The current paper studies equity markets for the contagion of squared index returns as a proxy for stock market volatility, which has not been studied earlier. The study examines squared stock index returns of equity in 35 markets, including the US, UK, Euro Zone and BRICS (Brazil, Russia, India, China and South Africa) countries, as a proxy for the measurement of volatility. Results from the conditional heteroskedasticity long memory model show the evidence of long memory in the squared stock returns of all 35 stock indices studied. Empirical findings show the evidence of contagion during the global financial crisis (GFC) and Euro Zone crisis (EZC). The intensity of contagion varies depending on its sources. This implies that the effects of shocks are not symmetric and may have led to some structural changes. The effect of contagion is also studied by decomposing the level series into explained and unexplained behaviors.