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Testing Explosive Bubbles with Time-Varying Volatility: The Case of Spanish Public Debt

In this paper the dynamics of the Spanish public debt-GDP ratio is analysed during the period 1850-2021. We use recent procedures to test for explosive bubbles in the presence under time-varying volatility (Harvey, Leybourne, Sollis and Taylor (2016), Harvey, Leybourne and Zu (2019, 2020), Kurozumi, Skorobotov and Tsarev (2022)) in order to test the explosive behavior of Spanish public debt over this long period. We extend previous analysis of Esteve and Prats (2022) where assume constant unconditional volatility in the underlying error process.