical BETI.

Chart 2 - Historical BETI (red)
  - Chart should match jl2012's BETI chart he posts from time to time
  - This chart shows high and low of BETI value
  - As jl2012 says, for each day, a regression is fitted with all data of and before that day, so it is not a straight line.
  - Historical BETI only use the VWAP data from today and all previous days
  - Someone commented on the sloping green trendline.  I think it's just an artifact of the mathematics, but don't know. Small tilt, don't think it means much

Chart 3 - Log chart - Historical Expected Price (red) vs Current Expected Price (orange)
  - Chart should match jl2012's original chart on page 1
  - All lines are natural logs of the argument other than the black BTC price
  - Red line is Historical Expected Price.  (ln(Historical Expected Price))
  - Orange line is Current Expected Price. (ln(Current Expected Price))
  - Notice how much variance there is between the two?
  - Notice how they are currently converging?
  - Do you think the Orange Current Expected price is a trendline?
  - Let's see what happens if you put a trendline on it -- see Chart 4
  - Blue line is VWAP. (ln(VWAP))
  - Black line is actual BTC price.
  - y-axis is ln(price)

Chart 4 - Same as Chart 3, but a green trendline added
  - A green trendline of the ln(VWAP) has been added  R^2 0.861
  - Notice that the green trendline perfectly overlaps the orange Current Expected Price?
  - Which looks like a better trendline, the orange/green Current Expected Price, or the red Historical Expected Price?
  - If you like the orange/green Current Expected Price better, do you also like orange Chart 1 better?
  - If you like the red Historical Price better, do you also like the red Chart 2 better?

Chart 5 - Sanity check of Chart 3
  - Notice the chart has the same structure as Chart 3?
  - But it a non log version
  - y-axis is actual BTC VWAP

Chart 6 - Same as Chart 5, but with a green Exponential trendline thrown in
  - Why does the green trendline look like that?

Chart 7 - Same as Chart 5, but with a green Linear trendline thrown in
  - Wild curve trendline
  - I think it resembles the popular Trolololo regression chart


Later, I'll post some examples of how Expected values vs Current values change over time.  
For example, the VWAP Rankings change over time.

Charts:

https://imgur.com/a/sYJTGII

Date   6/26/18
VWAP   $6,186.03
x   2901
y   8.730048748
a (slope) historical   0.003304925
b (intercept) historical   -0.106917332
Rsq historical   0.860802
BETI historical   -0.750
Expected Price historical   $13,089.53
Actual price / expected price historical   47.26%
Expected Date historical   11/11/17
# of Days ahead historical   -226.79
Daily VWAP Rank historical   236
Next expected price historical   $13,132.86
   
   
-2.25   $1,379.63
-2.00   $1,771.48
-1.75   $2,274.62
-1.50   $2,920.67
-1.25   $3,750.21
-1.14   $4,190.47
-1.00   $4,815.37
-0.75   $6,183.06
-0.50   $7,939.20
-0.25   $10,194.14
0.00   $13,089.53
0.25   $16,807.29
0.50   $21,580.99
0.75   $27,710.54
1.00   $35,581.03
1.25   $45,686.95
1.50   $58,663.20
1.75   $75,325.05
2.00   $96,719.27

Date   6/24/18
VWAP   $5,987.55
x   2899
y   8.697437835
a (slope) historical   0.003305994
b (intercept) historical   -0.107952957
Rsq historical   0.860669
BETI historical   -0.778
Expected Price historical   $13,030.17
Actual price / expected price historical   45.95%
Expected Date historical   10/31/2017 19:05:20
# of Days ahead historical   -235.2046313
Daily VWAP Rank historical   240
Next expected price historical   $13,073.32
   
   
-2.25   $1,373.37
-2.00   $1,763.44
-1.75   $2,264.30
-1.50   $2,907.42
-1.25   $3,733.21
-1.00   $4,793.53
-0.75   $6,155.02
-0.50   $7,903.20
-0.25   $10,147.91
0.00   $13,030.17
0.25   $16,731.08
0.50   $21,483.13
0.75   $27,584.88
1.00   $35,419.69
1.25   $45,479.78
1.50   $58,397.19
1.75   $74,983.48
2.00   $96,280.69

OK.  Give me a bit of time.

Date   6/23/18
VWAP   $6,137.49
x   2898
y   8.72217093
a (slope) historical   0.003306552
b (intercept) historical   -0.108492314
Rsq historical   0.860605
BETI historical   -0.751
Expected Price historical   $13,001.15
Actual price / expected price historical   47.21%
Expected Date historical   11/7/17
# of Days ahead historical   -227.01
Daily VWAP Rank historical   235
Next expected price historical   $13,044.21
   
   
-2.25   $1,370.31
-2.00   $1,759.51
-1.75   $2,259.26
-1.50   $2,900.95
-1.25   $3,724.89
-1.00   $4,782.85
-0.75   $6,141.31
-0.50   $7,885.59
-0.25   $10,125.30
0.00   $13,001.15
0.25   $16,693.80
0.50   $21,435.27
0.75   $27,523.43
1.00   $35,340.78
1.25   $45,378.46
1.50   $58,267.09
1.75   $74,816.43
2.00   $96,066.19

OK. I hear and understand your point and it would be interesting to see the results you speak of.

But what about the 'current' chart? One can argue that since we are now in the future and have more data,  it is best to apply that data going backwards to make a more accurate chart. At this point I am not convinced the historical chart is as accurate as the current chart.

And the current chart already has a perfectly flat 0 trendline.

---

Date   6/22/18
VWAP   $6,283.20
x   2897
y   8.745634836
a (slope) historical   0.003307090
b (intercept) historical   -0.109013175
Rsq historical   0.860539
BETI historical   -0.725
Expected Price historical   $12,971.70
Actual price / expected price historical   48.44%
Expected Date historical   11/14/17
# of Days ahead historical   -219.19
Daily VWAP Rank historical   234
Next expected price historical   $13,014.67
   
   
-2.25   $1,367.21
-2.00   $1,755.53
-1.75   $2,254.14
-1.50   $2,894.38
-1.25   $3,716.45
-1.00   $4,772.02
-0.75   $6,127.40
-0.50   $7,867.73
-0.25   $10,102.37
0.00   $12,971.70
0.25   $16,655.99
0.50   $21,386.71
0.75   $27,461.08
1.00   $35,260.73
1.25   $45,275.67
1.50   $58,135.11
1.75   $74,646.96
2.00   $95,848.59

Early indications:  BETI dropped to roughly -0.725.

I see what you are saying.  I'd first have to see how to generate all the coordinates of that green line. Right now its just an auto generated green line.

I made 2 charts.  "Historical" and "Current".

I think zero is still zero and relevant in both of the charts.

"Historical" chart computes its regression parameters (slope and intercept) based on that day's parameters and all days preceding it.  However as new regression becomes available, it never uses any future data to recompute the past.

"Current" chart re-computes all past regression parameters (slope and intercept) based on all knowledge to date using current data regression parameters.  Past BETI values will change.

The latest BETI (todays) will always match on each chart.

Thereafter, the values will diverge.

My naming may be backwards or confusing.  Perhaps a better name for "Historical" would have been "Instantaneous", and maybe I should call "Current", "Historical".  

I guess its all the way you look at it.

I am not sure of the significance of the green line.  I am no maths nor stats major.

Perhaps jl2012 will be back and chime in.

Yes.  But it would take a bit of work to gather the data sources.  Merge and sort them, then I can rerun the calculations.  If someone wants to send me the merged file.