Some of the examples of Gaussian white noise-driven nonlinear AR(2) models are shown here:

1. ExpAR(2) model (see Ozaki 1980, 1981b, Haggan and Ozaki 1981):

x e x e x wt x

= + + + +− −

− −( ) ( ) .φ pi φ piγ γ1 1 1 2 2 21 2

2. RBF-AR(2) model (see Vesin 1993, Ozaki et al. 1997, 2004):

= + +( ) + +

− −φ pi pi

φ pi

− −+( ) +γ γpi 3. STAR(2) model (see Terasvirta 1994):

x x x e x x e wt t t x

= +{ } + +{ } −( ) + − −

1 .