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Testing Garch-X Type Models

Listed author(s):
  • Rasmus Søndergaard Pedersen

    (Department of Economics, University of Copenhagen)

  • Anders Rahbek

    (Department of Economics, University of Copenhagen)

Registered author(s):

    We present novel theory for testing for reduction of GARCH-X type models with an exogenous (X) covariate to standard GARCH type models. To deal with the problems of potential nuisance parameters on the boundary of the parameter space as well as lack of identi?cation under the null, we exploit a noticeable property of speci?fic zero-entries in the inverse information of the GARCH-X type models. Speci?cally, we consider sequential testing based on two likelihood ratio tests and as demonstrated the structure of the inverse information implies that the proposed test neither depends on whether the nuisance parameters lie on the boundary of the parameter space, nor on lack of identi?cation. Our general results on GARCH-X type models are applied to Gaussian based GARCH-X models, GARCH-X models with Student'?s t-distributed innovations as well as the integer-valued GARCH-X (PAR-X) models.

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    File URL: http://www.econ.ku.dk/english/research/publications/wp/dp_2017/1715.pdf
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    Paper provided by University of Copenhagen. Department of Economics in its series Discussion Papers with number 17-15.

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    Length: 36 pages
    Date of creation: 23 Aug 2017
    Handle: RePEc:kud:kuiedp:1715
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    1. Fokianos, Konstantinos & Rahbek, Anders & Tjøstheim, Dag, 2009. "Poisson Autoregression," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1430-1439.
    2. Francq, Christian & Zakoïan, Jean-Michel, 2009. "Testing the Nullity of GARCH Coefficients: Correction of the Standard Tests and Relative Efficiency Comparisons," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 313-324.
    3. Ali Ahmad & Christian Francq, 2016. "Poisson QMLE of Count Time Series Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(3), pages 291-314, May.
    4. Andrews, Donald W K, 2001. "Testing When a Parameter Is on the Boundary of the Maintained Hypothesis," Econometrica, Econometric Society, vol. 69(3), pages 683-734, May.
    5. Agosto, Arianna & Cavaliere, Giuseppe & Kristensen, Dennis & Rahbek, Anders, 2016. "Modeling corporate defaults: Poisson autoregressions with exogenous covariates (PARX)," Journal of Empirical Finance, Elsevier, vol. 38(PB), pages 640-663.
    6. Donald W. K. Andrews, 1999. "Estimation When a Parameter Is on a Boundary," Econometrica, Econometric Society, vol. 67(6), pages 1341-1384, November.
    7. Pedersen, Rasmus Søndergaard, 2017. "Inference and testing on the boundary in extended constant conditional correlation GARCH models," Journal of Econometrics, Elsevier, vol. 196(1), pages 23-36.
    8. Heejoon Han, 2015. "Asymptotic Properties of GARCH-X Processes," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 13(1), pages 188-221.
    9. Han, Heejoon & Park, Joon Y., 2012. "ARCH/GARCH with persistent covariate: Asymptotic theory of MLE," Journal of Econometrics, Elsevier, vol. 167(1), pages 95-112.
    10. Herman J. Bierens & Werner Ploberger, 1997. "Asymptotic Theory of Integrated Conditional Moment Tests," Econometrica, Econometric Society, vol. 65(5), pages 1129-1152, September.
    11. Pedersen, Rasmus Søndergaard & Rahbek, Anders, 2016. "Nonstationary GARCH with t-distributed innovations," Economics Letters, Elsevier, vol. 138(C), pages 19-21.
    12. Heejoon Han & Dennis Kristensen, 2014. "Asymptotic Theory for the QMLE in GARCH-X Models With Stationary and Nonstationary Covariates," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 32(3), pages 416-429, July.
    13. Demos, Antonis & Sentana, Enrique, 1998. "Testing for GARCH effects: a one-sided approach," Journal of Econometrics, Elsevier, vol. 86(1), pages 97-127, June.
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