In order to provide a methodology to detect bubbles in time series, Phillips, Wu, and Yu [23] proposed the supremum augmented Dickey-Fuller (SADF) test. This applies a series of right-tailed unit root tests to expanding windows of a time series (with a fixed start date), defined by where r2 is the final data point to be considered in each window, starting at r0 which is a fraction representing the smallest allowed window size and expanding to 1(the complete data set).
Biais, B., C. Bisiere, M. Bouvard, C. Casamatta, and A. J. Menkveld (2018), “Equilibrium Bitcoin pricing”, Working paper .

But to understand the dynamic that led to this year’s depressing year for crypto, we actually should start a few years before 2018. In bitcoin’s early days, Mt. Gox was the go-to service for handling transactions. Then, in 2014, it halted transactions and slowly copped to a crypto-hack to the tune of $473 million, the biggest hack of its kind at the time, and it gave many people pause. But it was still early enough for people to believe that the blockchain system was still getting all the technical kinks out.
Cryptocurrencies work using a technology called blockchain. They are tokens that can be used as a form of payment in exchange for online goods and services. They carry a pre-determined store value of their own, just like any other fiat currency like the US dollar or the Indian rupee. Cryptocurrencies are digitally mined, where very sophisticated computers solve extremely complex computational mathematics problems. Their mining is painstaking, costly and only sporadically rewarding.