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Journal of Time Series Econometrics

Editor-in-Chief: Hidalgo, Javier

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Testing for Nonlinearity in Conditional Covariances

Bilel Sanhaji
Published Online: 2017-04-26 | DOI: https://doi.org/10.1515/jtse-2016-0010


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.

Keywords: Lagrange multiplier test; nonlinearity; smooth transition; scalar BEKK; multivariate GARCH

JEL Classification: C12; C32; C52; C58


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About the article

Published Online: 2017-04-26

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.

Citation Information: Journal of Time Series Econometrics, Volume 9, Issue 2, 20160010, ISSN (Online) 1941-1928, ISSN (Print) 2194-6507, DOI: https://doi.org/10.1515/jtse-2016-0010.

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