“…So some locally (i.e., in each "regime") linear or nonlinear representations were investigated in order to capture the probabilistic and statistical properties of such models. For instance, M S − ARM A: Francq and Zakoïan [10] and Stelzer [26]; M S−nonlinear ARM A : Lee [21] and Yao; M S − GARCH: Francq and Zakoïan [9]; Hass et al, [16]; Liu [22]; M S − DAR : Ghezal [14] among others. The M S − BLGARCH model generate series with a much more flexible dependence structure than in standard BLGARCH specifications proposed by Storti and Vitale (c.f., [27]) is a generalization of the classical M S − GARCH model studied by Cai (c.f., [3]), Hamilton and Susmel (c.f., [18]) and Francq et al (c.f., [11]), thereby explain the presence of leverage effects in the volatility dynamics.…”