IDEAS home Printed from https://ideas.repec.org/a/eee/econom/v211y2019i2p319-337.html
   My bibliography  Save this article

Strict stationarity testing and GLAD estimation of double autoregressive models

Author

Listed:
  • Guo, Shaojun
  • Li, Dong
  • Li, Muyi

Abstract

In this article we develop a tractable procedure for testing strict stationarity in a double autoregressive model and formulate the problem as testing if the top Lyapunov exponent is negative. Without strict stationarity assumption, we construct a consistent estimator of the associated top Lyapunov exponent and employ a random weighting approach for its variance estimation, which in turn are used in a t-type test. We also propose a GLAD estimation for parameters of interest, relaxing key assumptions on the commonly used QMLE. All estimators, except for the intercept, are shown to be consistent and asymptotically normal in both stationary and explosive situations. The finite-sample performance of the proposed procedures is evaluated via Monte Carlo simulation studies and a real dataset of interest rates is analyzed.

Suggested Citation

  • Guo, Shaojun & Li, Dong & Li, Muyi, 2019. "Strict stationarity testing and GLAD estimation of double autoregressive models," Journal of Econometrics, Elsevier, vol. 211(2), pages 319-337.
  • Handle: RePEc:eee:econom:v:211:y:2019:i:2:p:319-337
    DOI: 10.1016/j.jeconom.2019.01.012
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304407619300466
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.jeconom.2019.01.012?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. Dovonon, Prosper & Gonçalves, Sílvia, 2017. "Bootstrapping the GMM overidentification test under first-order underidentification," Journal of Econometrics, Elsevier, vol. 201(1), pages 43-71.
    2. Min Chen & Dong Li & Shiqing Ling, 2014. "Non-Stationarity And Quasi-Maximum Likelihood Estimation On A Double Autoregressive Model," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(3), pages 189-202, May.
    3. Dong Li & Shiqing Ling & Rongmao Zhang, 2016. "On a Threshold Double Autoregressive Model," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(1), pages 68-80, January.
    4. Shiqing Ling & Dong Li, 2008. "Asymptotic inference for a nonstationary double AR (1) model," Biometrika, Biometrika Trust, vol. 95(1), pages 257-263.
    5. Andrew A. Weiss, 1984. "Arma Models With Arch Errors," Journal of Time Series Analysis, Wiley Blackwell, vol. 5(2), pages 129-143, March.
    6. Ke Zhu, 2016. "Bootstrapping the portmanteau tests in weak auto-regressive moving average models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(2), pages 463-485, March.
    7. Guodong Li & Chenlei Leng & Chih-Ling Tsai, 2014. "A Hybrid Bootstrap Approach To Unit Root Tests," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(4), pages 299-321, July.
    8. Jensen, Søren Tolver & Rahbek, Anders, 2004. "Asymptotic Inference For Nonstationary Garch," Econometric Theory, Cambridge University Press, vol. 20(6), pages 1203-1226, December.
    9. Li, Dong & Ling, Shiqing & Zakoïan, Jean-Michel, 2015. "Asymptotic inference in multiple-threshold double autoregressive models," Journal of Econometrics, Elsevier, vol. 189(2), pages 415-427.
    10. Søren Tolver Jensen & Anders Rahbek, 2004. "Asymptotic Normality of the QMLE Estimator of ARCH in the Nonstationary Case," Econometrica, Econometric Society, vol. 72(2), pages 641-646, March.
    11. Kani Chen & Zhiliang Ying & Hong Zhang & Lincheng Zhao, 2008. "Analysis of least absolute deviation," Biometrika, Biometrika Trust, vol. 95(1), pages 107-122.
    12. Nielsen, Heino Bohn & Rahbek, Anders, 2014. "Unit root vector autoregression with volatility induced stationarity," Journal of Empirical Finance, Elsevier, vol. 29(C), pages 144-167.
    13. Feng Liu & Dong Li & Xinmei Kang, 2018. "Sample path properties of an explosive double autoregressive model," Econometric Reviews, Taylor & Francis Journals, vol. 37(5), pages 484-490, May.
    14. Guodong Li & Qianqian Zhu & Zhao Liu & Wai Keung Li, 2017. "On Mixture Double Autoregressive Time Series Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(2), pages 306-317, April.
    15. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    16. Christian Francq & Jean‐Michel Zakoïan, 2012. "Strict Stationarity Testing and Estimation of Explosive and Stationary Generalized Autoregressive Conditional Heteroscedasticity Models," Econometrica, Econometric Society, vol. 80(2), pages 821-861, March.
    17. 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.
    18. Chen, Kani & Guo, Shaojun & Lin, Yuanyuan & Ying, Zhiliang, 2010. "Least Absolute Relative Error Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 105(491), pages 1104-1112.
    19. Francq, Christian & Zakoian, Jean-Michel, 2013. "Inference in non stationary asymmetric garch models," MPRA Paper 44901, University Library of Munich, Germany.
    20. Francq, Christian & Zakoian, Jean-Michel, 2007. "Quasi-maximum likelihood estimation in GARCH processes when some coefficients are equal to zero," Stochastic Processes and their Applications, Elsevier, vol. 117(9), pages 1265-1284, September.
    21. Shiqing Ling, 2004. "Estimation and testing stationarity for double‐autoregressive models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(1), pages 63-78, February.
    22. Zhu, Qianqian & Zheng, Yao & Li, Guodong, 2018. "Linear double autoregression," Journal of Econometrics, Elsevier, vol. 207(1), pages 162-174.
    23. 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. Lee, Sangyeol & Meintanis, Simos G. & Pretorius, Charl, 2022. "Monitoring procedures for strict stationarity based on the multivariate characteristic function," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    2. Li, Muyi & Zhang, Yanfen, 2022. "Bootstrapping multivariate portmanteau tests for vector autoregressive models with weak assumptions on errors," Computational Statistics & Data Analysis, Elsevier, vol. 165(C).
    3. Wang, Xuqin & Li, Muyi, 2023. "Bootstrapping the transformed goodness-of-fit test on heavy-tailed GARCH models," Computational Statistics & Data Analysis, Elsevier, vol. 184(C).
    4. Huan Gong & Dong Li, 2020. "On the three‐step non‐Gaussian quasi‐maximum likelihood estimation of heavy‐tailed double autoregressive models," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(6), pages 883-891, November.
    5. Denys Pommeret & Laurence Reboul & Anne-francoise Yao, 2023. "Testing the equality of the laws of two strictly stationary processes," Statistical Inference for Stochastic Processes, Springer, vol. 26(1), pages 193-214, April.
    6. Li, Dong & Tao, Yuxin & Yang, Yaxing & Zhang, Rongmao, 2023. "Maximum likelihood estimation for α-stable double autoregressive models," Journal of Econometrics, Elsevier, vol. 236(1).

