Testing for Nonlinearity in Conditional Covariances
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Bilel Sanhaji
Abstract
We propose two Lagrange multiplier tests for nonlinearity in conditional covariances in multivariate GARCH models. The null hypothesis is the scalar BEKK model in which covolatilities of time series are driven by a linear function of their own lags and lagged squared innovations. The alternative hypothesis is an extension of the model in which covolatilities are modeled by a nonlinear function of the lagged squared innovations, represented by an exponential or a logistic transition function. Moreover, on the same basis we develop two other tests that are robust to leverage effects. We investigate the size and power of these tests through Monte Carlo experiments, and we provide empirical illustrations in many of which cases these tests encourage the use of nonlinearity in conditional covariances.
Funding statement: This work was granted access to the HPC resources of Aix-Marseille Université financed by the project Equip@Meso (ANR-10-EQPX-29-01) of the program “Investissement d’avenir” supervised by the Agence Nationale de la Recherche.
Acknowledgments
I am grateful to the editor, Javier Hidalgo, and an anonymous referee for detailed comments and suggestions. I thank Luc Bauwens, Christophe Hurlin, Sébatien Laurent, Anne Péguin-Feissolle, and Timo Teräsvirta for their suggestions throughout this project. Part of this research was carried out while I was visiting the Center of Research in Econometric Analysis of Time Series (CREATES, Aarhus University) in Spring 2013. I thank Niels Haldrup for hospitality and Aix-Marseille School of Economics for financial support.
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© 2017 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Testing for Nonlinearity in Conditional Covariances
- Tail Behavior and Dependence Structure in the APARCH Model
- Analyzing the Full BINMA Time Series Process Using a Robust GQL Approach
- Do They Still Matter? – Impact of Fossil Fuels on Electricity Prices in the Light of Increased Renewable Generation
Articles in the same Issue
- Testing for Nonlinearity in Conditional Covariances
- Tail Behavior and Dependence Structure in the APARCH Model
- Analyzing the Full BINMA Time Series Process Using a Robust GQL Approach
- Do They Still Matter? – Impact of Fossil Fuels on Electricity Prices in the Light of Increased Renewable Generation
