IDEAS home Printed from https://ideas.repec.org/a/kap/compec/v64y2024i3d10.1007_s10614-023-10501-4.html
   My bibliography  Save this article

A Unit Root Test with Markov Switching Deterministic Components: A Special Emphasis on Nonlinear Optimization Algorithms

Author

Listed:
  • Tolga Omay

    (Atilim University)

  • Aysegul Corakci

    (Çankaya University)

Abstract

In this study, we investigate the performance of different optimization algorithms in estimating the Markov switching (MS) deterministic components of the traditional ADF test. For this purpose, we consider Broyden, Fletcher, Goldfarb, and Shanno (BFGS), Berndt, Hall, Hall, Hausman (BHHH), Simplex, Genetic, and Expectation-Maximization (EM) algorithms. The simulation studies show that the Simplex method has significant advantages over the other commonly used hill-climbing methods and EM. It gives unbiased estimates of the MS deterministic components of the ADF unit root test and delivers good size and power properties. When Hamilton’s (Econometrica 57:357–384, 1989) MS model is re-evaluated in conjunction with the alternative algorithms, we furthermore show that Simplex converges to the global optima in stationary MS models with remarkably high precision and even when convergence criterion is raised, or initial values are altered. These advantages of the Simplex routine in MS models allow us to contribute to the current literature. First, we produce the exact critical values of the generalized ADF unit root test with MS breaks in trends. Second, we derive the asymptotic distribution of this test and provide its invariance feature.

