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A model specification test for GARCH(1,1) processes

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  • Leucht, Anne
  • Neumann, Michael H.
  • Kreiss, Jens-Peter
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    Abstract

    We provide a consistent specification test for GARCH(1,1) models based on a test statistic of Cramér-von Mises type. Since the limit distribution of the test statistic under the null hypothesis depends on unknown quantities in a complicated manner, we propose a model-based (semiparametric)bootstrap method to approximate critical values of the test and verify its asymptotic validity. Finally, we illuminate the finite sample behavior of the test by some simulations.

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    File URL: https://ub-madoc.bib.uni-mannheim.de/35107/1/Leucht_%26_Neumann_%26_Kreiss_13%2D11.pdf
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    Bibliographic Info

    Paper provided by University of Mannheim, Department of Economics in its series Working Papers with number 13-11.

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    Date of creation: 2013
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    Handle: RePEc:mnh:wpaper:35107

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    Web page: http://www2.vwl.uni-mannheim.de/10.1.html
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    Related research

    Keywords: Bootstrap ; Cramér-von Mises test ; GARCH processes ; V-statistic;

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    1. Sentana, Enrique, 1995. "Quadratic ARCH Models," Review of Economic Studies, Wiley Blackwell, vol. 62(4), pages 639-61, October.
    2. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-70, March.
    3. Lawrence R. Glosten & Ravi Jagannathan & David E. Runkle, 1993. "On the relation between the expected value and the volatility of the nominal excess return on stocks," Staff Report 157, Federal Reserve Bank of Minneapolis.
    4. Juan Carlos Escanciano, 2005. "Goodness-of-fit Tests for Linear and Non-linear Time Series Models," Faculty Working Papers 02/05, School of Economics and Business Administration, University of Navarra.
    5. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    6. Kristensen, Dennis & Linton, Oliver, 2006. "A Closed-Form Estimator For The Garch(1,1) Model," Econometric Theory, Cambridge University Press, vol. 22(02), pages 323-337, April.
    7. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
    8. Dehling, H. & Mikosch, T., 1994. "Random Quadratic Forms and the Bootstrap for U-Statistics," Journal of Multivariate Analysis, Elsevier, vol. 51(2), pages 392-413, November.
    9. Leucht, Anne & Neumann, Michael H., 2013. "Dependent wild bootstrap for degenerate U- and V-statistics," Journal of Multivariate Analysis, Elsevier, vol. 117(C), pages 257-280.
    10. Tinkl, Fabian, 2013. "Quasi-maximum likelihood estimation in generalized polynomial autoregressive conditional heteroscedasticity models," IWQW Discussion Paper Series 03/2013, Friedrich-Alexander-Universität Erlangen-Nürnberg, Institut für Wirtschaftspolitik und Quantitative Wirtschaftsforschung (IWQW).
    11. Nelson, Daniel B., 1990. "Stationarity and Persistence in the GARCH(1,1) Model," Econometric Theory, Cambridge University Press, vol. 6(03), pages 318-334, September.
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