IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v100y2016icp616-630.html
   My bibliography  Save this article

Bayesian model selection for unit root testing with multiple structural breaks

Author

Listed:
  • Vosseler, Alexander

Abstract

A fully Bayesian approach to unit root testing with multiple structural breaks is presented. For this purpose the number of breaks, the corresponding break dates as well as the number of autoregressive lags are treated as model indicators, whose posterior distributions are explored using a hybrid Markov chain Monte Carlo sampling strategy. The performance of the sampling algorithm is demonstrated on the basis of several Monte Carlo experiments. In a next step the most likely model is used to test for a unit root with possible multiple breaks by computing the posterior probability of this point hypothesis under different prior distributions. The sensitivity of the test results with regard to the assumed prior distribution is analyzed and the Bayes test is compared with some classical unit root tests by means of power functions. Finally, in an empirical application the yearly unemployment rates of 17 OECD countries are analyzed to answer the question if there is persistence after a labor market shock.

Suggested Citation

  • Vosseler, Alexander, 2016. "Bayesian model selection for unit root testing with multiple structural breaks," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 616-630.
    • Handle: RePEc:eee:csdana:v:100:y:2016:i:c:p:616-630
    DOI: 10.1016/j.csda.2014.08.016
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947314002485
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2014.08.016?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. Geweke, John, 1994. "Priors for Macroeconomic Time Series and Their Application," Econometric Theory, Cambridge University Press, vol. 10(3-4), pages 609-632, August.
    2. Sims, Christopher A., 1988. "Bayesian skepticism on unit root econometrics," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 463-474.
    3. Perron, Pierre & Vogelsang, Timothy J., "undated". "Level Shifts and Purchasing Power Parity," Instructional Stata datasets for econometrics levshift, Boston College Department of Economics.
    4. J. Vermaak & C. Andrieu & A. Doucet & S. J. Godsill, 2004. "Reversible Jump Markov Chain Monte Carlo Strategies for Bayesian Model Selection in Autoregressive Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(6), pages 785-809, November.
    5. Cathy Chen & Shu-Yu Chen & Sangyeol Lee, 2013. "Bayesian Unit Root Test in Double Threshold Heteroskedastic Models," Computational Economics, Springer;Society for Computational Economics, vol. 42(4), pages 471-490, December.
    6. Olivier Jean Blanchard & Lawrence F. Katz, 1992. "Regional Evolutions," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 23(1), pages 1-76.
    7. Zivot, Eric & Andrews, Donald W K, 2002. "Further Evidence on the Great Crash, the Oil-Price Shock, and the Unit-Root Hypothesis," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 25-44, January.
    8. Wang, Jiahui & Zivot, Eric, 2000. "A Bayesian Time Series Model of Multiple Structural Changes in Level, Trend, and Variance," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(3), pages 374-386, July.
    9. Lubrano, Michel, 1995. "Testing for unit roots in a Bayesian framework," Journal of Econometrics, Elsevier, vol. 69(1), pages 81-109, September.
    10. Koop, Gary & Steel, Mark F J, 1994. "A Decision-Theoretic Analysis of the Unit-Root Hypothesis Using Mixtures of Elliptical Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(1), pages 95-107, January.
    11. Summers, Peter M., 2004. "Bayesian evidence on the structure of unemployment," Economics Letters, Elsevier, vol. 83(3), pages 299-306, June.
    12. Sims, Christopher A & Uhlig, Harald, 1991. "Understanding Unit Rooters: A Helicopter Tour," Econometrica, Econometric Society, vol. 59(6), pages 1591-1599, November.
    13. Olivier J. Blanchard & Lawrence H. Summers, 1986. "Hysteresis and the European Unemployment Problem," NBER Chapters, in: NBER Macroeconomics Annual 1986, Volume 1, pages 15-90, National Bureau of Economic Research, Inc.
    14. 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.
    15. 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.
    16. Gabriel Huerta & Mike West, 1999. "Bayesian Inference on Periodicities and Component Spectral Structure in Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 20(4), pages 401-416, July.
    17. O. Mikhail & C. J. Eberwein & J. Handa, 2006. "Estimating persistence in Canadian unemployment: evidence from a Bayesian ARFIMA," Applied Economics, Taylor & Francis Journals, vol. 38(15), pages 1809-1819.
    18. Stock, James H., 1994. "Deciding between I(1) and I(0)," Journal of Econometrics, Elsevier, vol. 63(1), pages 105-131, July.
    19. Perron, Pierre & Vogelsang, Timothy J, 1992. "Nonstationarity and Level Shifts with an Application to Purchasing Power Parity," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(3), pages 301-320, July.
    20. Philippe, Anne, 2006. "Bayesian analysis of autoregressive moving average processes with unknown orders," Computational Statistics & Data Analysis, Elsevier, vol. 51(3), pages 1904-1923, December.
