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Most asset return series, especially those in high frequency, show high excess kurtosis and persistence in volatility that cannot be adequately described by the generalized conditional heteroscedastic (GARCH) model, even with heavy-tailed innovations. Many researchers have argued that these characteristics are due to shifts in volatility that may be associated with significant economic events such as financial crises. Indeed, several authors have investigated the case of pure structural changes, in which all of the parameters in the GARCH model are assumed to change simultaneously. In this paper, we take an alternative approach by studying the case in which changes occur in individual parameters of a GARCH model. We investigate the impacts of such changes on the underlying return series and its volatility, and propose an iterative procedure to detect them. In all cases, the changes affect permanently the level of the volatility, but in some cases, the changes also alter the dynamic structure of the volatility series. Monte Carlo experiments are used to investigate the performance of the proposed procedure in finite samples, and real examples are used to demonstrate the impacts of detected volatility changes and the efficacy of the proposed procedure. Practical implications of the parameter changes in financial applications are also discussed.