Title: A note on the Nelson-Cao inequality constraints in the GJR-GARCH model: is there a leverage effect?

Authors: Stavros Stavroyiannis

Addresses: Department of Accounting and Finance, School of Management and Economics, Technological Educational Institute of Peloponnese, Greece

Abstract: The majority of the stylised facts of financial time series and several value-at-risk measures are modelled via univariate or multivariate GARCH processes. It is not rare that advanced GARCH models fail to converge for computational reasons, and a usual parsimonious approach is the GJR-GARCH model. There is a disagreement in the literature and the specialised econometric software, on which constraints should be used for the parameters, introducing indirectly the distinction between asymmetry and leverage. We show that the approach used by various software packages is not consistent with the Nelson-Cao inequality constraints. Implementing Monte Carlo simulations, despite of the results being empirically correct, the estimated parameters are not theoretically coherent with the Nelson-Cao constraints for ensuring positivity of conditional variances. On the other hand ruling out the leverage hypothesis, the asymmetry term in the GJR model can take negative values when typical constraints are imposed.

Keywords: GJR-GARCH; asymmetry; leverage; Nelson-Cao constraints.

DOI: 10.1504/IJEBR.2018.095345

International Journal of Economics and Business Research, 2018 Vol.16 No.4, pp.442 - 452

Received: 20 Jun 2017
Accepted: 21 Nov 2017
Published online: 03 Oct 2018 *

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