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Catastrophic breaks of high-frequency financial data usually contain important information, and it is crucial for investment decision making to accurately detect and analyze these catastrophic breaks. In this paper, we use a robust algorithm, the local linear scale approximation (LLSA), which enriches nonlinear filtering methods in data mining to detect and reconstruct catastrophic breaks. Guided by this methodology, we detect the catastrophic breaks in the high-frequency financial data of the Shanghai composite index from 2015 to 2018, and ten catastrophic breaks are found. Our results confirm that the LLSA is able to preserve smooth trends and accurately display any catastrophic breaks. In addition, we find that all these breaks are consistent with three types of economic events — the adjustment of monetary policies, the introduction of macroeconomic policies or government guidance, and the revolutionary events of the securities market. Explanations are given for the emergence of these events. • We employ local linear scaling approximation to investigate its implementation in detecting catastrophic breaks of high-frequency financial time series. • We conduct an empirical study using the one-minute data of the Shanghai composite index and ten catastrophic breaks are determined. • Local linear scaling approximation improves accuracy of the detection and reconstruction of catastrophic breaks compared with maximal overlap discrete wavelet transform. • Catastrophic breaks in high-frequency financial time series and major economic and financial events are closely related. • Local linear scaling approximation is suitable for high-frequency data mining. [ABSTRACT FROM AUTHOR]