  The year 2017 saw the rise and fall of the crypto-currency market, followed
by high variability in the price of all crypto-currencies. In this work, we
study the abrupt transition in crypto-currency residuals, which is associated
with the critical transition (the phenomenon of critical slowing down) or the
stochastic transition phenomena. We find that, regardless of the specific
crypto-currency or rolling window size, the autocorrelation always fluctuates
around a high value, while the standard deviation increases monotonically.
Therefore, while the autocorrelation does not display signals of critical
slowing down, the standard deviation can be used to anticipate critical or
stochastic transitions. In particular, we have detected two sudden jumps in the
standard deviation, in the second quarter of 2017 and at the beginning of 2018,
which could have served as early warning signals of two majors price collapses
that have happened in the following periods. We finally propose a mean-field
phenomenological model for the price of crypto-currency to show how the use of
the standard deviation of the residuals is a better leading indicator of the
collapse in price than the time series' autocorrelation. Our findings represent
a first step towards a better diagnostic of the risk of critical transition in
the price and/or volume of crypto-currencies.
