IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v183y2022ics0167715221002911.html
   My bibliography  Save this article

A proof of consistency of the MLE for nonlinear Markov-switching AR processes

Author

Listed:
  • Fermín, Lisandro
  • Marcano, José
  • Rodríguez, Luis-Angel

Abstract

We propose a new approach to demonstrate the consistency of the maximum likelihood estimator for nonlinear Markov-switching AR processes (abbreviated MS-NAR). We obtain a uniform exponential memory loss property for the prediction filter by approximating it by a filter with finite memory. From the α-mixing property for the MS-NAR process we obtain an ergodic theorem. Finally, we show that in the linear and Gaussian case our assumptions are fully satisfied.

Suggested Citation

  • Fermín, Lisandro & Marcano, José & Rodríguez, Luis-Angel, 2022. "A proof of consistency of the MLE for nonlinear Markov-switching AR processes," Statistics & Probability Letters, Elsevier, vol. 183(C).
    • Handle: RePEc:eee:stapro:v:183:y:2022:i:c:s0167715221002911
    DOI: 10.1016/j.spl.2021.109347
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715221002911
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2021.109347?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. Vikram Krishnamurthy & Tobias Ryden, 1998. "Consistent Estimation of Linear and Non‐linear Autoregressive Models with Markov Regime," Journal of Time Series Analysis, Wiley Blackwell, vol. 19(3), pages 291-307, May.
    2. Goldfeld, Stephen M. & Quandt, Richard E., 1973. "A Markov model for switching regressions," Journal of Econometrics, Elsevier, vol. 1(1), pages 3-15, March.
    3. 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.
    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. Xi, Xiaojing & Mamon, Rogemar, 2011. "Parameter estimation of an asset price model driven by a weak hidden Markov chain," Economic Modelling, Elsevier, vol. 28(1-2), pages 36-46, January.
    2. Hendry, David F. & Clements, Michael P., 2003. "Economic forecasting: some lessons from recent research," Economic Modelling, Elsevier, vol. 20(2), pages 301-329, March.
    3. Nemati, Mehdi & Saghaian, Sayed H., 2016. "Dynamics of Price Adjustment in Qualitatively Differentiated Markets in the U.S.: The Case of Organic and Conventional Apples," 2016 Annual Meeting, February 6-9, 2016, San Antonio, Texas 229950, Southern Agricultural Economics Association.
    4. Elvio Accinelli & Juan Gabriel Brida, 2007. "Modelos económicos con múltiples regímenes," Revista de Administración, Finanzas y Economía (Journal of Management, Finance and Economics), Tecnológico de Monterrey, Campus Ciudad de México, vol. 1(2), pages 96-115.
    5. Aastveit, Knut Are & Jore, Anne Sofie & Ravazzolo, Francesco, 2016. "Identification and real-time forecasting of Norwegian business cycles," International Journal of Forecasting, Elsevier, vol. 32(2), pages 283-292.
    6. Liu, Wen-Hsien & Chyi, Yih-Luan, 2006. "A Markov regime-switching model for the semiconductor industry cycles," Economic Modelling, Elsevier, vol. 23(4), pages 569-578, July.
    7. Wang, Hong & Forbes, Catherine S. & Fenech, Jean-Pierre & Vaz, John, 2020. "The determinants of bank loan recovery rates in good times and bad – New evidence," Journal of Economic Behavior & Organization, Elsevier, vol. 177(C), pages 875-897.
    8. Hunt, Julien & Devolder, Pierre, 2011. "Semi Markov regime switching interest rate models and minimal entropy measure," LIDAM Discussion Papers ISBA 2011010, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    9. Grace Lee, 2011. "Aggregate shocks decomposition for eight East Asian countries," Journal of the Asia Pacific Economy, Taylor & Francis Journals, vol. 16(2), pages 215-232.
    10. Wong, Jian Cheng & Lian, Heng & Cheong, Siew Ann, 2009. "Detecting macroeconomic phases in the Dow Jones Industrial Average time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(21), pages 4635-4645.
    11. Custodio João, Igor & Lucas, André & Schaumburg, Julia & Schwaab, Bernd, 2023. "Dynamic clustering of multivariate panel data," Journal of Econometrics, Elsevier, vol. 237(2).
    12. Racicot, François-Éric & Théoret, Raymond, 2018. "Multi-moment risk, hedging strategies, & the business cycle," International Review of Economics & Finance, Elsevier, vol. 58(C), pages 637-675.
    13. Houda Rharrabti Zaid, 2015. "Transmission du stress financier de la zone euro aux Pays de l’Europe Centrale et Orientale," EconomiX Working Papers 2015-37, University of Paris Nanterre, EconomiX.
    14. Ali, Wajid & Ahmad, Iftikhar & Rafiq, Sara, 2020. "Regime Switches in Pakistan’s Fiscal Policy: Markov-Switching VAR Approach," Asian Journal of Applied Economics/ Applied Economics Journal, Kasetsart University, Faculty of Economics, Center for Applied Economic Research, vol. 27(2), pages 45-76, December.
    15. repec:wsr:wpaper:y:2010:i:057 is not listed on IDEAS
    16. 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.
    17. Fukuda, Kosei, 2009. "Distribution switching in financial time series," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(5), pages 1711-1720.
    18. 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).
    19. Constantino Hevia & Martín Sola & Ivan Petrella, 2022. "Bond risk premia, priced regime shifts, and macroeconomic fundamentals," Department of Economics Working Papers 2022_03, Universidad Torcuato Di Tella.
    20. Masaru Chiba, 2023. "Robust and efficient specification tests in Markov-switching autoregressive models," Statistical Inference for Stochastic Processes, Springer, vol. 26(1), pages 99-137, April.
    21. Alexander, Carol & Kaeck, Andreas, 2008. "Regime dependent determinants of credit default swap spreads," Journal of Banking & Finance, Elsevier, vol. 32(6), pages 1008-1021, June.

    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:stapro:v:183:y:2022:i:c:s0167715221002911. 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/wps/find/journaldescription.cws_home/622892/description#description .

    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.