IDEAS home Printed from https://ideas.repec.org/a/bla/obuest/v83y2021i2p518-539.html
   My bibliography  Save this article

Mildly Explosive Autoregression with Anti‐persistent Errors

Author

Listed:
  • Yiu Lim Lui
  • Weilin Xiao
  • Jun Yu

Abstract

An asymptotic distribution is derived for the least squares (LS) estimate of a first‐order autoregression with a mildly explosive root and anti‐persistent errors. While the sample moments depend on the Hurst parameter asymptotically, the Cauchy limiting distribution theory remains valid for the LS estimates in the model without intercept and a model with an asymptotically negligible intercept. Monte Carlo studies are designed to check the precision of the Cauchy distribution in finite samples. An empirical study based on the monthly NASDAQ index highlights the usefulness of the model and the new limiting distribution.

Suggested Citation

  • Yiu Lim Lui & Weilin Xiao & Jun Yu, 2021. "Mildly Explosive Autoregression with Anti‐persistent Errors," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 83(2), pages 518-539, April.
    • Handle: RePEc:bla:obuest:v:83:y:2021:i:2:p:518-539
    DOI: 10.1111/obes.12395
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/obes.12395
    Download Restriction: no
    File URL: https://libkey.io/10.1111/obes.12395?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
    ---><---

    References listed on IDEAS

    as
    1. Peter C. B. Phillips & Shuping Shi & Jun Yu, 2015. "Testing For Multiple Bubbles: Historical Episodes Of Exuberance And Collapse In The S&P 500," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 56(4), pages 1043-1078, November.
    2. Park, Joon, 2003. "Weak Unit Roots," Working Papers 2003-17, Rice University, Department of Economics.
    3. Peter C. B. Phillips & Shuping Shi & Jun Yu, 2014. "Specification Sensitivity in Right-Tailed Unit Root Testing for Explosive Behaviour," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 76(3), pages 315-333, June.
    4. Magdalinos, Tassos, 2012. "Mildly explosive autoregression under weak and strong dependence," Journal of Econometrics, Elsevier, vol. 169(2), pages 179-187.
    5. Xiao, Weilin & Yu, Jun, 2019. "Asymptotic theory for rough fractional Vasicek models," Economics Letters, Elsevier, vol. 177(C), pages 26-29.
    6. Wang, Xiaohu & Xiao, Weilin & Yu, Jun, 2019. "Estimation and Inference of Fractional Continuous-Time Model with Discrete-Sampled Data," Economics and Statistics Working Papers 17-2019, Singapore Management University, School of Economics.
    7. Stelios Arvanitis & Tassos Magdalinos, 2018. "Mildly explosive autoregression under stationary conditional heteroskedasticity," Working Paper series 18-25, Rimini Centre for Economic Analysis.
    8. Stelios Arvanitis & Tassos Magdalinos, 2018. "Mildly Explosive Autoregression Under Stationary Conditional Heteroskedasticity," Journal of Time Series Analysis, Wiley Blackwell, vol. 39(6), pages 892-908, November.
    9. Peter C. B. Phillips & Shuping Shi & Jun Yu, 2015. "Testing For Multiple Bubbles: Limit Theory Of Real‐Time Detectors," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 56, pages 1079-1134, November.
    10. Pedersen, Thomas Quistgaard & Schütte, Erik Christian Montes, 2020. "Testing for explosive bubbles in the presence of autocorrelated innovations," Journal of Empirical Finance, Elsevier, vol. 58(C), pages 207-225.
    11. Peter C. B. Phillips & Shuping Shi & Jun Yu, 2015. "Testing For Multiple Bubbles: Historical Episodes Of Exuberance And Collapse In The S&P 500," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 56, pages 1043-1078, November.
    12. Xiao, Weilin & Yu, Jun, 2019. "Asymptotic Theory For Estimating Drift Parameters In The Fractional Vasicek Model," Econometric Theory, Cambridge University Press, vol. 35(1), pages 198-231, February.
    13. Peter C. B. Phillips & Shu-Ping Shi & Jun Yu, 2011. "Specification Sensitivity in Right-Tailed Unit Root Testing for Explosive Behavior," Working Papers 15-2011, Singapore Management University, School of Economics.
    14. Peter C. B. Phillips & Shuping Shi & Jun Yu, 2015. "Testing For Multiple Bubbles: Limit Theory Of Real‐Time Detectors," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 56(4), pages 1079-1134, November.
    15. David I. Harvey & Stephen J. Leybourne & Yang Zu, 2019. "Testing explosive bubbles with time-varying volatility," Econometric Reviews, Taylor & Francis Journals, vol. 38(10), pages 1131-1151, November.
    16. 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.
    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. Yijie Fei & Yiu Lim Lui & Jun Yu, 2024. "Testing Predictability in the Presence of Persistent Errors," Working Papers 202401, University of Macau, Faculty of Business Administration.
    2. Skrobotov Anton, 2023. "Testing for explosive bubbles: a review," Dependence Modeling, De Gruyter, vol. 11(1), pages 1-26, January.