Suggested Citation

  • Tolga Omay & Aysegul Corakci, 2024. "A Unit Root Test with Markov Switching Deterministic Components: A Special Emphasis on Nonlinear Optimization Algorithms," Computational Economics, Springer;Society for Computational Economics, vol. 64(3), pages 1837-1856, September.
    • Handle: RePEc:kap:compec:v:64:y:2024:i:3:d:10.1007_s10614-023-10501-4
    DOI: 10.1007/s10614-023-10501-4
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10614-023-10501-4
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10614-023-10501-4?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. 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.
    2. Camacho, Maximo, 2011. "Markov-switching models and the unit root hypothesis in real US GDP," Economics Letters, Elsevier, vol. 112(2), pages 161-164, August.
    3. Nelson, Charles R & Piger, Jeremy & Zivot, Eric, 2001. "Markov Regime Switching and Unit-Root Tests," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(4), pages 404-415, October.
    4. Kanas, Angelos & Genius, Margarita, 2005. "Regime (non)stationarity in the US/UK real exchange rate," Economics Letters, Elsevier, vol. 87(3), pages 407-413, June.
    5. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-384, March.
    6. 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.
    7. Giuseppe Cavaliere, 2003. "Asymptotics for unit root tests under Markov regime-switching," Econometrics Journal, Royal Economic Society, vol. 6(1), pages 193-216, June.
    8. Hall, Stephen G & Psaradakis, Zacharias & Sola, Martin, 1999. "Detecting Periodically Collapsing Bubbles: A Markov-Switching Unit Root Test," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 14(2), pages 143-154, March-Apr.
    9. Tolga Omay & Furkan Emirmahmutoğlu, 2017. "The Comparison of Power and Optimization Algorithms on Unit Root Testing with Smooth Transition," Computational Economics, Springer;Society for Computational Economics, vol. 49(4), pages 623-651, April.
    10. Hamilton, James D., 1990. "Analysis of time series subject to changes in regime," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 39-70.
    11. Kanas, Angelos, 2006. "Purchasing Power Parity and Markov Regime Switching," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 38(6), pages 1669-1687, September.
    12. Stephen Leybourne & Paul Newbold & Dimitrios Vougas, 1998. "Unit roots and smooth transitions," Journal of Time Series Analysis, Wiley Blackwell, vol. 19(1), pages 83-97, January.
    13. Zacharias Psaradakis, 2001. "Markov level shifts and the unit-root hypothesis," Econometrics Journal, Royal Economic Society, vol. 4(2), pages 1-4.
    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. Emrah Çevik & Erdal Atukeren & Turhan Korkmaz, 2013. "Nonlinearity and nonstationarity in international art market prices: evidence from Markov-switching ADF unit root tests," Empirical Economics, Springer, vol. 45(2), pages 675-695, October.
    2. Cevik, Emrah Ismail & Dibooglu, Sel, 2013. "Persistence and non-linearity in US unemployment: A regime-switching approach," Economic Systems, Elsevier, vol. 37(1), pages 61-68.
    3. Brian M. Lucey & Fergal A. O’Connor, 2013. "Do bubbles occur in the gold price? An investigation of gold lease rates and Markov Switching models," Borsa Istanbul Review, Research and Business Development Department, Borsa Istanbul, vol. 13(3), pages 53-63, September.
    4. Carlo Di Giorgio, 2016. "Business Cycle Synchronization of CEECs with the Euro Area: A Regime Switching Approach," Journal of Common Market Studies, Wiley Blackwell, vol. 54(2), pages 284-300, March.
    5. Shyh-Wei Chen, 2008. "Non-stationarity and Non-linearity in Stock Prices: Evidence from the OECD Countries," Economics Bulletin, AccessEcon, vol. 3(11), pages 1-11.
    6. Wang, Fang, 2023. "Do emerging art market segments have their own price dynamics? Evidence from the Chinese art market," International Review of Economics & Finance, Elsevier, vol. 84(C), pages 318-331.
    7. Lee, Hwa-Taek & Yoon, Gawon, 2007. "Does Purchasing Power Parity Hold Sometimes? Regime Switching in Real Exchange Rates," Economics Working Papers 2007-24, Christian-Albrechts-University of Kiel, Department of Economics.
    8. Robinson Kruse & Michael Frömmel & Lukas Menkhoff & Philipp Sibbertsen, 2012. "What do we know about real exchange rate nonlinearities?," Empirical Economics, Springer, vol. 43(2), pages 457-474, October.
    9. Hwa-Taek Lee & Gawon Yoon, 2013. "Does purchasing power parity hold sometimes? Regime switching in real exchange rates," Applied Economics, Taylor & Francis Journals, vol. 45(16), pages 2279-2294, June.
    10. Marcos José Dal Bianco, 2008. "Argentinean real exchange rate 1900-2006, test purchasing power parity theory," Estudios de Economia, University of Chile, Department of Economics, vol. 35(1 Year 20), pages 33-64, June.
    11. repec:dau:papers:123456789/11721 is not listed on IDEAS
    12. Aksoy Yunus & Leon-Ledesma Miguel A., 2008. "Non-Linearities and Unit Roots in G7 Macroeconomic Variables," The B.E. Journal of Macroeconomics, De Gruyter, vol. 8(1), pages 1-44, February.
    13. Chew Lian Chua & Sandy Suardi, 2005. "Is There a Unit Root in East-Asian Short-Term Interest Rates?," Melbourne Institute Working Paper Series wp2005n14, Melbourne Institute of Applied Economic and Social Research, The University of Melbourne.
    14. Kuhanathan Ano Sujithan & Sanvi Avouyi-Dovi, 2013. "The links between some European financial factors and the BRICS credit default swap spreads," Post-Print hal-01511898, HAL.
    15. Camacho, Maximo, 2011. "Markov-switching models and the unit root hypothesis in real US GDP," Economics Letters, Elsevier, vol. 112(2), pages 161-164, August.
    16. repec:ebl:ecbull:v:3:y:2008:i:11:p:1-11 is not listed on IDEAS
    17. 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.
    18. Balcilar, Mehmet & Gupta, Rangan & Jooste, Charl & Ranjbar, Omid, 2016. "Characterising the South African business cycle: is GDP difference-stationary or trend-stationary in a Markov-switching setup? - Il ciclo economico del Sud Africa: il PIL è stazion ario alle differenz," Economia Internazionale / International Economics, Camera di Commercio Industria Artigianato Agricoltura di Genova, vol. 69(1), pages 33-44.
    19. Gaia Garino & Lucio Sarno, 2004. "Speculative Bubbles in U.K. House Prices: Some New Evidence," Southern Economic Journal, John Wiley & Sons, vol. 70(4), pages 777-795, April.
    20. Randolph & Xiao Qin & Tan Gee Kwang, 2004. "Unit Root Tests with Markov-Switching," Econometric Society 2004 Australasian Meetings 145, Econometric Society.
    21. Dmitry Kulikov, 2012. "Testing for Rational Speculative Bubbles on the Estonian Stock Market," Research in Economics and Business: Central and Eastern Europe, Tallinn School of Economics and Business Administration, Tallinn University of Technology, vol. 4(1).
    22. Kanas, Angelos, 2008. "On real interest rate dynamics and regime switching," Journal of Banking & Finance, Elsevier, vol. 32(10), pages 2089-2098, October.

    More about this item

    Keywords

    Markov switching model; Unit root; Optimization algorithm;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C24 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Truncated and Censored Models; Switching Regression Models; Threshold Regression Models

    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:kap:compec:v:64:y:2024:i:3:d:10.1007_s10614-023-10501-4. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.