IDEAS home Printed from https://ideas.repec.org/a/eee/econom/v178y2014ip2p259-272.html
   My bibliography  Save this article

Testing for unit roots in bounded time series

Author

Listed:
  • Cavaliere, Giuseppe
  • Xu, Fang

Abstract

Many key economic and financial series are bounded either by construction or through policy controls. Conventional unit root tests are potentially unreliable in the presence of bounds, since they tend to over-reject the null hypothesis of a unit root, even asymptotically. So far, very little work has been undertaken to develop unit root tests which can be applied to bounded time series. In this paper we address this gap in the literature by proposing unit root tests which are valid in the presence of bounds. We present new augmented Dickey–Fuller type tests as well as new versions of the modified ‘M’ tests developed by Ng and Perron [Ng, S., Perron, P., 2001. LAG length selection and the construction of unit root tests with good size and power. Econometrica 69, 1519–1554] and demonstrate how these tests, combined with a simulation-based method to retrieve the relevant critical values, make it possible to control size asymptotically. A Monte Carlo study suggests that the proposed tests perform well in finite samples. Moreover, the tests outperform the Phillips–Perron type tests originally proposed in Cavaliere [Cavaliere, G., 2005. Limited time series with a unit root. Econometric Theory 21, 907–945]. An illustrative application to U.S. interest rate data is provided.

Suggested Citation

  • Cavaliere, Giuseppe & Xu, Fang, 2014. "Testing for unit roots in bounded time series," Journal of Econometrics, Elsevier, vol. 178(P2), pages 259-272.
  • Handle: RePEc:eee:econom:v:178:y:2014:i:p2:p:259-272
    DOI: 10.1016/j.jeconom.2013.08.026
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304407613001905
    Download Restriction: Full text for ScienceDirect subscribers only

