IDEAS home Printed from https://ideas.repec.org/a/spr/sistpr/v26y2023i3d10.1007_s11203-023-09290-2.html
   My bibliography  Save this article

Consistency and asymptotic normality in a class of nearly unstable processes

Author

Listed:
  • Marie Badreau

    (Le Mans Université)

  • Frédéric Proïa

    (Univ Angers)

Abstract

This paper deals with inference in a class of stable but nearly-unstable processes. Autoregressive processes are considered, in which the bridge between stability and instability is expressed by a time-varying companion matrix $$A_{n}$$ A n with spectral radius $$\rho (A_{n})

Suggested Citation

  • Marie Badreau & Frédéric Proïa, 2023. "Consistency and asymptotic normality in a class of nearly unstable processes," Statistical Inference for Stochastic Processes, Springer, vol. 26(3), pages 619-641, October.
    • Handle: RePEc:spr:sistpr:v:26:y:2023:i:3:d:10.1007_s11203-023-09290-2
    DOI: 10.1007/s11203-023-09290-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11203-023-09290-2
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11203-023-09290-2?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. Yu Miao & Yanling Wang & Guangyu Yang, 2015. "Moderate Deviation Principles for Empirical Covariance in the Neighbourhood of the Unit Root," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(1), pages 234-255, March.
    2. Liudas Giraitis & Peter C. B. Phillips, 2006. "Uniform Limit Theory for Stationary Autoregression," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(1), pages 51-60, January.
    3. Lorenzo Trapani, 2021. "Testing for strict stationarity in a random coefficient autoregressive model," Econometric Reviews, Taylor & Francis Journals, vol. 40(3), pages 220-256, April.
    4. Trapani, Lorenzo, 2021. "A test for strict stationarity in a random coefficient autoregressive model of order 1," Statistics & Probability Letters, Elsevier, vol. 177(C).
    5. 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.
    6. Peter C. B. Phillips & Ji Hyung Lee, 2015. "Limit Theory for VARs with Mixed Roots Near Unity," Econometric Reviews, Taylor & Francis Journals, vol. 34(6-10), pages 1035-1056, December.
    7. Horváth, Lajos & Trapani, Lorenzo, 2016. "Statistical inference in a random coefficient panel model," Journal of Econometrics, Elsevier, vol. 193(1), pages 54-75.
    8. Lai, T. L. & Wei, C. Z., 1983. "Asymptotic properties of general autoregressive models and strong consistency of least-squares estimates of their parameters," Journal of Multivariate Analysis, Elsevier, vol. 13(1), pages 1-23, March.
    9. Phillips, Peter C.B. & Magdalinos, Tassos, 2007. "Limit theory for moderate deviations from a unit root," Journal of Econometrics, Elsevier, vol. 136(1), pages 115-130, January.
    10. 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.
    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. Xinghui Wang & Wenjing Geng & Ruidong Han & Qifa Xu, 2023. "Asymptotic Properties of the M-estimation for an AR(1) Process with a General Autoregressive Coefficient," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-23, March.
    2. Lorenzo Trapani, 2021. "Testing for strict stationarity in a random coefficient autoregressive model," Econometric Reviews, Taylor & Francis Journals, vol. 40(3), pages 220-256, April.
    3. Ye Chen & Jian Li & Qiyuan Li, 2023. "Seemingly Unrelated Regression Estimation for VAR Models with Explosive Roots," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 85(4), pages 910-937, August.
    4. Nannan Ma & Hailin Sang & Guangyu Yang, 2023. "Least absolute deviation estimation for AR(1) processes with roots close to unity," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 75(5), pages 799-832, October.
    5. 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.
    6. Patrik Guggenberger, "undated". "Asymptotics for Stationary Very Nearly Unit Root Processes (joint with D.W.K. Andrews), this version November 2006," UCLA Economics Online Papers 402, UCLA Department of Economics.
    7. Yabe, Ryota, 2017. "Asymptotic distribution of the conditional-sum-of-squares estimator under moderate deviation from a unit root in MA(1)," Statistics & Probability Letters, Elsevier, vol. 125(C), pages 220-226.
    8. Giraitis, Liudas & Phillips, Peter C.B., 2012. "Mean and autocovariance function estimation near the boundary of stationarity," Journal of Econometrics, Elsevier, vol. 169(2), pages 166-178.
    9. Phillips, Peter C.B. & Lee, Ji Hyung, 2016. "Robust econometric inference with mixed integrated and mildly explosive regressors," Journal of Econometrics, Elsevier, vol. 192(2), pages 433-450.
    10. Andrews, Donald W.K. & Guggenberger, Patrik, 2012. "Asymptotics for LS, GLS, and feasible GLS statistics in an AR(1) model with conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 169(2), pages 196-210.
    11. Donald W. K. Andrews & Patrik Guggenberger, 2008. "Asymptotics for stationary very nearly unit root processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(1), pages 203-212, January.
    12. Zhishui Hu & Ioannis Kasparis & Qiying Wang, 2020. "Locally trimmed least squares: conventional inference in possibly nonstationary models," Papers 2006.12595, arXiv.org.
    13. Bailey, N. & Giraitis, L., 2013. "Weak convergence in the near unit root setting," Statistics & Probability Letters, Elsevier, vol. 83(5), pages 1411-1415.
    14. Lin, Yingqian & Tu, Yundong, 2020. "Robust inference for spurious regressions and cointegrations involving processes moderately deviated from a unit root," Journal of Econometrics, Elsevier, vol. 219(1), pages 52-65.
    15. 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.
    16. Chevillon, Guillaume & Mavroeidis, Sophocles, 2011. "Learning generates Long Memory," ESSEC Working Papers WP1113, ESSEC Research Center, ESSEC Business School.
    17. Kurozumi, Eiji & Hayakawa, Kazuhiko, 2009. "Asymptotic properties of the efficient estimators for cointegrating regression models with serially dependent errors," Journal of Econometrics, Elsevier, vol. 149(2), pages 118-135, April.
    18. Norbert Christopeit & Michael Massmann, 2018. "Strong consistency of the least squares estimator in regression models with adaptive learning," Tinbergen Institute Discussion Papers 18-045/III, Tinbergen Institute.
    19. Peter C. B. Phillips, 2014. "On Confidence Intervals for Autoregressive Roots and Predictive Regression," Econometrica, Econometric Society, vol. 82(3), pages 1177-1195, May.
    20. Tao, Yubo & Phillips, Peter C.B. & Yu, Jun, 2019. "Random coefficient continuous systems: Testing for extreme sample path behavior," Journal of Econometrics, Elsevier, vol. 209(2), pages 208-237.

    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:spr:sistpr:v:26:y:2023:i:3:d:10.1007_s11203-023-09290-2. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.