IDEAS home Printed from https://ideas.repec.org/p/ime/imedps/09-e-23.html
   My bibliography  Save this paper

Inconsistency of a Unit Root Test against Stochastic Unit Root Processes

Author

Listed:
  • Daisuke Nagakura

    (Institute for Monetary and Economic Studies, Bank of Japan (E-mail: daisuke.nagakura@boj.or.jp))

Abstract

In this paper, we develop the asymptotic theory of Hwang and Basawa (2005) for explosive random coefficient autoregressive (ERCA) models. Applying the theory, we prove that a locally best invariant (LBI) test in McCabe and Tremayne (1995), which is for the null of a unit root (UR) process against the alternative of a stochastic unit root (STUR) process, is inconsistent against a class of ERCA models. This class includes a class of STUR processes as special cases. We show, however, that the well-known Dickey-Fuller (DF) UR tests and an LBI test of Lee (1998) are consistent against a particular case of this class of ERCA models.

Suggested Citation

  • Daisuke Nagakura, 2009. "Inconsistency of a Unit Root Test against Stochastic Unit Root Processes," IMES Discussion Paper Series 09-E-23, Institute for Monetary and Economic Studies, Bank of Japan.
    • Handle: RePEc:ime:imedps:09-e-23
    as

    Download full text from publisher

    File URL: http://www.imes.boj.or.jp/research/papers/english/09-E-23.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. B. G. Quinn, 1982. "A Note On The Existence Of Strictly Stationary Solutions To Bilinear Equations," Journal of Time Series Analysis, Wiley Blackwell, vol. 3(4), pages 249-252, July.
    2. 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.
    3. Alexander Aue & Lajos Horváth & Josef Steinebach, 2006. "Estimation in Random Coefficient Autoregressive Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(1), pages 61-76, January.
    4. Robert Sollis & Paul Newbold & Stephen Leybourne, 2000. "Stochastic unit roots modelling of stock price indices," Applied Financial Economics, Taylor & Francis Journals, vol. 10(3), pages 311-315.
    5. Michael Bleaney & Stephen J. Leybourne, 2003. "Real Exchange Rate Dynamics Under The Current Float: A Re–Examination," Manchester School, University of Manchester, vol. 71(2), pages 156-171, March.
    6. Daisuke Nagakura, 2007. "Testing for Coefficient Stability of AR(1) Model When the Null is an Integrated or a Stationary Process," IMES Discussion Paper Series 07-E-20, Institute for Monetary and Economic Studies, Bank of Japan.
    7. Michael F. Bleaney & Stephen J. Leybourne & Paul Mizen, 1999. "Mean Reversion of Real Exchange Rates in High-Inflation Countries," Southern Economic Journal, John Wiley & Sons, vol. 65(4), pages 839-854, April.
    8. István Berkes & Lajos Horváth & Shiqing Ling, 2009. "Estimation in nonstationary random coefficient autoregressive models," Journal of Time Series Analysis, Wiley Blackwell, vol. 30(4), pages 395-416, 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. 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. Lajos Horvath & Lorenzo Trapani, 2021. "Changepoint detection in random coefficient autoregressive models," Papers 2104.13440, arXiv.org.
    3. Trapani, Lorenzo, 2021. "A test for strict stationarity in a random coefficient autoregressive model of order 1," Statistics & Probability Letters, Elsevier, vol. 177(C).
    4. 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.
    5. Jonathan Hill & Liang Peng, 2014. "Unified Interval Estimation For Random Coefficient Autoregressive Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(3), pages 282-297, May.
    6. Tao, Yubo & Phillips, Peter C.B. & Yu, Jun, 2017. "Random Coefficient Continuous Systems: Testing for Extreme Sample Path Behaviour," Economics and Statistics Working Papers 18-2017, Singapore Management University, School of Economics.
    7. Horváth, Lajos & Trapani, Lorenzo, 2019. "Testing for randomness in a random coefficient autoregression model," Journal of Econometrics, Elsevier, vol. 209(2), pages 338-352.

