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"Detecting multiple level shifts in bounded time series"

Author

Listed:
  • Josep Lluís Carrion-i-Silvestre

    (AQR-IREA Research Group, Department of Econometrics, Statistics, and Spanish Economy, University of Barcelona. Av. Diagonal, 690. 08034 Barcelona.)

  • María Dolores Gadea

    (Department of Applied Economics, University of Zaragoza. Gran Vía, 4, 50005 Zaragoza (Spain).)

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"," IREA Working Papers 202115, University of Barcelona, Research Institute of Applied Economics, revised Jul 2021.
    • Handle: RePEc:ira:wpaper:202115
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    References listed on IDEAS

    as
    1. 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.
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    4. 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.
    5. 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.
    6. Cavaliere, Giuseppe, 2005. "Limited Time Series With A Unit Root," Econometric Theory, Cambridge University Press, vol. 21(5), pages 907-945, October.
    7. Cavaliere, Giuseppe & Xu, Fang, 2014. "Testing for unit roots in bounded time series," Journal of Econometrics, Elsevier, vol. 178(P2), pages 259-272.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
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    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

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