Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Journal of Time Series Econometrics

Editor-in-Chief: Hidalgo, Javier

2 Issues per year


Mathematical Citation Quotient (MCQ) 2016: 0.10

Online
ISSN
1941-1928
See all formats and pricing
More options …

Testing for Nonlinearity in Conditional Covariances

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

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.

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

JEL Classification: C12; C32; C52; C58

References

  • Barndorff-Nielsen, O.E., P.R. Hansen, A. Lunde, and N. Shephard. 2011. “Multivariate Realised Kernels: Consistent Positive Semi-Definite Estimators of the Covariation of Equity Prices with Noise and Non-Synchronous Trading.” Journal of Econometrics 162:149–169.CrossrefWeb of ScienceGoogle Scholar

  • Bauwens, L., S. Laurent, and J.V.K. Rombouts. 2006. “Multivariate GARCH Models: A Survey.” Journal of Applied Econometrics 21:79–109.CrossrefGoogle Scholar

  • Bollerslev, T. 1990. “Modeling the Coherence in Short Run Nominal Exchange Rates: A Multivariate Generalized ARCH Model.” Review of Economics and Statistics 72:498–505.CrossrefGoogle Scholar

  • Bollerslev, T., A.J. Patton, and R. Quaedvlieg. 2016. “Exploiting the Errors: A Simple Approach for Improved Volatility Forecasting.” Journal of Econometrics 192:1–18.Web of ScienceCrossrefGoogle Scholar

  • Boudt, K., J. Daníelsson, and S. Laurent. 2013. “Robust Forecasting of Dynamic Conditional Correlation GARCH Models.” International Journal of Forecasting 29:244–257.Web of ScienceCrossrefGoogle Scholar

  • Caporin, M., and M. McAleer. 2008. “Scalar BEKK and Indirect DCC.” Journal of Forecasting 27:537–549.Web of ScienceCrossrefGoogle Scholar

  • Caporin, M., and M. McAleer. 2012. “Do We Really Need Both BEKK and DCC? A Tale of Two Multivariate GARCH Models.” Journal of Economic Surveys 26:736–751.Web of ScienceCrossrefGoogle Scholar

  • Comte, F., and O. Lieberman. 2003. “Asymptotic Theory for Multivariate GARCH Processes.” Journal of Multivariate Analysis 84:61–84.CrossrefGoogle Scholar

  • Ding, Z., and R.F. Engle. 2001. “Large Scale Conditional Covariance Matrix Modeling, Estimation and Testing.” Academia Economic Papers 29:157–184.Google Scholar

  • Engle, R.F. 2002. “Dynamic Conditional Correlation: A Simple Class of Multivariate GARCH Models.” Journal of Business & Economic Statistics 20:339–350.CrossrefGoogle Scholar

  • Engle, R.F. 2015. “Dynamic Conditional Beta (June 10, 2015).” Available at SSRN: http://ssrn.com/abstract=2404020 or http://dx.doi.org/10.2139/ssrn.2404020.

  • Engle, R.F., and K.F. Kroner. 1995. “Multivariate Simultaneous Generalized ARCH.” Econometric Theory 11:122–150.CrossrefGoogle Scholar

  • Filis, G., S. Degiannakis, and C. Floros. 2011. “Dynamic Correlation between Stock Market and Oil Prices: The Case of Oil-Importing and Oil-Exporting Countries.” International Review of Financial Analysis 20:152–164.Web of ScienceCrossrefGoogle Scholar

  • Francq, C., and J.M. Zakoïan. 2012. “QML Estimation of a Class of Multivariate Asymmetric GARCH Models.” Econometric Theory 28:179–206.CrossrefWeb of ScienceGoogle Scholar

  • Glosten, L., R. Jagannathan, and D. Runkle. 1992. “On the Relation between the Expected Value and Volatility of Nominal Excess Return on Stocks.” Journal of Finance 46:1779–1801.Google Scholar

  • Hafner, C.M., and A. Preminger. 2009. “On Asymptotic Theory for Multivariate GARCH Models.” Journal of Multivariate Analysis 100:2044–2054.Web of ScienceCrossrefGoogle Scholar

  • Kroner, K., and V. Ng. 1998. “Modeling Asymmetric Comovements of Asset Returns.” Review of Financial Studies 11:817–844.CrossrefGoogle Scholar

  • Kwan, W., W.K. Li, and K.W. Ng. 2010. “A Multivariate Threshold Varying Conditional Correlations Model.” Econometric Reviews 29:20–38.Web of ScienceCrossrefGoogle Scholar

  • Lee, T.H., and X. Long. 2009. “Copula-Based Multivariate GARCH Model with Uncorrelated Dependent Errors.” Journal of Econometrics 150:207–218.CrossrefWeb of ScienceGoogle Scholar

  • Luukkonen, R., P. Saikkonen, and T. Teräsvirta. 1988. “Testing Linearity against Smooth Transition Autoregressive Models.” Biometrika 75:491–499.CrossrefGoogle Scholar

  • McAleer, M., S. Hoti, and F. Chan. 2009. “Structure and Asymptotic Theory for Multivariate Asymmetric Conditional Volatility.” Econometric Reviews 28:422–440.Web of ScienceCrossrefGoogle Scholar

  • Noureldin, D., N. Shephard, and K. Sheppard. 2014. “Multivariate Rotated ARCH Models.” Journal of Econometrics 179:16–30.Web of ScienceCrossrefGoogle Scholar

  • Pedersen, R.S., and A. Rahbek. 2014. “Multivariate Variance Targeting in the BEKK-GARCH Model.” Econometrics Journal 17:24–55.Web of ScienceCrossrefGoogle Scholar

  • Sanhaji, B. 2016. “Appendix to Testing for nonlinearity in conditional covariances.” Unpublished work.

  • Silvennoinen, A., and T. Teräsvirta. 2009. “Multivariate GARCH Models.” In Handbook of Financial Time Series, edited by T.G. Andersen, R.A. Davis, J.P. Kreiss and T. Mikosch, 201–229. New York: Springer.Google Scholar

  • Silvennoinen, A., and T. Teräsvirta. 2015. “Modelling Conditional Correlations in Asset Returns: A Smooth Transition Approach.” Econometric Reviews 34:174–197.CrossrefGoogle Scholar

  • Tsay, R.S. 1998. “Testing and Modeling Multivariate Threshold Models.” Journal of the American Statistical Association 93:1188–1202.CrossrefGoogle Scholar

  • Van Dijk, D., T. Teräsvirta, and P.H. Franses. 2002. “Smooth Transition Autoregressive Models – a Survey of Recent Developments.” Econometric Reviews 21:1–47.CrossrefGoogle Scholar

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.

Export Citation

© 2017 Walter de Gruyter GmbH, Berlin/Boston. Copyright Clearance Center

Comments (0)

Please log in or register to comment.
Log in