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I did my undergrad in computer science and have minimal background in statistics (i.e., several courses during my undergrad). I've been working on a side project attempting to validate Metcalfe's Law in the context of the network value of cryptocurrencies (i.e., their price X number of coins in circulation).

Metcalfe's Law states that the value of a network is proportional to the squared number of users on the network (Y = A * X^2), where V = value of network A = a constant N = # of users on network

I am currently using Bitcoin's daily pricing data across the past ~8 years as a proxy to the value of the network, and daily transaction volume / # unique addresses as a proxy to the number of users on the network (from blockchain.info).

The question I have regarding the project is whether I have to convert the raw non-stationary time-series data into a stationary one before I conduct statistical analysis (e.g., correlation, regression). There's a huge difference in the results:

Augmented Dickey-Fuller Test on Raw Data enter image description here

Augmented Dickey-Fuller Test on Differenced Data (First Order Differencing) enter image description here

Correlation Heatmap on Raw Data enter image description here

Correlation Heatmap on Differenced Data enter image description here

The main reason I ask is because the two studies I know of that attempt to validate Metcalfe's Law with respect to Facebook and Tencent do not convert non-stationary time series data (e.g., Facebook revenue) into a stationary one before doing a least squares fit.

This has me a bit confused on whether there are instances where it's okay to conduct statistical analysis on non-stationary time series data, and any help would be appreciated.

Just in case it helps, the two studies mentioned are: (1) From Metcalfe himself: http://ieeexplore.ieee.org/document/6636305/ (2) A similar approach, but for both Facebook and Tencent: https://link.springer.com/article/10.1007/s11390-015-1518-1

Junsu Choi
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  • Welcome to CV Junsu. Your post does not seem to have a ***question*** in it! Stackexchange sites exist to [ask](https://stats.stackexchange.com/help/on-topic) and [answer](https://stats.stackexchange.com/help/how-to-answer) questions. If you simply want to discuss a topic, another kind of internet resource, such as reddit, or Andrew Gelman's blog might be a better place. Alternately, if you did mean to ask a question, you can click the "edit" link at the lower left to incorporate a question into your post. – Alexis Nov 18 '17 at 05:41
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    @Alexis I did intend to ask a question, but maybe I got too caught up in explaining the context of the question. Thanks for pointing that out, I'll edit the text to make the question clearer. – Junsu Choi Nov 18 '17 at 17:42
  • +1 Thank you. You might be interested in [a question I asked recently about (unit root) non-stationary processes and correlation](https://stats.stackexchange.com/questions/313119/how-to-prove-that-the-probability-of-spurious-correlation-increases-with-random). – Alexis Nov 19 '17 at 04:06

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