IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v23y2021i3d10.1007_s11009-020-09781-2.html
   My bibliography  Save this article

Asymptotic Theory for a Stochastic Unit Root Model with Intercept and Under Mis-Specification of Intercept

Author

Listed:
  • Lingjie Du

    (Zhejiang University)

  • Tianxiao Pang

    (Zhejiang University)

Abstract

Lieberman and Phillips (J Time Ser Anal 35(6):592–623 2014, J Econ 196(1):99–110 2017) proposed a stochastic unit root model, where the source of the variation of the autoregressive coefficient is driven by a stationary process. In this paper, we study a new stochastic unit root model, in which the source of the variation of the autoregressive coefficient is driven by a (nearly) non-stationary process. The asymptotic theory for this model is established not only in the presence of an intercept but also under a mis-specification of intercept. Our study reveals some new findings which are different from those established in Lieberman and Phillips (J Time Ser Anal 35(6):592–623 2014, J Econ 196(1):99–110 2017). Our theoretical results demonstrate that the statistical properties of the estimators of the model parameters vary from case to case, and depend not only on whether the parameters are zero or not, and the validity of the model specification, but also on the degree of the persistence of the source of the variation of the autoregressive coefficient. The application to a hypothesis testing with null hypothesis of a deterministic unit root model is briefly discussed. Monte Carlo simulations are conducted to examine the finite-sample performance for the estimators of model parameters. Our theoretical findings are supported by the simulation results.

