IDEAS home Printed from https://ideas.repec.org/a/ris/apltrx/0273.html
   My bibliography  Save this article

Statistical analysis of variable-structure models

Author

Listed:
  • Aivazian, Sergey

    (CEMI RAS, Moscow; School of Economics, Moscow, Russia)

  • Bereznyatskiy, Alexander

    (Economics and Mathematics Institute (CEMI RAS), Moscow, Russian Federation)

  • Brodsky, Boris

    (Economics and Mathematics Institute (CEMI RAS), Moscow, Russian Federation)

  • Darkhovsky, Boris

    (Institute for Systems Analysis, Moscow, Russian Federation)

Abstract

Classification problems for univariate and multivariate observations are often encountered in statistics and economics. However, all existing approaches to solving these problems have several essential drawbacks: 1. All these methods cannot help in testing the null hypothesis of no different classes; 2. The number of classes is assumed to be known a priori; 3. Theoretical justification of performance effectiveness of these methods is lacking. In this paper a new nonparametric method is proposed which can help us to solve these problems. This method enables us to construct consistent estimate of an unknown number of classes and to test the null hypothesis of no different classes. Besides theoretical findings, we present results of experimental analysis of this method including comparison of its characteristics with the maximum likelihood method and k-means method in different situations.

Suggested Citation

  • Aivazian, Sergey & Bereznyatskiy, Alexander & Brodsky, Boris & Darkhovsky, Boris, 2015. "Statistical analysis of variable-structure models," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 39(3), pages 84-105.
    • Handle: RePEc:ris:apltrx:0273
    as

    Download full text from publisher

    File URL: http://pe.cemi.rssi.ru/pe_2015_3_84-105.pdf
    File Function: Full text
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Garcia, Rene & Luger, Richard & Renault, Eric, 2003. "Empirical assessment of an intertemporal option pricing model with latent variables," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 49-83.
    2. Andrew Ang & Geert Bekaert, 2002. "International Asset Allocation With Regime Shifts," The Review of Financial Studies, Society for Financial Studies, vol. 15(4), pages 1137-1187.
    3. Davig, Troy, 2004. "Regime-switching debt and taxation," Journal of Monetary Economics, Elsevier, vol. 51(4), pages 837-859, May.
    4. Dag Tjøstheim, 1986. "Some Doubly Stochastic Time Series Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 7(1), pages 51-72, January.
    5. Jeanne, Olivier & Masson, Paul, 2000. "Currency crises, sunspots and Markov-switching regimes," Journal of International Economics, Elsevier, vol. 50(2), pages 327-350, April.
    6. Cosslett, Stephen R. & Lee, Lung-Fei, 1985. "Serial correlation in latent discrete variable models," Journal of Econometrics, Elsevier, vol. 27(1), pages 79-97, January.
    7. Francq, C. & Zakoian, J. -M., 2001. "Stationarity of multivariate Markov-switching ARMA models," Journal of Econometrics, Elsevier, vol. 102(2), pages 339-364, June.
    8. Goldfeld, Stephen M. & Quandt, Richard E., 1973. "A Markov model for switching regressions," Journal of Econometrics, Elsevier, vol. 1(1), pages 3-15, March.
    9. Valerie Cerra & Sweta Chaman Saxena, 2005. "Did Output Recover from the Asian Crisis?," IMF Staff Papers, Palgrave Macmillan, vol. 52(1), pages 1-23, April.
    10. repec:pri:cepsud:110sims is not listed on IDEAS
    11. Yang, Minxian, 2000. "Some Properties Of Vector Autoregressive Processes With Markov-Switching Coefficients," Econometric Theory, Cambridge University Press, vol. 16(1), pages 23-43, February.
    12. Lee, Lung-Fei & Porter, Robert H, 1984. "Switching Regression Models with Imperfect Sample Separation Information-With an Application on Cartel Stability," Econometrica, Econometric Society, vol. 52(2), pages 391-418, March.
    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. repec:arp:tjssrr:2019:p:233-241 is not listed on IDEAS
    2. Mislavskaya N. A. & Polenova S. N. & Sotnikova L. V., 2018. "Real Estate Sale: The Predominance of Economic Substance over Legal Form in Some Jurisdictions is Problematic," The Journal of Social Sciences Research, Academic Research Publishing Group, pages 1101-1109:5.