    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. Nagakura, Daisuke, 2009. "Asymptotic theory for explosive random coefficient autoregressive models and inconsistency of a unit root test against a stochastic unit root process," Statistics & Probability Letters, Elsevier, vol. 79(24), pages 2476-2483, December.
    2. Daisuke Nagakura, 2007. "Testing for Coefficient Stability of AR(1) Model When the Null is an Integrated or a Stationary Process," IMES Discussion Paper Series 07-E-20, Institute for Monetary and Economic Studies, Bank of Japan.
    3. Jonathan Hill & Liang Peng, 2014. "Unified Interval Estimation For Random Coefficient Autoregressive Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(3), pages 282-297, May.
    4. 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.
    5. Yoon, Gawon, 2004. "On the existence of expected utility with CRRA under STUR," Economics Letters, Elsevier, vol. 83(2), pages 219-224, May.
    6. Gawon Yoon, 2010. "Nonlinear mean-reversion to purchasing power parity: exponential smooth transition autoregressive models and stochastic unit root processes," Applied Economics, Taylor & Francis Journals, vol. 42(4), pages 489-496.
    7. Horváth, Lajos & Trapani, Lorenzo, 2019. "Testing for randomness in a random coefficient autoregression model," Journal of Econometrics, Elsevier, vol. 209(2), pages 338-352.
    8. 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.
    9. Yoon, Gawon, 2005. "Has the U.S. economy really become less correlated with that of the rest of the world?," Economic Modelling, Elsevier, vol. 22(1), pages 147-158, January.
    10. Horváth, Lajos & Trapani, Lorenzo, 2016. "Statistical inference in a random coefficient panel model," Journal of Econometrics, Elsevier, vol. 193(1), pages 54-75.
    11. Trapani, Lorenzo, 2021. "A test for strict stationarity in a random coefficient autoregressive model of order 1," Statistics & Probability Letters, Elsevier, vol. 177(C).
    12. Yoon, Gawon, 2016. "Stochastic unit root processes: Maximum likelihood estimation, and new Lagrange multiplier and likelihood ratio tests," Economic Modelling, Elsevier, vol. 52(PB), pages 725-732.
    13. Charemza, Wojciech W. & Lifshits, Mikhail & Makarova, Svetlana, 2005. "Conditional testing for unit-root bilinearity in financial time series: some theoretical and empirical results," Journal of Economic Dynamics and Control, Elsevier, vol. 29(1-2), pages 63-96, January.
    14. Mohammed Benmoumen & Imane Salhi, 2023. "The Strong Consistency of Quasi-Maximum Likelihood Estimators for p-order Random Coefficient Autoregressive (RCA) Models," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 617-632, February.
    15. Chi Yao & Wei Yu & Xuejun Wang, 2023. "Strong Consistency for the Conditional Self-weighted M Estimator of GRCA(p) Models," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-21, March.
    16. Angelos Kanas, 2009. "Real exchange rate, stationarity, and economic fundamentals," Journal of Economics and Finance, Springer;Academy of Economics and Finance, vol. 33(4), pages 393-409, October.
    17. Zheqi Wang & Dehui Wang & Jianhua Cheng, 2023. "A new autoregressive process driven by explanatory variables and past observations: an application to PM 2.5," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 32(2), pages 619-658, June.
    18. 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.
    19. Ramaprasad Bhar, 2010. "Stochastic Filtering with Applications in Finance," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 7736, December.
    20. Proïa, Frédéric & Soltane, Marius, 2021. "Comments on the presence of serial correlation in the random coefficients of an autoregressive process," Statistics & Probability Letters, Elsevier, vol. 170(C).

    More about this item

    Keywords

    Locally Best Invariant Test; Consistency; Dickey-Fuller Test; LBI; RCA; STUR;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:ime:imedps:09-e-23. 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: Kinken (email available below). General contact details of provider: https://edirc.repec.org/data/imegvjp.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.