A Test for Time-Varying Smooth Transition Conditional Covariance Models in Multivariate Time Series

Abstract This paper introduces a novel test designed to assess the validity of time-varying smooth transition conditional covariance models. We develop a model driven by five scalar parameters in order to build the Lagrange Multiplier test within the framework of multivariate conditional heteroskedastic time series models with smooth transition functions. We detail the development of these tests, emphasizing their applicability. The methodology is scrutinized through Monte Carlo simulations, providing insights into its finite sample properties. Additionally, empirical illustrations underscore the practical relevance of the proposed tests, demonstrating their efficiency in capturing time-varying smooth transitions within financial datasets.