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The year 2017 saw the rise and fall of the crypto-currency market, followedby high variability in the price of all crypto-currencies. In this work, westudy the abrupt transition in crypto-currency residuals, which is associatedwith the critical transition (the phenomenon of critical slowing down) or thestochastic transition phenomena. We find that, regardless of the specificcrypto-currency or rolling window size, the autocorrelation always fluctuatesaround a high value, while the standard deviation increases monotonically.Therefore, while the autocorrelation does not display signals of criticalslowing down, the standard deviation can be used to anticipate critical orstochastic transitions. In particular, we have detected two sudden jumps in thestandard 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 collapsesthat have happened in the following periods. We finally propose a mean-fieldphenomenological model for the price of crypto-currency to show how the use ofthe standard deviation of the residuals is a better leading indicator of thecollapse in price than the time series' autocorrelation. Our findings representa first step towards a better diagnostic of the risk of critical transition inthe price and/or volume of crypto-currencies.

Critical slowing down associated with critical transition and risk of collapse in cryptocurrency