    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. Ait-Sahalia, Yacine, 1996. "Testing Continuous-Time Models of the Spot Interest Rate," Review of Financial Studies, Society for Financial Studies, vol. 9(2), pages 385-426.
    2. Granger, Clive W.J., 2010. "Some thoughts on the development of cointegration," Journal of Econometrics, Elsevier, vol. 158(1), pages 3-6, September.
    3. Hansen, Bruce E, 1996. "Inference When a Nuisance Parameter Is Not Identified under the Null Hypothesis," Econometrica, Econometric Society, vol. 64(2), pages 413-430, March.
    4. Pierre Perron & Serena Ng, 1996. "Useful Modifications to some Unit Root Tests with Dependent Errors and their Local Asymptotic Properties," Review of Economic Studies, Oxford University Press, vol. 63(3), pages 435-463.
    5. Rose, Andrew Kenan, 1988. " Is the Real Interest Rate Stable?," Journal of Finance, American Finance Association, vol. 43(5), pages 1095-1112, December.
    6. Nicolau, Jo o, 2002. "Stationary Processes That Look Like Random Walks The Bounded Random Walk Process In Discrete And Continuous Time," Econometric Theory, Cambridge University Press, vol. 18(01), pages 99-118, February.
    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. Hansen, Bruce E., 2000. "Testing for structural change in conditional models," Journal of Econometrics, Elsevier, vol. 97(1), pages 93-115, July.
    9. Rodrigues, Paulo M.M. & Rubia, Antonio, 2005. "The performance of unit root tests under level-dependent heteroskedasticity," Economics Letters, Elsevier, vol. 89(3), pages 262-268, December.
    10. Cavaliere, Giuseppe & Taylor, A.M. Robert, 2009. "Heteroskedastic Time Series With A Unit Root," Econometric Theory, Cambridge University Press, vol. 25(05), pages 1228-1276, October.
    11. Campbell, John Y & Shiller, Robert J, 1987. "Cointegration and Tests of Present Value Models," Journal of Political Economy, University of Chicago Press, vol. 95(5), pages 1062-1088, October.
    12. Cavaliere, Giuseppe & Taylor, A.M. Robert, 2007. "Testing for unit roots in time series models with non-stationary volatility," Journal of Econometrics, Elsevier, vol. 140(2), pages 919-947, October.
    13. Elliott, Graham, 1999. "Efficient Tests for a Unit Root When the Initial Observation Is Drawn from Its Unconditional Distribution," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 40(3), pages 767-783, August.
    14. Andrews, Donald W K & Ploberger, Werner, 1994. "Optimal Tests When a Nuisance Parameter Is Present Only under the Alternative," Econometrica, Econometric Society, vol. 62(6), pages 1383-1414, November.
    15. Yoosoon Chang & Joon Y. Park, 2003. "A Sieve Bootstrap For The Test Of A Unit Root," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(4), pages 379-400, July.
    16. Cavaliere, Giuseppe, 2005. "Limited Time Series With A Unit Root," Econometric Theory, Cambridge University Press, vol. 21(05), pages 907-945, October.
    17. Giuseppe Cavaliere, 2000. "A Rescaled Range Statistics Approach to Unit Root Tests," Econometric Society World Congress 2000 Contributed Papers 0318, Econometric Society.
    18. Perron, Pierre & Rodriguez, Gabriel, 2003. "GLS detrending, efficient unit root tests and structural change," Journal of Econometrics, Elsevier, vol. 115(1), pages 1-27, July.
    19. Ulrich K. M¸ller & Graham Elliott, 2003. "Tests for Unit Roots and the Initial Condition," Econometrica, Econometric Society, vol. 71(4), pages 1269-1286, July.
    20. Lewis, Richard & Reinsel, Gregory C., 1985. "Prediction of multivariate time series by autoregressive model fitting," Journal of Multivariate Analysis, Elsevier, vol. 16(3), pages 393-411, June.
    21. Elliott, Graham & Rothenberg, Thomas J & Stock, James H, 1996. "Efficient Tests for an Autoregressive Unit Root," Econometrica, Econometric Society, vol. 64(4), pages 813-836, July.
    22. Johansen, Søren & Juselius, Katarina, 1992. "Testing structural hypotheses in a multivariate cointegration analysis of the PPP and the UIP for UK," Journal of Econometrics, Elsevier, vol. 53(1-3), pages 211-244.
    23. Yoosoon Chang & Joon Park, 2002. "On The Asymptotics Of Adf Tests For Unit Roots," Econometric Reviews, Taylor & Francis Journals, vol. 21(4), pages 431-447.
    24. Schmidt, Peter & Phillips, C B Peter, 1992. "LM Tests for a Unit Root in the Presence of Deterministic Trends," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 54(3), pages 257-287, August.
    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. 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.
    2. Niklas Potrafke & Markus Reischmann, 2012. "Fiscal Equalization Schemes and Fiscal Sustainability," ifo Working Paper Series 141, ifo Institute - Leibniz Institute for Economic Research at the University of Munich.
    3. repec:ebl:ecbull:eb-17-00577 is not listed on IDEAS
    4. Mathias Klein, 2015. "Inequality and household debt: a panel cointegration analysis," Empirica, Springer;Austrian Institute for Economic Research;Austrian Economic Association, vol. 42(2), pages 391-412, May.
    5. Niels Haldrup & Robinson Kruse & Timo Teräsvirta & Rasmus T. Varneskov, 2013. "Unit roots, non-linearities and structural breaks," Chapters,in: Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 4, pages 61-94 Edward Elgar Publishing.
    6. 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.
    7. Ott, Herve, 2012. "Which factors drive which volatility in the grain sector?," 123rd Seminar, February 23-24, 2012, Dublin, Ireland 122486, European Association of Agricultural Economists.
    8. Rengel, Malte & Herwartz, Helmut & Xu, Fang, 2013. "Persistence in the price-to-dividend ratio and its macroeconomic fundamentals," Annual Conference 2013 (Duesseldorf): Competition Policy and Regulation in a Global Economic Order 79860, Verein für Socialpolitik / German Economic Association.
    9. Bakas, Dimitrios & Papapetrou, Evangelia, 2014. "Unemployment in Greece: Evidence from Greek regions using panel unit root tests," The Quarterly Review of Economics and Finance, Elsevier, vol. 54(4), pages 551-562.
    10. Niklas Potrafke, 2015. "The Evidence on Globalisation," The World Economy, Wiley Blackwell, vol. 38(3), pages 509-552, March.
    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. Tiwari, Aviral Kumar & Albulescu, Claudiu Tiberiu, 2016. "Renewable-to-total electricity consumption ratio: Estimating the permanent or transitory fluctuations based on flexible Fourier stationarity and unit root tests," Renewable and Sustainable Energy Reviews, Elsevier, vol. 57(C), pages 1409-1427.
    13. Krenz, Astrid, 2016. "Do political institutions influence international trade? Measurement of institutions and the Long-Run effects," Center for European, Governance and Economic Development Research Discussion Papers 276, University of Goettingen, Department of Economics.
    14. repec:kap:iaecre:v:20:y:2014:i:1:p:103-111 is not listed on IDEAS
    15. repec:bla:ecinqu:v:55:y:2017:i:1:p:501-526 is not listed on IDEAS
    16. Niklas Potrafke & Markus Reischmann, 2015. "Fiscal Transfers and Fiscal Sustainability," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 47(5), pages 975-1005, August.
    17. Casalin, Fabrizio, 2013. "Testing the expectations hypothesis of the term structure with permanent-transitory component models," Journal of Banking & Finance, Elsevier, vol. 37(8), pages 3192-3203.
    18. Dimitrios Bakas & Theodore Panagiotidis & Gianluigi Pelloni, 2017. "Regional And Sectoral Evidence Of The Macroeconomic Effects Of Labor Reallocation: A Panel Data Analysis," Economic Inquiry, Western Economic Association International, vol. 55(1), pages 501-526, January.
    19. Steven Salaga & Rodney Fort, 2017. "Structural Change in Competitive Balance in Big-Time College Football," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 50(1), pages 27-41, February.
    20. Hertrich, Markus, 2015. "Does Credit Risk Impact Liquidity Risk? Evidence from Credit Default Swap Markets," MPRA Paper 67837, University Library of Munich, Germany.
    21. Maurizio Bovi, 2014. "Shocks and the Expectations Formation Process. A Tale of Two Expectations," Natural Field Experiments 00390, The Field Experiments Website.
    22. Salvatore Morelli, 2014. "Banking Crises in the US: the Response of Top Income Shares in a Historical Perspective," CSEF Working Papers 359, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy.
    23. Albanese, Marina & Bonasia, Mariangela & Napolitano, Oreste & Spagnolo, Nicola, 2015. "Happiness, taxes and social provision: A note," Economics Letters, Elsevier, vol. 135(C), pages 100-103.

    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:eee:econom:v:178:y:2014:i:p2:p:259-272. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: http://www.elsevier.com/locate/jeconom .

    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 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.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.