June 29, 2026

BTCONOMETRICS.COM – Nick – Medium

BTCONOMETRICS.COM – Nick – Medium

Introducing a free Bitcoin stock to flow quantitative analysis resource

There are two kinds of indicators presented here. Both relate to the statistical model for value driven by scarcity known as Stock-to-Flow

You may recall from an earlier article https://medium.com/@phraudsta/falsifying-stock-to-flow-as-a-model-of-bitcoin-value-b2d9e61f68af:

The model is a log-log Ordinary Least Squares (OLS) regression of the stock to flow value vs the bitcoin price. The model summary is presented in the top right panel at the side.

OLS regression is a way to estimate a linear relationship between two or more variables. First, let us define a linear model as some function of X that equals Y with some error.

Y = βX+ε

where Y is the dependent variable, X is the independent variable, ε is the error term and β is the multiplier of X. The goal of OLS is to estimate β such that ε is minimised.

The indicators presented at https://btconometrics.com/ are the Residual Likelihood Indicator, the Mean Reversion Indicator and the Engle-Granger Test for Cointegration.

RESIDUAL LIKELIHOOD INDICATOR

The Residual Likelihood Indicator utilises non-parametric statistical techniques to estimate the likelihood of the current difference of the price to the model. If the likelihood is low, then there is a higher chance that the price will revert to the model price, should the requirements of the model hold (i.e. the cointegration)

Figure 1 — Example of residual likelihood gauge for a particular moment in time
Figure 2 — Residual likelihood over time on the daily time step

MEAN REVERSION INDICATOR

The next indicator is simply — where the price is relative to the model. Is it above or below the expected value (or the Expectation, also known as the mean).

Now, we are making some distributional assumptions here — that is that the residuals are relatively close to normally distributed, and that the Gauss-Markov assumptions for the OLS model are not violated. This gives us the knowledge that the mean residual should be zero, the 95th quantile should be about 2 and the 5th quantile should be about -2. To avoid reliance on distributional assumptions, we are using the rank based estimate of the quantiles.

If the residuals are greater than the upper limit (roughly 2) then the price is significantly high compared to the model. If it is under the lower limit (roughly -2) then the price is significantly low compared to the model.

Used in conjunction with the Residual Likelihood, this can give some strong signals when the price is behaving not in accordance with the model, and the likelihood of such behaviour (and thus the likelihood of such behaviour continuing).

Mean Distance on a given day
When the red line crosses the 95th quantile, there is a high chance the price will not continue increasing in the short term. When the red line crosses the 5th, there is a high chance the price will not decrease any further.
Plotting the quantiles over the model and the real price shows this idea works reasonably well.

ENGLE-GRANGER COINTEGRATION TEST

I provide one very important measure of the model — the cointegration test. If the cointegration test fails then the concepts behind the mean reversion and residual likelihood indicators would also be invalid. Thus it is very important to check for the cointegration prior to assessing the other indicators. Other model diagnostics will be included in the future.

Engle-Granger cointegration test. The more negative the better. Greater than about -3 means cointegration is unlikely.

Thanks for reading, and don’t forget to visit.

If you like it — don’t forget to send me a tip via the tippin me button or the support page.

Sincerely

Nick.

Published at Sat, 01 Feb 2020 13:43:15 +0000

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