    21. Marriott, John & Newbold, Paul, 2000. "The strength of evidence for unit autoregressive roots and structural breaks: A Bayesian perspective," Journal of Econometrics, Elsevier, vol. 98(1), pages 1-25, September.
    22. Kenneth F. Wallis, 1987. "Time Series Analysis Of Bounded Economic Variables," Journal of Time Series Analysis, Wiley Blackwell, vol. 8(1), pages 115-123, January.
    23. Kadane, Joseph B. & Chan, Ngai Hang & Wolfson, Lara J., 1996. "Priors for unit root models," Journal of Econometrics, Elsevier, vol. 75(1), pages 99-111, November.
    24. Barnett, Glen & Kohn, Robert & Sheather, Simon, 1996. "Bayesian estimation of an autoregressive model using Markov chain Monte Carlo," Journal of Econometrics, Elsevier, vol. 74(2), pages 237-254, October.
    25. Phillips, P C B, 1991. "To Criticize the Critics: An Objective Bayesian Analysis of Stochastic Trends," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 6(4), pages 333-364, Oct.-Dec..
    26. Banerjee, Anindya & Dolado, Juan J. & Galbraith, John W. & Hendry, David, 1993. "Co-integration, Error Correction, and the Econometric Analysis of Non-Stationary Data," OUP Catalogue, Oxford University Press, number 9780198288107.
    27. 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.
    28. Tino Berger & Gerdie Everaert, 2008. "Unemployment Persistence And The Nairu: A Bayesian Approach," Scottish Journal of Political Economy, Scottish Economic Society, vol. 55(3), pages 281-299, July.
    29. Christiano, Lawrence J, 1992. "Searching for a Break in GNP," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(3), pages 237-250, July.
    30. Blanchard, Olivier J. & Summers, Lawrence H., 1987. "Hysteresis in unemployment," European Economic Review, Elsevier, vol. 31(1-2), pages 288-295.
    31. David H. Papell & Christian J. Murray & Hala Ghiblawi, 2000. "The Structure of Unemployment," The Review of Economics and Statistics, MIT Press, vol. 82(2), pages 309-315, May.
    32. Schotman, Peter & van Dijk, Herman K., 1991. "A Bayesian analysis of the unit root in real exchange rates," Journal of Econometrics, Elsevier, vol. 49(1-2), pages 195-238.
    33. Papell, David H & Prodan, Ruxandra, 2004. "The Uncertain Unit Root in U.S. Real GDP: Evidence with Restricted and Unrestricted Structural Change," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 36(3), pages 423-427, June.
    34. Hassler Uwe & Wolters Jürgen, 2009. "Hysteresis in Unemployment Rates? A Comparison between Germany and the US," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 229(2-3), pages 119-129, April.
    35. Geweke, J, 1993. "Bayesian Treatment of the Independent Student- t Linear Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(S), pages 19-40, Suppl. De.
    36. Gary Koop & Simon M. Potter, 2004. "Forecasting and estimating multiple change-point models with an unknown number of change points," Staff Reports 196, Federal Reserve Bank of New York.
    37. Uhlig, Harald, 1994. "What Macroeconomists Should Know about Unit Roots: A Bayesian Perspective," Econometric Theory, Cambridge University Press, vol. 10(3-4), pages 645-671, August.
    38. Chib, Siddhartha, 1998. "Estimation and comparison of multiple change-point models," Journal of Econometrics, Elsevier, vol. 86(2), pages 221-241, June.
    39. Hall, Alastair R, 1994. "Testing for a Unit Root in Time Series with Pretest Data-Based Model Selection," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(4), pages 461-470, October.
    40. Chen, Cathy W.S. & So, Mike K.P., 2006. "On a threshold heteroscedastic model," International Journal of Forecasting, Elsevier, vol. 22(1), pages 73-89.
    41. Nelson, Charles R. & Plosser, Charles I., 1982. "Trends and random walks in macroeconmic time series : Some evidence and implications," Journal of Monetary Economics, Elsevier, vol. 10(2), pages 139-162.
    42. Arestis, Philip & Biefang-Frisancho Mariscal, Iris, 1999. "Unit roots and structural breaks in OECD unemployment," Economics Letters, Elsevier, vol. 65(2), pages 149-156, November.
    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. Alexander Vosseler, 2022. "Unsupervised Insurance Fraud Prediction Based on Anomaly Detector Ensembles," Risks, MDPI, vol. 10(7), pages 1-20, June.
    2. Alexander Vosseler & Enzo Weber, 2017. "Bayesian analysis of periodic unit roots in the presence of a break," Applied Economics, Taylor & Francis Journals, vol. 49(38), pages 3841-3862, August.
    3. Magris Martin & Iosifidis Alexandros, 2021. "Approximate Bayes factors for unit root testing," Papers 2102.10048, arXiv.org, revised Feb 2021.
    4. Badri Narayan Rath & Vaseem Akram, 2021. "Popularity of Unit Root Tests - A Review," Asian Economics Letters, Asia-Pacific Applied Economics Association, vol. 2(4), pages 1-5.
    5. Niels Framroze Møller, 2019. "Decoding unemployment persistence: an econometric framework for identifying and comparing the sources of persistence with an application to UK macrodata," Empirical Economics, Springer, vol. 56(5), pages 1489-1514, May.
    6. Alexander Vosseler & Enzo Weber, 2018. "Forecasting seasonal time series data: a Bayesian model averaging approach," Computational Statistics, Springer, vol. 33(4), pages 1733-1765, December.

