“…There is ample evidence that S&P return index possesses nonlinear characteristics (Abhyankar et al, 1997;Brock et al, 1991;Hinich andPatterson, 1985, 1989;Hsieh, 1989;Vaidyanathan and Krehbiel, 1992). There is also some research based on Hinich's linearity test indicating the US real GNP growth data is nonlinear (Ashley and Patterson, 1989;Scheinkman and LeBaron, 1989) and many threshold autoregressive models and generalizations have been used to model the series (Potter, 1995;Scheinkman and LeBaron, 1989;Terasvirta, 1994;Tiao and Tsay, 1994).…”