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).
Gas shortages at the pumps have spread from the South, all but emptying stations in Washington, D.C., following a ransomware cyberattack that forced a shutdown of the nation’s largest gasoline pipeline.

Using your mobile phone camera - scan the code below and download the Kindle app.
In the case of cryptocurrencies, academia has barely scratched the surface with respect to identifying the determinants of their prices. For example, studies by Cheah and Fry (2015) and Corbet et al. (2018) claim that Bitcoin has no intrinsic value and that its price has persistently exhibited ‘bubble-like’ behaviour. Makarov and Schoar (2018) find that the prices of Bitcoin, Ethereum, and Ripple differ across exchanges for weeks. Outside of academia, the President of the United States recently tweeted that cryptocurrencies are based on “thin air”.1