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)
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).
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.
Thanks for reading, and don’t forget to visit.
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Sincerely
Nick.
Published at Sat, 01 Feb 2020 13:43:15 +0000
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