“…They also include in the basic HAR model financial and macroeconomic variables, as in Fernandes, Medeiros, and Scharth (2014). Contrary to Campos et al (2017), the existence of an asymmetric response of the index is tested in this paper by fitting the asymmetric extension of the HAR model proposed by Corsi, Audrino, and Reno (2012) named HARL and new proposals based on alternative oil price asymmetric measures instead of negative oil returns. HAR models with leverage have been successfully used for forecasting the volatility of stock market returns; see, among others, Liu and Maheu (2009), Scharth and Medeiros (2009), Asai, McAleer, and Medeiros (2012, Corsi and Renò (2012), Byun and Kim (2013), Patton and Sheppard (2015) and Shin (2018, 2019).…”