IDEAS home Printed from https://ideas.repec.org/a/eee/econom/v189y2015i2p457-472.html
   My bibliography  Save this article

Statistical inference for conditional quantiles in nonlinear time series models

Author

Listed:
  • So, Mike K.P.
  • Chung, Ray S.W.

Abstract

This paper studies the statistical properties of a two-step conditional quantile estimator in nonlinear time series models with unspecified error distribution. The asymptotic distribution of the quasi-maximum likelihood estimators and the filtered empirical percentiles is derived. Three applications of the asymptotic result are considered. First, we construct an interval estimator of the conditional quantile without any distributional assumptions. Second, we develop a specification test for the error distribution. Finally, using the specification test, we propose methods for estimating the tail index of the error distribution that supports the construction of a new estimator for the conditional quantile at the extreme tail. The asymptotic results and their applications are illustrated by simulations and real data analyses in which our methods for analyzing daily and intraday financial return series have been adopted.

Suggested Citation

  • So, Mike K.P. & Chung, Ray S.W., 2015. "Statistical inference for conditional quantiles in nonlinear time series models," Journal of Econometrics, Elsevier, vol. 189(2), pages 457-472.
    • Handle: RePEc:eee:econom:v:189:y:2015:i:2:p:457-472
    DOI: 10.1016/j.jeconom.2015.03.037
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304407615001153
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jeconom.2015.03.037?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Koenker, Roger & Xiao, Zhijie, 2006. "Quantile Autoregression," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 980-990, September.
    2. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
    3. Gerlach, Richard H. & Chen, Cathy W. S. & Chan, Nancy Y. C., 2011. "Bayesian Time-Varying Quantile Forecasting for Value-at-Risk in Financial Markets," Journal of Business & Economic Statistics, American Statistical Association, vol. 29(4), pages 481-492.
    4. Mike K. P. So & Chi-Ming Wong, 2012. "Estimation of multiple period expected shortfall and median shortfall for risk management," Quantitative Finance, Taylor & Francis Journals, vol. 12(5), pages 739-754, March.
    5. Timotheos Angelidis & Alexandros Benos & Stavros Degiannakis, 2007. "A robust VaR model under different time periods and weighting schemes," Review of Quantitative Finance and Accounting, Springer, vol. 28(2), pages 187-201, February.
    6. Xiao, Zhijie & Koenker, Roger, 2009. "Conditional Quantile Estimation for Generalized Autoregressive Conditional Heteroscedasticity Models," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1696-1712.
    7. Chen, Cathy W.S. & Gerlach, Richard & Wei, D.C.M., 2009. "Bayesian causal effects in quantiles: Accounting for heteroscedasticity," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 1993-2007, April.
    8. Lee, Sang-Won & Hansen, Bruce E., 1994. "Asymptotic Theory for the Garch(1,1) Quasi-Maximum Likelihood Estimator," Econometric Theory, Cambridge University Press, vol. 10(1), pages 29-52, March.
    9. Koenker, Roger & Zhao, Quanshui, 1996. "Conditional Quantile Estimation and Inference for Arch Models," Econometric Theory, Cambridge University Press, vol. 12(5), pages 793-813, December.
    10. Michael McAleer, 2014. "Asymmetry and Leverage in Conditional Volatility Models," Econometrics, MDPI, vol. 2(3), pages 1-6, September.
    11. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521845731.
    12. Lumsdaine, Robin L, 1996. "Consistency and Asymptotic Normality of the Quasi-maximum Likelihood Estimator in IGARCH(1,1) and Covariance Stationary GARCH(1,1) Models," Econometrica, Econometric Society, vol. 64(3), pages 575-596, May.
    13. Escanciano, Juan Carlos & Velasco, Carlos, 2010. "Specification tests of parametric dynamic conditional quantiles," Journal of Econometrics, Elsevier, vol. 159(1), pages 209-221, November.
    14. Ling, Shiqing & McAleer, Michael, 2002. "Stationarity and the existence of moments of a family of GARCH processes," Journal of Econometrics, Elsevier, vol. 106(1), pages 109-117, January.
    15. Giovanni Barone Adesi & Robert F. Engle & Loriano Mancini, 2014. "A GARCH Option Pricing Model with Filtered Historical Simulation," Palgrave Macmillan Books, in: Giovanni Barone Adesi (ed.), Simulating Security Returns: A Filtered Historical Simulation Approach, chapter 4, pages 66-108, Palgrave Macmillan.
    16. repec:hal:journl:peer-00732534 is not listed on IDEAS
    17. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    18. Hall, Peter & Yao, Qiwei, 2003. "Inference in ARCH and GARCH models with heavy-tailed errors," LSE Research Online Documents on Economics 5875, London School of Economics and Political Science, LSE Library.
    19. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    20. Ngai Hang Chan & Liang Peng, 2005. "Weighted least absolute deviations estimation for an AR(1) process with ARCH(1) errors," Biometrika, Biometrika Trust, vol. 92(2), pages 477-484, June.
    21. Peter Hall & Qiwei Yao, 2003. "Inference in Arch and Garch Models with Heavy--Tailed Errors," Econometrica, Econometric Society, vol. 71(1), pages 285-317, January.
    22. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Wang, Guochang & Zhu, Ke & Li, Guodong & Li, Wai Keung, 2022. "Hybrid quantile estimation for asymmetric power GARCH models," Journal of Econometrics, Elsevier, vol. 227(1), pages 264-284.
    2. Li, Haiqi & Zheng, Chaowen & Guo, Yu, 2016. "Estimation and test for quantile nonlinear cointegrating regression," Economics Letters, Elsevier, vol. 148(C), pages 27-32.
    3. Ling, Shiqing & McAleer, Michael & Tong, Howell, 2015. "Frontiers in Time Series and Financial Econometrics: An overview," Journal of Econometrics, Elsevier, vol. 189(2), pages 245-250.
    4. Manabu Asai & Mike K. P. So, 2021. "Quasi‐maximum likelihood estimation of conditional autoregressive Wishart models," Journal of Time Series Analysis, Wiley Blackwell, vol. 42(3), pages 271-294, May.
    5. Guochang Wang & Ke Zhu & Guodong Li & Wai Keung Li, 2019. "Hybrid quantile estimation for asymmetric power GARCH models," Papers 1911.09343, arXiv.org.
    6. Tomohiro Ando & Jushan Bai, 2020. "Quantile Co-Movement in Financial Markets: A Panel Quantile Model With Unobserved Heterogeneity," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(529), pages 266-279, January.
    7. Ling, S. & McAleer, M.J. & Tong, H., 2015. "Frontiers in Time Series and Financial Econometrics," Econometric Institute Research Papers EI 2015-07, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    8. Yuzhi Cai & Guodong Li, 2018. "A novel approach to modelling the distribution of financial returns," Working Papers 2018-22, Swansea University, School of Management.

