IDEAS home Printed from https://ideas.repec.org/p/aqr/wpaper/202106.html
   My bibliography  Save this paper

“Detecting multiple level shifts in bounded time series”

Author

Listed:
  • Josep Lluís Carrion-i-Silvestre

    (AQR-IREA, University of Barcelona)

  • María Dolores Gadea

    (University of Zaragoza)

Abstract

The paper proposes a sequential statistical procedure to test for the presence of level shifts affecting bounded time series, regardless of their order of integration. The paper shows that bounds are relevant for the statistic that assume that the time series are integrated of order one, whereas they do not affect the limiting distribution of the statistic that is defined for time series that are integrated of order zero. The paper proposes a union rejection statistic for bounded processes that does not require information about the order of integration of the stochastic processes. The model specification is general enough to consider the existence of structural breaks that can affect either the level of the time series and/or the bounds that limit its evolution. Monte Carlo simulations indicate that the procedure works well in finite samples. An empirical application that focuses on the Swiss franc against the euro exchange rate evolution illustrates the usefulness of the proposal.

Suggested Citation

  • Josep Lluís Carrion-i-Silvestre & María Dolores Gadea, 2021. "“Detecting multiple level shifts in bounded time series”," AQR Working Papers 202106, University of Barcelona, Regional Quantitative Analysis Group, revised Jul 2021.
    • Handle: RePEc:aqr:wpaper:202106
    as