    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. Hamilton, J.D., 2016. "Macroeconomic Regimes and Regime Shifts," Handbook of Macroeconomics, in: J. B. Taylor & Harald Uhlig (ed.), Handbook of Macroeconomics, edition 1, volume 2, chapter 0, pages 163-201, Elsevier.
    2. Sergei Koulayev & Marc Rysman & Scott Schuh & Joanna Stavins, 2016. "Explaining adoption and use of payment instruments by US consumers," RAND Journal of Economics, RAND Corporation, vol. 47(2), pages 293-325, May.
    3. López-Herrera, Francisco & Venegas-Martínez, Francisco, 2012. "Is There a Relationship between the Mexican and the US Real Business Cycles during 1930-2010?," Sección de Estudios de Posgrado e Investigación de la Escuela Superios de Economía del Instituto Politécnico Nacional, in: Espinosa-Ramírez, Rafael Salvador (ed.), Research Issues Economic Relations, volume 1, chapter 6, pages 145-160, Escuela Superior de Economía, Instituto Politécnico Nacional.
    4. Agnello, Luca & Castro, Vítor & Sousa, Ricardo M., 2012. "How does fiscal policy react to wealth composition and asset prices?," Journal of Macroeconomics, Elsevier, vol. 34(3), pages 874-890.
    5. Marianna Oliskevych & Iryna Lukianenko, 2020. "European unemployment nonlinear dynamics over the business cycles: Markov switching approach," Global Business and Economics Review, Inderscience Enterprises Ltd, vol. 22(4), pages 375-401.
    6. Luca Agnello & Gilles Dufrénot & Ricardo M. Sousa, 2012. "Adjusting the U.S. Fiscal Policy for Asset Prices: Evidence from a TVP-MS Framework," NIPE Working Papers 20/2012, NIPE - Universidade do Minho.
    7. Marjan Petreski, 2010. "An Overhaul of a Doctrine: Has Inflation Targeting Opened a New Era in Developing-country Peggers?," FIW Working Paper series 057, FIW.
    8. 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.
    9. Nan Li & Simon S. Kwok, 2021. "Jointly determining the state dimension and lag order for Markov‐switching vector autoregressive models," Journal of Time Series Analysis, Wiley Blackwell, vol. 42(4), pages 471-491, July.
    10. Fiorentini, Gabriele & Planas, Christophe & Rossi, Alessandro, 2016. "Skewness and kurtosis of multivariate Markov-switching processes," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 153-159.
    11. Kole, Erik & van Dijk, Dick, 2023. "Moments, shocks and spillovers in Markov-switching VAR models," Journal of Econometrics, Elsevier, vol. 236(2).
    12. Ozdemir, Dicle, 2019. "Sectoral Business Cycle Asymmetries and Regime Shifts: Evidence from Turkey," Asian Journal of Applied Economics, Kasetsart University, Center for Applied Economics Research, vol. 26(2), December.
    13. Yudong Wang & Chongfeng Wu & Li Yang, 2015. "Hedging with Futures: Does Anything Beat the Naïve Hedging Strategy?," Management Science, INFORMS, vol. 61(12), pages 2870-2889, December.
    14. Lee, Lung-Fei, 1997. "Simulation estimation of dynamic switching regression and dynamic disequilibrium models -- some Monte Carlo results," Journal of Econometrics, Elsevier, vol. 78(2), pages 179-184, June.
    15. Adnan Haider & Musleh ud Din & Ejaz Ghani, 2011. "Consequences of Political Instability, Governance and Bureaucratic Corruption on Inflation and Growth: The Case of Pakistan," The Pakistan Development Review, Pakistan Institute of Development Economics, vol. 50(4), pages 773-807.
    16. Bildirici, Melike & Ersin, Özgür, 2012. "Nonlinear volatility models in economics: smooth transition and neural network augmented GARCH, APGARCH, FIGARCH and FIAPGARCH models," MPRA Paper 40330, University Library of Munich, Germany, revised May 2012.
    17. Degras, David & Ting, Chee-Ming & Ombao, Hernando, 2022. "Markov-switching state-space models with applications to neuroimaging," Computational Statistics & Data Analysis, Elsevier, vol. 174(C).
    18. Xiaoquan (Michael) Zhang & Juan Feng, 2011. "Cyclical Bid Adjustments in Search-Engine Advertising," Management Science, INFORMS, vol. 57(9), pages 1703-1719, February.
    19. López-Herrera, Francisco & Ortiz-Arango, Francisco & Venegas-Martínez, Francisco, 2011. "Modelado de la volatilidad del Índice de Precios y Cotizaciones de la Bolsa Mexicana de Valores con cambios markovianos de régimen," Sección de Estudios de Posgrado e Investigación de la Escuela Superios de Economía del Instituto Politécnico Nacional, in: Perrotini-Hernández, Ignacio (ed.), Crecimiento y Desarrollo Económico en México, volume 1, chapter 10, pages 153-164, Escuela Superior de Economía, Instituto Politécnico Nacional.
    20. Hamilton, James D., 1996. "Specification testing in Markov-switching time-series models," Journal of Econometrics, Elsevier, vol. 70(1), pages 127-157, January.

    More about this item

    Keywords

    nonparametric methods; cluster analysis; classification methods; EM algorithm; k-means; mixture models;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C38 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Classification Methdos; Cluster Analysis; Principal Components; Factor Analysis

    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:ris:apltrx:0273. 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: Anatoly Peresetsky (email available below). General contact details of provider: http://appliedeconometrics.cemi.rssi.ru/ .

    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.