Testing for Nonlinearity in Conditional Covariances

Bilel Sanhaji

Journal of Time Series Econometrics, 2017, vol. 9, issue 2, 22

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 (search for similar items in EconPapers)
JEL-codes: C12 C32 C52 C58 (search for similar items in EconPapers)
Date: 2017
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Working Paper: Testing for nonlinearity in conditional covariances (2017)
Working Paper: Testing for Nonlinearity in Conditional Covariances (2017)
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DOI: 10.1515/jtse-2016-0010

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