    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. Nieto, Maria Rosa & Ruiz, Esther, 2016. "Frontiers in VaR forecasting and backtesting," International Journal of Forecasting, Elsevier, vol. 32(2), pages 475-501.
    2. Cathy Chen & Richard Gerlach, 2013. "Semi-parametric quantile estimation for double threshold autoregressive models with heteroskedasticity," Computational Statistics, Springer, vol. 28(3), pages 1103-1131, June.
    3. Mohamed El Ghourabi & Christian Francq & Fedya Telmoudi, 2016. "Consistent Estimation of the Value at Risk When the Error Distribution of the Volatility Model is Misspecified," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(1), pages 46-76, January.
    4. Zhu, Ke & Ling, Shiqing, 2013. "Global self-weighted and local quasi-maximum exponential likelihood estimators for ARMA-GARCH/IGARCH models," MPRA Paper 51509, University Library of Munich, Germany.
    5. Meister, Alexander & Kreiß, Jens-Peter, 2016. "Statistical inference for nonparametric GARCH models," Stochastic Processes and their Applications, Elsevier, vol. 126(10), pages 3009-3040.
    6. Francq, Christian & Zakoïan, Jean-Michel, 2015. "Risk-parameter estimation in volatility models," Journal of Econometrics, Elsevier, vol. 184(1), pages 158-173.
    7. Jianqing Fan & Lei Qi & Dacheng Xiu, 2014. "Quasi-Maximum Likelihood Estimation of GARCH Models With Heavy-Tailed Likelihoods," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 32(2), pages 178-191, April.
    8. Li, Dong & Li, Muyi & Wu, Wuqing, 2014. "On dynamics of volatilities in nonstationary GARCH models," Statistics & Probability Letters, Elsevier, vol. 94(C), pages 86-90.
    9. Komunjer, Ivana, 2013. "Quantile Prediction," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 961-994, Elsevier.
    10. 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.
    11. Eric Beutner & Julia Schaumburg & Barend Spanjers, 2024. "Bootstrapping GARCH Models Under Dependent Innovations," Tinbergen Institute Discussion Papers 24-008/III, Tinbergen Institute.
    12. Luc Bauwens & Sébastien Laurent & Jeroen V. K. Rombouts, 2006. "Multivariate GARCH models: a survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(1), pages 79-109, January.
    13. Dominique Guegan & Bertrand K. Hassani, 2019. "Risk Measurement," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-02119256, HAL.
    14. Cathy Chen & Simon Lin & Philip Yu, 2012. "Smooth Transition Quantile Capital Asset Pricing Models with Heteroscedasticity," Computational Economics, Springer;Society for Computational Economics, vol. 40(1), pages 19-48, June.
    15. Degiannakis, Stavros & Xekalaki, Evdokia, 2004. "Autoregressive Conditional Heteroskedasticity (ARCH) Models: A Review," MPRA Paper 80487, University Library of Munich, Germany.
    16. Hubner, Stefan, 2016. "Topics in nonparametric identification and estimation," Other publications TiSEM 08fce56b-3193-46e0-871b-0, Tilburg University, School of Economics and Management.
    17. Beutner, Eric & Heinemann, Alexander & Smeekes, Stephan, 2024. "A residual bootstrap for conditional Value-at-Risk," Journal of Econometrics, Elsevier, vol. 238(2).
    18. Harvey,Andrew C., 2013. "Dynamic Models for Volatility and Heavy Tails," Cambridge Books, Cambridge University Press, number 9781107630024.
    19. Demos Antonis & Kyriakopoulou Dimitra, 2019. "Finite-Sample Theory and Bias Correction of Maximum Likelihood Estimators in the EGARCH Model," Journal of Time Series Econometrics, De Gruyter, vol. 11(1), pages 1-20, January.
    20. Wang, Hui & Pan, Jiazhu, 2014. "Normal mixture quasi maximum likelihood estimation for non-stationary TGARCH(1,1) models," Statistics & Probability Letters, Elsevier, vol. 91(C), pages 117-123.

    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:eee:econom:v:189:y:2015:i:2:p:457-472. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jeconom .

    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.