# Metcalfe's Law, regression / correlation across non-stationary time series vs. stationary data

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

Augmented Dickey-Fuller Test on Differenced Data (First Order Differencing)

Correlation Heatmap on Raw Data

Correlation Heatmap on Differenced Data

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

• Welcome to CV Junsu. Your post does not seem to have a question in it! Stackexchange sites exist to ask and 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. Nov 18, 2017 at 5:41
• @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. Nov 18, 2017 at 17:42
• +1 Thank you. You might be interested in a question I asked recently about (unit root) non-stationary processes and correlation. Nov 19, 2017 at 4:06