Research paper on bitcoin bubbles – the bitcoin price is “decorated with accelerating log-periodic volatility fluctuations, embodying spirals of competing expectations of higher returns (bullish) and an impending crash (bearish)”

https://arxiv.org/abs/1803.05663

The whole thing is great, here’s some more excerpts

>the price exhibits a transient faster-than-exponential growth (i.e., where the growth rate itself is growing)—resulting from positive feedbacks like herding [
24]—that is modeled by a hyperbolic power law with a singularity in finite time, i.e., endogenous ly approaching an infinite value and therefore necessitating a crash or correction before the singularity is reached

>In this paper, we have combined a generalized Metcalfe’s law, providing a fundamental value based on network characteristics, with the Log-periodic Power law Singularity (LPPLS) model, to develop a rich diagnostic of bubbles and their crashes that have punctuated the cryptocurrency’s history. In doing so, we were able to diagnose four distinct bubbles, being periods of high overvaluation and LPPLS-like trajectories, which were followed by crashes or strong corrections. Although the height and length of the bubbles vary substantially, we showed that, when scaled to the same log-height and length, a near-universal super-exponential growth is documented. This is in radical contrast to the view that crypto-markets follow a random walk and are essentially unpredictable.

>Focusing on the outlook for bitcoin, the active user data indicates a shrinking growth rate, which a range of parameterizations of our generalized Metcalfe’s law translates into slowing growth in market capitalization. Further, our Metcalfe-based analysis indicates current support levels for the bitcoin market in the range of 22–44 billion USD, at least four times less than the current level. On this basis alone, the current market resembles that of early 2014, which was followed by a year of sideways and downward movement.

I think they are pretty correct, we are in long term exponential growth, and metcalf’s law is a component of that. Due to market herding though, we also have sigmoidal bubbles along the way. It was interesting to see the sigmoidal steps in the [scatter plot](https://i.imgur.com/tFq58xs.png) of # of users against market cap.



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