A Testing Procedure for Constant Parameters in Stochastic Volatility Models

  • Juan del Hoyo
  • Guillermo Llorente
  • Carlos RiveroEmail author


This paper proposes a two-step method for an omnibus misspecification test for constant parameters in the volatility equation of stochastic volatility models. The proposed test has a well-known null asymptotic distribution free of nuisance parameters. It is easy to implement and has low computational cost. Monte Carlo simulations support the relevance of the proposed method, evaluate the performance of the procedure, and highlight its small computational load. An empirical application shows the relevance of the procedure.


Structural change Sup-Wald test Monte Carlo simulations Recursive statistics Time-varying parameters 



The authors appreciate the helpful comments from M. Carrasco, P. Perron, W. Ploberger, T. Valdés, and H. White(\(\dagger \)). We also appreciate comments on earlier drafts made by participants in the Econometrics workshop at the University of Rochester, the 8th International Conference on Computational and Financial Econometrics, 3rd. International Workshop on Financial Markets and Nonlinear Dynamics, and the 5th International Symposium in Computational Economics and Finance (ISCEF). We acknowledge Dr. Fredj Jawadi (the editor) and the referees for their helpful comments and insights that helped to improve the paper. Financial support from the Regional Government of Madrid and European Social Fund (Ref. EARLYFIN, S2015/HUM-3353), the Spanish Ministry of Economy and Competitiveness (ECO2017-85356 -P), and Grant UAMA13-4E-2328 is acknowledged. Computing time at the CCC-UAM was very important in the development of this project.

Compliance with ethical standards

Conflicts of interest

The authors declare that they have no conflict of interest


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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Juan del Hoyo
    • 1
  • Guillermo Llorente
    • 1
  • Carlos Rivero
    • 2
    Email author
  1. 1.Departamento de Financiación e Investigación ComercialUniversidad Autónoma de MadridMadridSpain
  2. 2.Departamento de Economía Financiera y Actuarial y EstadísticaUniversidad Complutense de MadridMadridSpain

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