“…Papers by Hencic and Gouriéroux (2015), Gouriéroux and Zakoian (2015), Gouriéroux and Jasiak (2016), Gouriéroux and Zakoian (2017) and Fries and Zakoian (2019), assume Cauchy distributed disturbances in (1), that is, very fat-tailed distributions needed to capture bubble-like dynamics. For other macroeconomic variables such as inflation or interest rates, a popular choice is the Student's t-distribution with scale parameter > 0 and > 2 degrees of freedom, see inter alia Lanne and Saikkonen (2011), Nyberg, Lanne and Saarinen (2012), Lanne and Saikkonen (2013), Lof (2013) or Lof and Nyberg (2017). With these Student's t-disturbances, the approximate maximum likelihood estimation (MLE) approach has been advocated by , Andrews, Davis and Breidt (2006) and further promoted by Lanne and Saikkonen (2011).…”