Suggested Citation

  • Lingjie Du & Tianxiao Pang, 2021. "Asymptotic Theory for a Stochastic Unit Root Model with Intercept and Under Mis-Specification of Intercept," Methodology and Computing in Applied Probability, Springer, vol. 23(3), pages 767-799, September.
    • Handle: RePEc:spr:metcap:v:23:y:2021:i:3:d:10.1007_s11009-020-09781-2
    DOI: 10.1007/s11009-020-09781-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-020-09781-2
    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/s11009-020-09781-2?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. 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. Matei Demetrescu, 2010. "On the Dickey–Fuller test with White standard errors," Statistical Papers, Springer, vol. 51(1), pages 11-25, January.
    3. Peter C. B. Phillips & Yangru Wu & Jun Yu, 2011. "EXPLOSIVE BEHAVIOR IN THE 1990s NASDAQ: WHEN DID EXUBERANCE ESCALATE ASSET VALUES?," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 52(1), pages 201-226, February.
    4. Choi, In & Phillips, Peter C. B., 1993. "Testing for a unit root by frequency domain regression," Journal of Econometrics, Elsevier, vol. 59(3), pages 263-286, October.
    5. Gawon Yoon, 2006. "A Note on Some Properties of STUR Processes," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 68(2), pages 253-260, April.
    6. Lieberman, Offer & Phillips, Peter C.B., 2017. "A multivariate stochastic unit root model with an application to derivative pricing," Journal of Econometrics, Elsevier, vol. 196(1), pages 99-110.
    7. Peter C.B. Phillips, 2008. "Unit Root Model Selection," Cowles Foundation Discussion Papers 1653, Cowles Foundation for Research in Economics, Yale University.
    8. Hansen, Bruce E., 1992. "Convergence to Stochastic Integrals for Dependent Heterogeneous Processes," Econometric Theory, Cambridge University Press, vol. 8(4), pages 489-500, December.
    9. Phillips, Peter C.B. & Shi, Shu-Ping, 2018. "Financial Bubble Implosion And Reverse Regression," Econometric Theory, Cambridge University Press, vol. 34(4), pages 705-753, August.
    10. 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.
    11. Granger, Clive W. J. & Swanson, Norman R., 1997. "An introduction to stochastic unit-root processes," Journal of Econometrics, Elsevier, vol. 80(1), pages 35-62, September.
    12. 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.
    13. Offer Lieberman & Peter C. B. Phillips, 2014. "Norming Rates And Limit Theory For Some Time-Varying Coefficient Autoregressions," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(6), pages 592-623, November.
    14. Phillips, Peter C.B. & Magdalinos, Tassos & Giraitis, Liudas, 2010. "Smoothing local-to-moderate unit root theory," Journal of Econometrics, Elsevier, vol. 158(2), pages 274-279, October.
    15. Emre Aylar & Stephan Smeekes & Joakim Westerlund, 2019. "Lag truncation and the local asymptotic distribution of the ADF test for a unit root," Statistical Papers, Springer, vol. 60(6), pages 2109-2118, December.
    16. Aue, Alexander, 2008. "Near-Integrated Random Coefficient Autoregressive Time Series," Econometric Theory, Cambridge University Press, vol. 24(5), pages 1343-1372, October.
    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. 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.
    2. Horváth, Lajos & Trapani, Lorenzo, 2019. "Testing for randomness in a random coefficient autoregression model," Journal of Econometrics, Elsevier, vol. 209(2), pages 338-352.
    3. Lieberman, Offer & Phillips, Peter C.B., 2020. "Hybrid stochastic local unit roots," Journal of Econometrics, Elsevier, vol. 215(1), pages 257-285.
    4. Francisco Blasques & Siem Jan Koopman & Gabriele Mingoli, 2023. "Observation-Driven filters for Time- Series with Stochastic Trends and Mixed Causal Non-Causal Dynamics," Tinbergen Institute Discussion Papers 23-065/III, Tinbergen Institute, revised 01 Mar 2024.
    5. Wang, Xichen & Yan, Ji (Karena) & Yan, Cheng & Gozgor, Giray, 2021. "Emerging stock market exuberance and international short-term flows," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 75(C).
    6. Bykhovskaya, Anna & Phillips, Peter C.B., 2020. "Point optimal testing with roots that are functionally local to unity," Journal of Econometrics, Elsevier, vol. 219(2), pages 231-259.
    7. 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).
    8. Efthymios Pavlidis & Alisa Yusupova & Ivan Paya & David Peel & Enrique Martínez-García & Adrienne Mack & Valerie Grossman, 2016. "Episodes of Exuberance in Housing Markets: In Search of the Smoking Gun," The Journal of Real Estate Finance and Economics, Springer, vol. 53(4), pages 419-449, November.
    9. 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.
    10. Akcora, Begum & Kandemir Kocaaslan, Ozge, 2023. "Price bubbles in the European natural gas market between 2011 and 2020," Resources Policy, Elsevier, vol. 80(C).
    11. 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).
    12. Lieberman, Offer & Phillips, Peter C.B., 2022. "Understanding temporal aggregation effects on kurtosis in financial indices," Journal of Econometrics, Elsevier, vol. 227(1), pages 25-46.
    13. Gomis-Porqueras, Pedro & Shi, Shuping & Tan, David, 2022. "Gold as a financial instrument," Journal of Commodity Markets, Elsevier, vol. 27(C).
    14. Aktham Maghyereh & Hussein Abdoh, 2022. "Bubble contagion effect between the main precious metals," Studies in Economics and Finance, Emerald Group Publishing Limited, vol. 40(1), pages 43-63, March.
    15. Figuerola-Ferretti, Isabel & McCrorie, J. Roderick & Paraskevopoulos, Ioannis, 2020. "Mild explosivity in recent crude oil prices," Energy Economics, Elsevier, vol. 87(C).
    16. Liu, Yanbo & Phillips, Peter C.B., 2023. "Robust inference with stochastic local unit root regressors in predictive regressions," Journal of Econometrics, Elsevier, vol. 235(2), pages 563-591.
    17. Hansen, Jacob H. & Møller, Stig V. & Pedersen, Thomas Q. & Schütte, Christian M., 2024. "House price bubbles under the COVID-19 pandemic," Journal of Empirical Finance, Elsevier, vol. 75(C).
    18. Pang, Tianxiao & Du, Lingjie & Chong, Terence Tai-Leung, 2021. "Estimating multiple breaks in nonstationary autoregressive models," Journal of Econometrics, Elsevier, vol. 221(1), pages 277-311.
    19. Astill, Sam & Taylor, A.M. Robert & Kellard, Neil & Korkos, Ioannis, 2023. "Using covariates to improve the efficacy of univariate bubble detection methods," Journal of Empirical Finance, Elsevier, vol. 70(C), pages 342-366.
    20. Gharib, Cheima & Mefteh-Wali, Salma & Serret, Vanessa & Ben Jabeur, Sami, 2021. "Impact of COVID-19 pandemic on crude oil prices: Evidence from Econophysics approach," Resources Policy, Elsevier, vol. 74(C).

    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:metcap:v:23:y:2021:i:3:d:10.1007_s11009-020-09781-2. 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.