Before revision:  We account for the damping condition of LPPLS model in the search space and implement the stricter filter conditions for the qualification of the valid LPPLS fits by taking account of the maximum relative error,  Lomb log-periodic test of the detrended residual, and unit-root tests of the logarithmic residual based on both the Phillips-Perron test and Dickey-Fuller test to improve the performance of LPPLS confidence indicator.
After revision:  We account for the damping condition of LPPLS model in the search space and implement the stricter filter conditions for the qualification of the valid LPPLS fits by taking account of the maximum relative error, performing the Lomb log-periodic test of the detrended residual, and unit-root tests of the logarithmic residual based on both the Phillips-Perron test and Dickey-Fuller test to improve the performance of LPPLS confidence indicator.