    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. Li, Dong & Tao, Yuxin & Yang, Yaxing & Zhang, Rongmao, 2023. "Maximum likelihood estimation for α-stable double autoregressive models," Journal of Econometrics, Elsevier, vol. 236(1).
    2. Huan Gong & Dong Li, 2020. "On the three‐step non‐Gaussian quasi‐maximum likelihood estimation of heavy‐tailed double autoregressive models," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(6), pages 883-891, November.
    3. Min Chen & Dong Li & Shiqing Ling, 2014. "Non-Stationarity And Quasi-Maximum Likelihood Estimation On A Double Autoregressive Model," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(3), pages 189-202, May.
    4. Li, Dong & Zhang, Xingfa & Zhu, Ke & Ling, Shiqing, 2018. "The ZD-GARCH model: A new way to study heteroscedasticity," Journal of Econometrics, Elsevier, vol. 202(1), pages 1-17.
    5. Li, Dong & Ling, Shiqing & Zhu, Ke, 2016. "ZD-GARCH model: a new way to study heteroscedasticity," MPRA Paper 68621, University Library of Munich, Germany.
    6. Aknouche, Abdelhakim, 2015. "Unified quasi-maximum likelihood estimation theory for stable and unstable Markov bilinear processes," MPRA Paper 69572, University Library of Munich, Germany.
    7. 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.
    8. Zhu, Huafeng & Zhang, Xingfa & Liang, Xin & Li, Yuan, 2017. "On a vector double autoregressive model," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 86-95.
    9. 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.
    10. 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.
    11. Guochang Wang & Ke Zhu & Guodong Li & Wai Keung Li, 2019. "Hybrid quantile estimation for asymmetric power GARCH models," Papers 1911.09343, arXiv.org.
    12. Zhu Huafeng & Zhang Xingfa & Liang Xin & Li Yuan, 2018. "Moving Average Model with an Alternative GARCH-Type Error," Journal of Systems Science and Information, De Gruyter, vol. 6(2), pages 165-177, April.
    13. Kai Yang & Qingqing Zhang & Xinyang Yu & Xiaogang Dong, 2023. "Bayesian inference for a mixture double autoregressive model," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 77(2), pages 188-207, May.
    14. Songhua Tan & Qianqian Zhu, 2022. "Asymmetric linear double autoregression," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(3), pages 371-388, May.
    15. Dong Li & Shiqing Ling & Rongmao Zhang, 2016. "On a Threshold Double Autoregressive Model," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(1), pages 68-80, January.
    16. Jiang, Feiyu & Li, Dong & Zhu, Ke, 2020. "Non-standard inference for augmented double autoregressive models with null volatility coefficients," Journal of Econometrics, Elsevier, vol. 215(1), pages 165-183.
    17. Francq, Christian & Zakoïan, Jean-Michel, 2022. "Testing the existence of moments for GARCH processes," Journal of Econometrics, Elsevier, vol. 227(1), pages 47-64.
    18. Feiyu Jiang & Dong Li & Ke Zhu, 2019. "Non-standard inference for augmented double autoregressive models with null volatility coefficients," Papers 1905.01798, arXiv.org.
    19. Ke Zhu, 2016. "Bootstrapping the portmanteau tests in weak auto-regressive moving average models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(2), pages 463-485, March.
    20. Ke Zhu & Shiqing Ling, 2015. "LADE-Based Inference for ARMA Models With Unspecified and Heavy-Tailed Heteroscedastic Noises," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(510), pages 784-794, June.

    More about this item

    Keywords

    DAR model; GLAD estimation; Nonstationarity; Random weighting; Strict stationarity testing;
    All these keywords.

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

    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:eee:econom:v:211:y:2019:i:2:p:319-337. 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.