In this paper, we propose two parametric alternatives to the standard GARCH model. They allow the conditional variance to have a smooth time-varying structure of either additive or multiplicative type. The suggested parameterizations describe both nonlinearity and structural change in the...

In this paper we propose a method for determining the number of regimes in threshold autoregressive models using smooth transition autoregression as a tool. As the smooth transition model is just an approximation to the threshold autoregressive one, no asymptotic properties are claimed for the...

This paper suggests a unified framework for testing the adequacy of anestimated GARCH model. Nothing more complicated than standard asymptotictheory is required. Parametric tests of no ARCH in standardized errors,symmetry, and parameter constancy are suggested. Estimating the alternativewhen the...