    Download full text from publisher

    File URL: http://www.ub.edu/irea/working_papers/2021/202115.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Perron, Pierre & Yabu, Tomoyoshi, 2009. "Testing for Shifts in Trend With an Integrated or Stationary Noise Component," Journal of Business & Economic Statistics, American Statistical Association, vol. 27(3), pages 369-396.
    2. Mohitosh Kejriwal & Pierre Perron, 2010. "A sequential procedure to determine the number of breaks in trend with an integrated or stationary noise component," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(5), pages 305-328, September.
    3. Granger, Clive W.J., 2010. "Some thoughts on the development of cointegration," Journal of Econometrics, Elsevier, vol. 158(1), pages 3-6, September.
    4. Helmut Herwartz & Fang Xu, 2008. "Reviewing The Sustainability/Stationarity Of Current Account Imbalances With Tests For Bounded Integration," Manchester School, University of Manchester, vol. 76(3), pages 267-278, June.
    5. Perron, Pierre, 1989. "The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis," Econometrica, Econometric Society, vol. 57(6), pages 1361-1401, November.
    6. Cavaliere, Giuseppe, 2005. "Limited Time Series With A Unit Root," Econometric Theory, Cambridge University Press, vol. 21(5), pages 907-945, October.
    7. Serena Ng & Pierre Perron, 2001. "LAG Length Selection and the Construction of Unit Root Tests with Good Size and Power," Econometrica, Econometric Society, vol. 69(6), pages 1519-1554, November.
    8. Carrion-i-Silvestre, Josep Lluís & Gadea, María Dolores, 2013. "GLS-based unit root tests for bounded processes," Economics Letters, Elsevier, vol. 120(2), pages 184-187.
    9. Harvey, David I. & Leybourne, Stephen J. & Taylor, A.M. Robert, 2010. "Robust methods for detecting multiple level breaks in autocorrelated time series," Journal of Econometrics, Elsevier, vol. 157(2), pages 342-358, August.
    10. Cavaliere, Giuseppe & Xu, Fang, 2014. "Testing for unit roots in bounded time series," Journal of Econometrics, Elsevier, vol. 178(P2), pages 259-272.
    11. Josep Lluís Carrion-I-Silvestre & María Dolores Gadea, 2016. "Bounds, Breaks and Unit Root Tests," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(2), pages 165-181, March.
    12. Mirza Trokić, 2013. "Regulated fractionally integrated processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(5), pages 591-601, September.
    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. Niels Haldrup & Robinson Kruse & Timo Teräsvirta & Rasmus T. Varneskov, 2013. "Unit roots, non-linearities and structural breaks," Chapters, in: Nigar Hashimzade & Michael A. Thornton (ed.), Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 4, pages 61-94, Edward Elgar Publishing.
    2. James E. Payne & James W. Saunoris & Saban Nazlioglu & Cagin Karul, 2023. "The convergence dynamics of economic freedom across U.S. states," Southern Economic Journal, John Wiley & Sons, vol. 89(4), pages 1216-1241, April.
    3. James E. Payne & James W. Saunoris & Saban Nazlioglu & Cagin Karul, 2023. "Stochastic convergence analysis of US state economic freedom sub‐components: Evidence from unit root tests for bounded processes," American Journal of Economics and Sociology, Wiley Blackwell, vol. 82(4), pages 319-348, July.
    4. Alanya-Beltran, Willy, 2022. "Unit roots in lower-bounded series with outliers," Economic Modelling, Elsevier, vol. 115(C).
    5. Josep Lluís Carrion-i-Silvestre & María Dolores Gadea & Antonio Montañés, 2017. "“Unbiased estimation of autoregressive models forbounded stochastic processes," AQR Working Papers 201710, University of Barcelona, Regional Quantitative Analysis Group, revised Dec 2017.
    6. Mohitosh Kejriwal & Claude Lopez, 2013. "Unit Roots, Level Shifts, and Trend Breaks in Per Capita Output: A Robust Evaluation," Econometric Reviews, Taylor & Francis Journals, vol. 32(8), pages 892-927, November.
    7. Giorgio Canarella & Rangan Gupta & Stephen M. Miller & Stephen K. Pollard, 2019. "Unemployment rate hysteresis and the great recession: exploring the metropolitan evidence," Empirical Economics, Springer, vol. 56(1), pages 61-79, January.
    8. Skrobotov, Anton, 2020. "Survey on structural breaks and unit root tests," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 58, pages 96-141.
    9. Ghoshray Atanu & Kejriwal Mohitosh & Wohar Mark, 2014. "Breaks, trends and unit roots in commodity prices: a robust investigation," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 18(1), pages 23-40, February.
    10. Josep Lluís Carrion-I-Silvestre & María Dolores Gadea, 2016. "Bounds, Breaks and Unit Root Tests," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(2), pages 165-181, March.
    11. Ghoshray, Atanu & Kejriwal, Mohitosh & Wohar, Mark E., 2011. "Breaking Trends and the Prebisch-Singer Hypothesis: A Further Investigation," 2011 International Congress, August 30-September 2, 2011, Zurich, Switzerland 120387, European Association of Agricultural Economists.
    12. Josep Lluís Carrion‐i‐Silvestre & María Dolores Gadea & Antonio Montañés, 2021. "Nearly Unbiased Estimation of Autoregressive Models for Bounded Near‐Integrated Stochastic Processes," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 83(1), pages 273-297, February.
    13. Margherita Gerolimetto & Stefano Magrini, 2017. "On the power of the simulation-based ADF test in bounded time series," Economics Bulletin, AccessEcon, vol. 37(1), pages 539-552.
    14. Matteo Mogliani, 2010. "Residual-based tests for cointegration and multiple deterministic structural breaks: A Monte Carlo study," Working Papers halshs-00564897, HAL.
    15. Cavaliere, Giuseppe & Xu, Fang, 2014. "Testing for unit roots in bounded time series," Journal of Econometrics, Elsevier, vol. 178(P2), pages 259-272.
    16. Josep Lluís Carrion-i-Silvestre & Maria Dolores Gadea, 2015. "Testing for multiple level shifts in I(0) and I(1) stochastic processes," EcoMod2015 8702, EcoMod.
    17. Atanu Ghoshray & Issam Malki & Javier Ordóñez, 2022. "On the long-run dynamics of income and wealth inequality," Empirical Economics, Springer, vol. 62(2), pages 375-408, February.
    18. Skrobotov Anton, 2018. "On Trend Breaks and Initial Condition in Unit Root Testing," Journal of Time Series Econometrics, De Gruyter, vol. 10(1), pages 1-15, January.
    19. Bataa, Erdenebat & Izzeldin, Marwan & Osborn, Denise R., 2016. "Changes in the global oil market," Energy Economics, Elsevier, vol. 56(C), pages 161-176.
    20. Marcos Sanso-Navarro & María Vera-Cabello, 2020. "Income Inequality and Persistence Changes," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 152(2), pages 495-511, November.

    More about this item

    Keywords

    Structural breaks; bounded processes; changing bounds JEL classification: C12; C22;
    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:aqr:wpaper:202106. 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: Bibiana Barnadas (email available below). General contact details of provider: https://edirc.repec.org/data/aqrubes.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.