    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. Marriott, John & Newbold, Paul, 2000. "The strength of evidence for unit autoregressive roots and structural breaks: A Bayesian perspective," Journal of Econometrics, Elsevier, vol. 98(1), pages 1-25, September.
    2. 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.
    3. Loukia Meligkotsidou & Elias Tzavalis & Ioannis D. Vrontos, 2004. "A Bayesian Analysis of Unit Roots and Structural Breaks in the Level and the Error Variance of Autoregressive Models," Working Papers 514, Queen Mary University of London, School of Economics and Finance.
    4. Kelvin Balcombe & Iain Fraser & Abhijit Sharma, 2011. "Bayesian model averaging and identification of structural breaks in time series," Applied Economics, Taylor & Francis Journals, vol. 43(26), pages 3805-3818.
    5. Matteo Lanzafame, 2010. "The nature of regional unemployment in Italy," Empirical Economics, Springer, vol. 39(3), pages 877-895, December.
    6. Ewing, Bradley T. & Wunnava, Phanindra V., 2001. "Unit roots and structural breaks in North American unemployment rates," The North American Journal of Economics and Finance, Elsevier, vol. 12(3), pages 273-282, November.
    7. Gil-Alana, L. A. & Robinson, P. M., 1997. "Testing of unit root and other nonstationary hypotheses in macroeconomic time series," Journal of Econometrics, Elsevier, vol. 80(2), pages 241-268, October.
    8. Cuestas, Juan C. & Gil-Alana, Luis A. & Staehr, Karsten, 2011. "A further investigation of unemployment persistence in European transition economies," Journal of Comparative Economics, Elsevier, vol. 39(4), pages 514-532.
    9. Bayer Christian & Jüßen Falko, 2007. "Convergence in West German Regional Unemployment Rates," German Economic Review, De Gruyter, vol. 8(4), pages 510-535, December.
    10. 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.
    11. Paulo M. M. Rodrigues, 2013. "Recursive adjustment, unit root tests and structural breaks," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(1), pages 62-82, January.
    12. Clemente, Jesus & Lanaspa, Luis & Montanes, Antonio, 2005. "The unemployment structure of the US states," The Quarterly Review of Economics and Finance, Elsevier, vol. 45(4-5), pages 848-868, September.
    13. John D. Levendis, 2018. "Time Series Econometrics," Springer Texts in Business and Economics, Springer, number 978-3-319-98282-3, April.
    14. Aparicio, Felipe M. & García, Ana, 2003. "Range unit root tests," DES - Working Papers. Statistics and Econometrics. WS ws031126, Universidad Carlos III de Madrid. Departamento de Estadística.
    15. Diego Romero‐Ávila & Carlos Usabiaga, 2007. "Unit Root Tests, Persistence, and the Unemployment Rate of the U.S. States," Southern Economic Journal, John Wiley & Sons, vol. 73(3), pages 698-716, January.
    16. D. Ventosa-Santaulària, 2009. "Spurious Regression," Journal of Probability and Statistics, Hindawi, vol. 2009, pages 1-27, August.
    17. Marques, André M. & Lima, Gilberto Tadeu & Troster, Victor, 2017. "Unemployment persistence in OECD countries after the Great Recession," Economic Modelling, Elsevier, vol. 64(C), pages 105-116.
    18. Omay, Tolga & Shahbaz, Muhammad & Stewart, Chris, 2021. "Is There Really Hysteresis in OECD Countries’ Unemployment Rates? New Evidence Using a Fourier Panel Unit Root Test," MPRA Paper 107691, University Library of Munich, Germany, revised 10 May 2021.
    19. Ming Meng & Mark C. Strazicich & Junsoo Lee, 2017. "Hysteresis in unemployment? Evidence from linear and nonlinear unit root tests and tests with non-normal errors," Empirical Economics, Springer, vol. 53(4), pages 1399-1414, December.
    20. Bruce E. Hansen, 2001. "The New Econometrics of Structural Change: Dating Breaks in U.S. Labour Productivity," Journal of Economic Perspectives, American Economic Association, vol. 15(4), pages 117-128, Fall.

    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:csdana:v:100:y:2016:i:c:p:616-630. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    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.