This study examines the volatility of stock market indices in high-income and middle-income economies. Relying on daily closing prices from January 4, 2005 to May 4, 2021 and using the Generalized Autoregressive Conditional Heteroscedastic (GARCH) model with one ARCH term and one GARCH term, the study finds evidence of long memory and mean reversion, suggesting that volatility persists but that it returns to its mean. In addition, the study finds that the latest news and prior information about volatility influence the volatility of indices, but prior information exerts greater influence. By providing a deeper understanding of stock market volatility in high-income and middle-income economies, this study contributes to the literature and provides investors, policymakers, and regulators additional insight.