    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. Lui, Yiu Lim & Phillips, Peter C.B. & Yu, Jun, 2024. "Robust testing for explosive behavior with strongly dependent errors," Journal of Econometrics, Elsevier, vol. 238(2).
    2. Janusz Sobieraj & Dominik Metelski, 2021. "Testing Housing Markets for Episodes of Exuberance: Evidence from Different Polish Cities," JRFM, MDPI, vol. 14(9), pages 1-29, September.
    3. Wang, Xiaohu & Yu, Jun, 2016. "Double asymptotics for explosive continuous time models," Journal of Econometrics, Elsevier, vol. 193(1), pages 35-53.
    4. Gomis-Porqueras, Pedro & Shi, Shuping & Tan, David, 2022. "Gold as a financial instrument," Journal of Commodity Markets, Elsevier, vol. 27(C).
    5. Skrobotov Anton, 2023. "Testing for explosive bubbles: a review," Dependence Modeling, De Gruyter, vol. 11(1), pages 1-26, January.
    6. Funke, Michael & Tsang, Andrew & Zhu, Linxu, 2018. "Not all cities are alike: House price heterogeneity and the design of macro-prudential policies in China," BOFIT Discussion Papers 18/2018, Bank of Finland Institute for Emerging Economies (BOFIT).
    7. 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.
    8. Congregado, Emilio & Esteve, Vicente, 2022. "Cointegration with structural changes and classical model of inflation in Spain, 1830–1998," Structural Change and Economic Dynamics, Elsevier, vol. 60(C), pages 376-388.
    9. Guo, Gangzheng & Wang, Shaoping & Sun, Yixiao, 2018. "Testing for Moderate Explosiveness in the Presence of Drift," University of California at San Diego, Economics Working Paper Series qt2k26h10n, Department of Economics, UC San Diego.
    10. Yang Hu, 2023. "A review of Phillips‐type right‐tailed unit root bubble detection tests," Journal of Economic Surveys, Wiley Blackwell, vol. 37(1), pages 141-158, February.
    11. 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.
    12. Robinson Kruse & Christoph Wegener, 2019. "Explosive behaviour and long memory with an application to European bond yield spreads," Scottish Journal of Political Economy, Scottish Economic Society, vol. 66(1), pages 139-153, February.
    13. Caravello, Tomas E. & Psaradakis, Zacharias & Sola, Martin, 2023. "Rational bubbles: Too many to be true?," Journal of Economic Dynamics and Control, Elsevier, vol. 151(C).
    14. Esteve, Vicente & Prats, María A., 2023. "Testing explosive bubbles with time-varying volatility: The case of Spanish public debt," Finance Research Letters, Elsevier, vol. 51(C).
    15. Michaelides, Panayotis G. & Tsionas, Efthymios G. & Konstantakis, Konstantinos N., 2016. "Non-linearities in financial bubbles: Theory and Bayesian evidence from S&P500," Journal of Financial Stability, Elsevier, vol. 24(C), pages 61-70.
    16. Funke, Michael & Tsang, Andrew & Zhu, Linxu, 2018. "Not all cities are alike: House price heterogeneity and the design of macro-prudential policies in China," BOFIT Discussion Papers 18/2018, Bank of Finland Institute for Emerging Economies (BOFIT).
    17. Gangzheng Guo & Yixiao Sun & Shaoping Wang, 2019. "Testing for moderate explosiveness," The Econometrics Journal, Royal Economic Society, vol. 22(1), pages 73-95.
    18. Etienne, Xiaoli L. & Irwin, Scott H. & Garcia, Philip, 2014. "Bubbles in food commodity markets: Four decades of evidence," Journal of International Money and Finance, Elsevier, vol. 42(C), pages 129-155.
    19. Feng, Hao, 2023. "Testing for explosive bubbles in the presence of non-Gaussian conditions," Economics Letters, Elsevier, vol. 233(C).
    20. repec:zbw:bofitp:2018_018 is not listed on IDEAS
    21. Maynard, Alex & Ren, Dongmeng, 2019. "The finite sample power of long-horizon predictive tests in models with financial bubbles," International Review of Financial Analysis, Elsevier, vol. 63(C), pages 418-430.

    More about this item

    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:bla:obuest:v:83:y:2021:i:2:p:518-539. 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: Wiley Content Delivery (email available below). General contact details of provider: https://edirc.repec.org/data/sfeixuk.html .

    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.