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We investigate potential mean and volatility spillovers among sovereign bond yield spreads for five peripheral countries of the euro area. We focus on Greece, Ireland, Italy, Portugal and Spain during the European sovereign debt crisis. We propose a bootstrap bias-corrected bivariate Vector Autoregressive Moving Average (VARMA), GARCH-in-Mean, asymmetric BEKK model, and find that the level and the volatility of a bond yield spread are mainly dependent on its own past volatility, and thus, its past shocks mainly affect its volatility. Based on our findings, we suggest that the number one priority of the European policymakers be the economic and financial integration of the European peripheral countries into the core. • We investigate mean and volatility spillovers among bond yield spreads. • Both mean and volatility spillovers are studied. • We focus on Greece, Ireland, Italy, Portugal and Spain. • We find that the volatility of a bond yield spread are mainly dependent on its own volatility. [ABSTRACT FROM AUTHOR]