Bitcoin Growth Curves đ [BPLabs]
BlockParty Labs: Bitcoin Growth Curves đ
BTC/USD price shows logarithmic progression over time, famously described by the Logarithmic Growth Curve (LGC) model.
This relationship between price and time can be displayed on a so-called "log-log" plot, where both axes are plotted logarithmically. From the log-log plot, we can perform standard linear regression on all points to get the average (Mean) price over time. We call this the "Fair Value" line.
Regular "OLS Linear Regression" may not be the best choice here however due to the assumption of normal distribution about a mean (here we have skew and outliers). Instead we can perform "Quantile Regression" using Median instead of Mean to arrive at our Fair Value line and so we are less influenced by outliers or non-normal distribution. The 50% quantile gives us the Median line and we can also take the 0.1%, 1%, 99% & 99.9% quantiles to give us lower and upper bounds respectively. Fair Value regresses "close" data points, whereas extreme quantiles regress the wicks' datasets ("low" & "high"). Dividing the area into 5 sections between the Fair Value line and the lower and upper boundaries gives us Buy and Sell zones. (Percentages chosen using Golden Ratio to best average out the space on logarithmic scale.)
Here we explore several prediction models:
QR = Standard Quantile Regression (QR) Model without any adjustments
DXY = Deflate BTC price as DXY increases, use this as basis for regression
M2 = Inflate BTC price as USD M2 Money Supply increases
DXY/M2 = Combination of DXY and M2 adjustments
Note: Future price model assumes current debasement level continues flat as we cannot predict the multi-variate future here.
Stock-to-Flow Model from PlanB (@100trillion) has also been included. We explore three S2F variations:
S2F-Original = PlanB Logarithmic Regression on Stock-to-Flow with blocks produced evenly across epochs (theoretical assumption)
S2F-AnnualCycle = Variation where Epochs are split into four and flow rates regressed sub-cycle of the epoch: 1, 2, 3, 4 (i.e. each approximate year in every epoch use the same S2F assumption, etc.). Flow is historical and not theoretical (what was actually produced in that section of each epoch).
S2F-AnnualCycle_DXY/M2 = Same as S2F-AnnualCycle, but debased/inflated as above with DXY and M2 adjustments.
BTC/USD price shows logarithmic progression over time, famously described by the Logarithmic Growth Curve (LGC) model.
This relationship between price and time can be displayed on a so-called "log-log" plot, where both axes are plotted logarithmically. From the log-log plot, we can perform standard linear regression on all points to get the average (Mean) price over time. We call this the "Fair Value" line.
Regular "OLS Linear Regression" may not be the best choice here however due to the assumption of normal distribution about a mean (here we have skew and outliers). Instead we can perform "Quantile Regression" using Median instead of Mean to arrive at our Fair Value line and so we are less influenced by outliers or non-normal distribution. The 50% quantile gives us the Median line and we can also take the 0.1%, 1%, 99% & 99.9% quantiles to give us lower and upper bounds respectively. Fair Value regresses "close" data points, whereas extreme quantiles regress the wicks' datasets ("low" & "high"). Dividing the area into 5 sections between the Fair Value line and the lower and upper boundaries gives us Buy and Sell zones. (Percentages chosen using Golden Ratio to best average out the space on logarithmic scale.)
Here we explore several prediction models:
QR = Standard Quantile Regression (QR) Model without any adjustments
DXY = Deflate BTC price as DXY increases, use this as basis for regression
M2 = Inflate BTC price as USD M2 Money Supply increases
DXY/M2 = Combination of DXY and M2 adjustments
Note: Future price model assumes current debasement level continues flat as we cannot predict the multi-variate future here.
Stock-to-Flow Model from PlanB (@100trillion) has also been included. We explore three S2F variations:
S2F-Original = PlanB Logarithmic Regression on Stock-to-Flow with blocks produced evenly across epochs (theoretical assumption)
S2F-AnnualCycle = Variation where Epochs are split into four and flow rates regressed sub-cycle of the epoch: 1, 2, 3, 4 (i.e. each approximate year in every epoch use the same S2F assumption, etc.). Flow is historical and not theoretical (what was actually produced in that section of each epoch).
S2F-AnnualCycle_DXY/M2 = Same as S2F-AnnualCycle, but debased/inflated as above with DXY and M2 adjustments.
Versionsinformation:
Updated All Quantile Regression to include the latest data up to September 2022
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Added Pi Cycle Reversal
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Split out log-growth introduction for better visibility on smaller screens. Turned off forecast table by default.
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For those tracking the up-coming Pi-Cycle Bottom Reversal, added ability to display underlying moving-averages on which Pi-Cycle theory is based.
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Cosmetic update
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* Updated to latest data November 2022
* US Federal Reserve changed their reporting structure by removing the Billions denominator which caused a display bug - this is now fixed. I guess 9 more zeros are more palatable these days, lol
* DXY was off by 1% due to dataset, this is now fixed.
* Removed "BTC Supply" model as invalidated (previously noted it didn't adjust for lost supply, likely why it's off)
* Fixed bug with S2F Adjusted Model
* Future regression lines for display purposes expanded to 90 day average instead of 30 days (1-month doesn't smooth things out given all the recent changes)
* US Federal Reserve changed their reporting structure by removing the Billions denominator which caused a display bug - this is now fixed. I guess 9 more zeros are more palatable these days, lol
* DXY was off by 1% due to dataset, this is now fixed.
* Removed "BTC Supply" model as invalidated (previously noted it didn't adjust for lost supply, likely why it's off)
* Fixed bug with S2F Adjusted Model
* Future regression lines for display purposes expanded to 90 day average instead of 30 days (1-month doesn't smooth things out given all the recent changes)