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Spurious Inference in the GARCH(1,1) Model When It Is Weakly Identified

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  • Jun Ma
  • Charles Nelson
  • Richard Startz

Abstract

This paper shows that the Zero-Information-Limit-Condition (ZILC) formulated by Nelson and Startz (2006) holds in the GARCH(1,1) model. As a result, the GARCH estimate tends to have too small a standard error relative to the true one when the ARCH parameter is small, even when sample size becomes very large. In combination with an upward bias in the GARCH estimate, the small standard error will often lead to the spurious inference that volatility is highly persistent when it is not. We develop an empirical strategy to deal with this issue and show how it applies to real datasets.

Suggested Citation

  • Jun Ma & Charles Nelson & Richard Startz, 2007. "Spurious Inference in the GARCH(1,1) Model When It Is Weakly Identified," Working Papers UWEC-2006-14-P, University of Washington, Department of Economics, revised Mar 2007.
    • Handle: RePEc:udb:wpaper:uwec-2006-14-p
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    Cited by:

    1. Ardakani Omid M. & Kishor N. Kundan, 2018. "Examining the success of the central banks in inflation targeting countries: the dynamics of the inflation gap and institutional characteristics," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 22(1), pages 1-19, February.
    2. Jun Ma & Charles R. Nelson, 2008. "Valid Inference for a Class of Models Where Standard Inference Performs Poorly: Including Nonlinear Regression, ARMA, GARCH, and Unobserved Components," Working Papers UWEC-2008-06-R, University of Washington, Department of Economics, revised Sep 2008.
    3. Luger, Richard, 2012. "Finite-sample bootstrap inference in GARCH models with heavy-tailed innovations," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3198-3211.
    4. Donald W. K. Andrews & Patrik Guggenberger, 2014. "A Conditional-Heteroskedasticity-Robust Confidence Interval for the Autoregressive Parameter," The Review of Economics and Statistics, MIT Press, vol. 96(2), pages 376-381, May.
    5. Cristhian Mellado & Diego Escobari, 2015. "Virtual integration of financial markets: a dynamic correlation analysis of the creation of the Latin American Integrated Market," Applied Economics, Taylor & Francis Journals, vol. 47(19), pages 1956-1971, April.
    6. Jun Ma, 2013. "Long‐Run Risk and Its Implications for the Equity Premium Puzzle: New Evidence from a Multivariate Framework," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 45(1), pages 121-145, February.
    7. Kishor, N. Kundan & Kumari, Swati & Song, Suyong, 2015. "Time variation in the relative importance of permanent and transitory components in the U.S. housing market," Finance Research Letters, Elsevier, vol. 12(C), pages 92-99.
    8. Trypsteen, Steven, 2017. "The growth-volatility nexus: New evidence from an augmented GARCH-M model," Economic Modelling, Elsevier, vol. 63(C), pages 15-25.
    9. Kishor, N. Kundan & Marfatia, Hardik A., 2013. "The time-varying response of foreign stock markets to U.S. monetary policy surprises: Evidence from the Federal funds futures market," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 24(C), pages 1-24.
    10. Sarkar, Asani & Zhang, Lingjia, 2009. "Time varying consumption covariance and dynamics of the equity premium: Evidence from the G7 countries," Journal of Empirical Finance, Elsevier, vol. 16(4), pages 613-631, September.
    11. Steven Trypsteen, 2014. "Cross-Country Interactions, the Great Moderation and the Role of Output Volatility in Growth," Discussion Papers 2014/10, University of Nottingham, Centre for Finance, Credit and Macroeconomics (CFCM).
    12. Alfred A. Haug, 2014. "On real interest rate persistence: the role of breaks," Applied Economics, Taylor & Francis Journals, vol. 46(10), pages 1058-1066, April.
    13. Liu, Yan & Luger, Richard, 2009. "Efficient estimation of copula-GARCH models," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2284-2297, April.
    14. Steven Trypsteen, 2014. "The Importance of a Time-Varying Variance and Cross-Country Interactions in Forecast Models," Discussion Papers 2014/15, University of Nottingham, Centre for Finance, Credit and Macroeconomics (CFCM).
    15. Martin Vance L. & Sarkar Saikat & Kanto Antti Jaakko, 2014. "Modelling nonlinearities in equity returns: the mean impact curve analysis," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 18(1), pages 51-72, February.
    16. Christian Espinosa-Méndez & Juan Gorigoitía & João Vieito, 2020. "Stock exchange mergers: a dynamic correlation analysis on Euronext," Portuguese Economic Journal, Springer;Instituto Superior de Economia e Gestao, vol. 19(2), pages 81-98, May.
    17. Brownlees, Christian T., 2019. "Hierarchical GARCH," Journal of Empirical Finance, Elsevier, vol. 51(C), pages 17-27.
    18. Simeon Coleman & Vitor Leone, 2015. "An investigation of regime shifts in UK commercial property returns: a time series analysis," Applied Economics, Taylor & Francis Journals, vol. 47(60), pages 6479-6492, December.
    19. Enders, Walter & Ma, Jun, 2011. "Sources of the great moderation: A time-series analysis of GDP subsectors," Journal of Economic Dynamics and Control, Elsevier, vol. 35(1), pages 67-79, January.
    20. Olson, Eric & Enders, Walter & Wohar, Mark E., 2012. "An empirical investigation of the Taylor curve," Journal of Macroeconomics, Elsevier, vol. 34(2), pages 380-390.

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