This paper proposes a new nonlinear vector autoregressive (VAR) model referred to as the Gaussian mixture vector autoregressive (GMVAR) model. The GMVAR model belongs to the family of mixture vector autoregressive models and is designed for analyzing time series that exhibit regime-switching behavior. The main difference between the GMVAR model and previous mixture VAR models lies in the definition of the mixing weights that govern the regime probabilities. In the GMVAR model the mixing weights depend on past values of the series in a specific way that has very advantageous properties from both theoretical and practical point of view. A practical advantage is that there is a wide diversity of ways in which a researcher can associate different regimes with specific economically meaningful characteristics of the phenomenon modeled. A theoretical advantage is that stationarity and ergodicity of the underlying stochastic process are straightforward to establish and, contrary to most other nonlinear autoregressive models, explicit expressions of low order stationary marginal distributions are known. These theoretical properties are used to develop an asymptotic theory of maximum likelihood estimation for the GMVAR model whose practical usefulness is illustrated in a bivariate setting by examining the relationship between the EUR-USD exchange rate and a related interest rate data.

We consider estimation of the structural vector autoregression (SVAR) by the generalized method of moments (GMM). Given non-Gaussian errors and a suitable set of moment conditions, containing a sufficient number of relevant co-kurtosis conditions, the GMM estimator is shown to achieve global identification of the parameters of the SVAR model up to changing the signs of the structural shocks. We also propose a procedure, based on well-known moment selection criteria, to find the optimal set of moment conditions among the sets that guarantee identification. According to simulation results, the finite-sample performance of our estimation method is comparable, or even superior to that of the recently proposed pseudo maximum likelihood estimators. The two-step estimator is found to outperform the alternative GMM estimators. An empirical application to a small macroeconomic model estimated on postwar U.S. data illustrates the use of the methods. JEL Classification: C32 Keywords: structural VAR model, non-Gaussian time series, generalized method of moments