The next phase in the crypto mining process is to compile a list of all transactions, which is subsequently included in a new unconfirmed data block. It avoids “double spending” of any cryptocurrency and keeps a permanent and public record by adding their transaction to the blockchain, once the verification procedure is complete. The record is immutable, which means it can never be changed or corrupted.
Although this test successfully detects single isolated bubbles, Phillips, Shi, and Yu [24] acknowledge it may suffer from reduced discriminatory power when applied to time series with multiple occurrences of bubbles. To overcome this weakness, a further enhancement was proposed, as a new method, called a generalized supremum ADF (GSADF) test. This test allows both the start and end points of data subsets to vary, which in turn enables the identification of multiple bubble regimes in one observed time series. The GSADF test is defined by

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