IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2210.11398.html
   My bibliography  Save this paper

Allowing for weak identification when testing GARCH-X type models

Author

Listed:
  • Philipp Ketz

Abstract

In this paper, we use the results in Andrews and Cheng (2012), extended to allow for parameters to be near or at the boundary of the parameter space, to derive the asymptotic distributions of the two test statistics that are used in the two-step (testing) procedure proposed by Pedersen and Rahbek (2019). The latter aims at testing the null hypothesis that a GARCH-X type model, with exogenous covariates (X), reduces to a standard GARCH type model, while allowing the "GARCH parameter" to be unidentified. We then provide a characterization result for the asymptotic size of any test for testing this null hypothesis before numerically establishing a lower bound on the asymptotic size of the two-step procedure at the 5% nominal level. This lower bound exceeds the nominal level, revealing that the two-step procedure does not control asymptotic size. In a simulation study, we show that this finding is relevant for finite samples, in that the two-step procedure can suffer from overrejection in finite samples. We also propose a new test that, by construction, controls asymptotic size and is found to be more powerful than the two-step procedure when the "ARCH parameter" is "very small" (in which case the two-step procedure underrejects).

Suggested Citation

  • Philipp Ketz, 2022. "Allowing for weak identification when testing GARCH-X type models," Papers 2210.11398, arXiv.org.
    • Handle: RePEc:arx:papers:2210.11398
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2210.11398
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Ketz, Philipp, 2018. "Subvector inference when the true parameter vector may be near or at the boundary," Journal of Econometrics, Elsevier, vol. 207(2), pages 285-306.
    2. Hansen, Bruce E, 1996. "Inference When a Nuisance Parameter Is Not Identified under the Null Hypothesis," Econometrica, Econometric Society, vol. 64(2), pages 413-430, March.
    3. Donald W. K. Andrews & Xu Cheng, 2012. "Estimation and Inference With Weak, Semi‐Strong, and Strong Identification," Econometrica, Econometric Society, vol. 80(5), pages 2153-2211, September.
    4. Gregory Cox, 2020. "Weak Identification with Bounds in a Class of Minimum Distance Models," Papers 2012.11222, arXiv.org, revised Dec 2022.
    5. Donald W. K. Andrews, 1999. "Estimation When a Parameter Is on a Boundary," Econometrica, Econometric Society, vol. 67(6), pages 1341-1384, November.
    6. Leeb, Hannes & Pötscher, Benedikt M., 2008. "Can One Estimate The Unconditional Distribution Of Post-Model-Selection Estimators?," Econometric Theory, Cambridge University Press, vol. 24(2), pages 338-376, April.
    7. Andrews, Donald W.K. & Guggenberger, Patrik, 2010. "ASYMPTOTIC SIZE AND A PROBLEM WITH SUBSAMPLING AND WITH THE m OUT OF n BOOTSTRAP," Econometric Theory, Cambridge University Press, vol. 26(2), pages 426-468, April.
    8. Leeb, Hannes & Pötscher, Benedikt M., 2005. "Model Selection And Inference: Facts And Fiction," Econometric Theory, Cambridge University Press, vol. 21(1), pages 21-59, February.
    9. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. McCloskey, Adam, 2017. "Bonferroni-based size-correction for nonstandard testing problems," Journal of Econometrics, Elsevier, vol. 200(1), pages 17-35.
    2. Gregory Cox, 2022. "A Generalized Argmax Theorem with Applications," Papers 2209.08793, arXiv.org.
    3. Andrews, Donald W.K. & Cheng, Xu & Guggenberger, Patrik, 2020. "Generic results for establishing the asymptotic size of confidence sets and tests," Journal of Econometrics, Elsevier, vol. 218(2), pages 496-531.
    4. Gregory Fletcher Cox, 2024. "A Simple and Adaptive Confidence Interval when Nuisance Parameters Satisfy an Inequality," Papers 2409.09962, arXiv.org.
    5. Fan, Yanqin & Shi, Xuetao, 2023. "Wald, QLR, and score tests when parameters are subject to linear inequality constraints," Journal of Econometrics, Elsevier, vol. 235(2), pages 2005-2026.
    6. Ketz, Philipp, 2019. "Testing overidentifying restrictions with a restricted parameter space," Economics Letters, Elsevier, vol. 185(C).
    7. Ketz, Philipp, 2019. "On asymptotic size distortions in the random coefficients logit model," Journal of Econometrics, Elsevier, vol. 212(2), pages 413-432.
    8. Centorrino, Samuele & Pérez-Urdiales, María, 2023. "Maximum likelihood estimation of stochastic frontier models with endogeneity," Journal of Econometrics, Elsevier, vol. 234(1), pages 82-105.
    9. Ketz, Philipp, 2018. "Subvector inference when the true parameter vector may be near or at the boundary," Journal of Econometrics, Elsevier, vol. 207(2), pages 285-306.
    10. Gregory Cox, 2020. "Weak Identification with Bounds in a Class of Minimum Distance Models," Papers 2012.11222, arXiv.org, revised Dec 2022.
    11. Donald W. K. Andrews & Xu Cheng, 2012. "Estimation and Inference With Weak, Semi‐Strong, and Strong Identification," Econometrica, Econometric Society, vol. 80(5), pages 2153-2211, September.
    12. Philipp Ketz & Adam McCloskey, 2021. "Short and Simple Confidence Intervals when the Directions of Some Effects are Known," Papers 2109.08222, arXiv.org.
    13. Giuseppe Cavaliere & Heino Bohn Nielsen & Anders Rahbek, 2017. "On the Consistency of Bootstrap Testing for a Parameter on the Boundary of the Parameter Space," Journal of Time Series Analysis, Wiley Blackwell, vol. 38(4), pages 513-534, July.
    14. Cavaliere, Giuseppe & Nielsen, Heino Bohn & Pedersen, Rasmus Søndergaard & Rahbek, Anders, 2022. "Bootstrap inference on the boundary of the parameter space, with application to conditional volatility models," Journal of Econometrics, Elsevier, vol. 227(1), pages 241-263.
    15. Tae-Hwy Lee & Zhou Xi & Ru Zhang, 2013. "Testing for Neglected Nonlinearity Using Regularized Artificial Neural Networks," Working Papers 201422, University of California at Riverside, Department of Economics, revised Apr 2012.
    16. Meitz, Mika & Saikkonen, Pentti, 2021. "Testing for observation-dependent regime switching in mixture autoregressive models," Journal of Econometrics, Elsevier, vol. 222(1), pages 601-624.
    17. Corradi, Valentina & Silvapulle, Mervyn J. & Swanson, Norman R., 2018. "Testing for jumps and jump intensity path dependence," Journal of Econometrics, Elsevier, vol. 204(2), pages 248-267.
    18. Jin Seo Cho & Peter C. B. Phillips & Juwon Seo, 2019. "Parametric Inference on the Mean of Functional Data Applied to Lifetime Income Curves," Working papers 2019rwp-153, Yonsei University, Yonsei Economics Research Institute.
    19. Cho, Jin Seo & White, Halbert, 2010. "Testing for unobserved heterogeneity in exponential and Weibull duration models," Journal of Econometrics, Elsevier, vol. 157(2), pages 458-480, August.
    20. Chen, Heng & Fan, Yanqin & Liu, Ruixuan, 2016. "Inference for the correlation coefficient between potential outcomes in the Gaussian switching regime model," Journal of Econometrics, Elsevier, vol. 195(2), pages 255-270.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2210.11398. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.