The constant conditional correlation GARCH model is probably the most frequently applied multivariate GARCH model. In this paper we consider an extension to this model and examine its fourth-moment structure. The extension, first considered by Jeantheau (1998), is motivated by the result found...

This paper considers the use of smooth transition autoregressive models for forecasting. First, the modelling of time series with these nonlinear models is discussed. Techniques for obtaining multiperiod forecasts are presented. The usefulness of forecast densities in the case of nonlinear...

This paper considers the moments of a family of first-order GARCH processes. First, a general condition of the existence of any integer moment of the absolute values of the observations is given. Second, a general expression for this moment as a function of lower-order moments is derived. Third,...

In this paper we propose a new multivariate GARCH model with time-varying conditional correlation structure. The approach adopted here is based on the decomposition of the covariances into correlations and standard deviations. The time-varying conditional correlations change smoothly between two...

This paper reconsiders a nonlinear error-correction model of UK broad money demand by Ericsson, Hendry and Prestwich. Their model can be viewed as an approximation to a smooth transition regression (STR) type specification. The corresponding STR model, when estimated, turns out to encompass the...

In this paper a unified framework for testing the adequacy of an estimated GARCH model is presented. Parametric LM or LM type tests of no ARCH in standardized errors, linearity, and parameter constancy are proposed. The asymptotic null distributions of the tests are standard, which makes...

Applying nonparametric variable selection criteria in nonlinear regression models generally requires a substantial computational effort if the data set is large. In this paper we present a selection technique that is computationally much less demanding and performs well in comparison with...

In this paper we derive conditions for the conditional covariance matrix to be positive definite in a general vector ARCH model. The conditions can be easily extended to the diagonal vector GARCH model. For the general vector GARCH model, analytical expressions for the conditions in terms of the...

Nonlinearity, and regime-switching behavior in particular, and structural change have often been perceived as competing alternatives to linearity. In this paper we propose a model, based on the principle of smooth transition, that allows for regime-switching behavior in conjunction with...

This paper has been prepared for Handbook of Applied Economic Statistics, edited by David Giles and Aman Ullah. It considers a particular class of single-equation nonlinear multivariate models called smooth transition regression (STR) models. Inference in these models, including testing...