Testing explosive bubbles with time-varying volatility : the case of the Spanish public debt, 1850-2021

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