In this article, we test for the presence of structural breaks in volatility by two alternative approaches: the Iterative Cumulative Sum of Squares (ICSS) algorithm and wavelet analysis. Specifically, we look at the effect of the outbreak of the Asian crisis and the terrorist attacks of September 11, 2001 on Emerging Asia. Europe. Latin America and North America's stock markets. In addition, we focus on the behavior of interest rates in Chile after the Central Bank switched its monetary policy interest rate from an inflation-indexed to a nominal target in August 2001. Our estimation results show that the number of shifts detected by the two methods is substantially reduced when filtering out the data for both conditional heteroskedasticity and serial correlation.