IDEAS home Printed from https://ideas.repec.org/p/hhs/umnees/0564.html
   My bibliography  Save this paper

Characterizing the degree of stability of non-linear dynamic models

Author

Listed:
  • Bask, Mikael

    (Department of Economics, Umeå University)

  • de Luna, Xavier

    (Department of Statistics)

Abstract

non-linear dynamic models may be characterized and studied, where the degree of stability is defined by the effects of exogenous shocks on the evolution of the observed stochastic system. This type of stability concept is frequently of interest in economics, e.g., in real business cycle theory. We argue that smooth Lyapunov exponents can be used to measure the degree of stability of a stochastic dynamic model. It is emphasized that the stability properties of the model should be considered when the volatility of the variable modelled is of interest. When a parametric model is fitted to observed data, an estimator of the largest smooth Lyapunov exponent is presented which is consistent and asymptotically normal. The small sample properties of this estimator are examined in a Monte Carlo study. Finally, we illustrate how the presented framework can be used to study the degree of stability and the volatility of an exchange rate.

Suggested Citation

  • Bask, Mikael & de Luna, Xavier, 2001. "Characterizing the degree of stability of non-linear dynamic models," Umeå Economic Studies 564, Umeå University, Department of Economics.
  • Handle: RePEc:hhs:umnees:0564
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Plosser, Charles I, 1989. "Understanding Real Business Cycles," Journal of Economic Perspectives, American Economic Association, vol. 3(3), pages 51-77, Summer.
    2. Bask, Mikael & de Luna, Xavier, 2005. "EMU and the stability and volatility of foreign exchange: Some empirical evidence," Chaos, Solitons & Fractals, Elsevier, vol. 25(3), pages 737-750.
    3. Potter, Simon M., 2000. "Nonlinear impulse response functions," Journal of Economic Dynamics and Control, Elsevier, vol. 24(10), pages 1425-1446, September.
    4. Whang, Yoon-Jae & Linton, Oliver, 1999. "The asymptotic distribution of nonparametric estimates of the Lyapunov exponent for stochastic time series," Journal of Econometrics, Elsevier, vol. 91(1), pages 1-42, July.
    5. Yao, Qiwei & Tong, Howell, 1994. "Quantifying the influence of initial values on nonlinear prediction," LSE Research Online Documents on Economics 19426, London School of Economics and Political Science, LSE Library.
    6. White, Halbert & Domowitz, Ian, 1984. "Nonlinear Regression with Dependent Observations," Econometrica, Econometric Society, vol. 52(1), pages 143-161, January.
    7. Xavier De Luna, 1998. "Projected polynomial autoregression for prediction of stationary time series," Journal of Applied Statistics, Taylor & Francis Journals, vol. 25(6), pages 763-775.
    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. Shintani, Mototsugu & Linton, Oliver, 2004. "Nonparametric neural network estimation of Lyapunov exponents and a direct test for chaos," Journal of Econometrics, Elsevier, vol. 120(1), pages 1-33, May.
    2. Mototsugu Shintani, 2006. "A nonparametric measure of convergence towards purchasing power parity," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(5), pages 589-604.
    3. Bask, Mikael & Liu, Tung & Widerberg, Anna, 2007. "The stability of electricity prices: Estimation and inference of the Lyapunov exponents," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 376(C), pages 565-572.
    4. Bask, Mikael & Widerberg, Anna, 2009. "Market structure and the stability and volatility of electricity prices," Energy Economics, Elsevier, vol. 31(2), pages 278-288, March.
    5. Bask, Mikael, 2010. "Measuring potential market risk," Journal of Financial Stability, Elsevier, vol. 6(3), pages 180-186, September.
    6. Bask, Mikael & de Luna, Xavier, 2005. "EMU and the stability and volatility of foreign exchange: Some empirical evidence," Chaos, Solitons & Fractals, Elsevier, vol. 25(3), pages 737-750.
    7. Shintani, Mototsugu, 2008. "A dynamic factor approach to nonlinear stability analysis," Journal of Economic Dynamics and Control, Elsevier, vol. 32(9), pages 2788-2808, September.
    8. Bask, Mikael, 2003. "Chartists and Fundamentalists in the Currency Market and the Volatility of Exchange Rates," Umeå Economic Studies 605, Umeå University, Department of Economics.
    9. Bask, Mikael & Widerberg, Anna, 2007. "The Stability and Volatility of Electricity Prices: An Illustration of (lambda, sigma-2) Analysis," Working Papers in Economics 267, University of Gothenburg, Department of Economics.
    10. repec:zbw:bofrdp:2007_020 is not listed on IDEAS
    11. Bask, Mikael & Liu, Tung & Widerberg, Anna, 2007. "The stability of electricity prices: Estimation and inference of the Lyapunov exponents," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 376(C), pages 565-572.
    12. Elena Olmedo & Ricardo Gimeno & Lorenzo Escot & Ruth Mateos, 2007. "Convergencia y Estabilidad de los Tipos de Cambio Europeos: Una Aplicación de Exponentes de Lyapunov," Latin American Journal of Economics-formerly Cuadernos de Economía, Instituto de Economía. Pontificia Universidad Católica de Chile., vol. 44(129), pages 91-108.
    13. Miia Bask & Mikael Bask, 2015. "Cumulative (Dis)Advantage and the Matthew Effect in Life-Course Analysis," PLOS ONE, Public Library of Science, vol. 10(11), pages 1-14, November.
    14. repec:zbw:bofrdp:2006_009 is not listed on IDEAS
    15. Bask, Mikael, 2010. "Measuring potential market risk," Journal of Financial Stability, Elsevier, vol. 6(3), pages 180-186, September.
    16. Sekandary, Ghezal & Bask, Mikael, 2023. "Monetary policy uncertainty, monetary policy surprises and stock returns," Journal of Economics and Business, Elsevier, vol. 124(C).

    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. Bask, Mikael, 2010. "Measuring potential market risk," Journal of Financial Stability, Elsevier, vol. 6(3), pages 180-186, September.
    2. Bask, Mikael & de Luna, Xavier, 2005. "EMU and the stability and volatility of foreign exchange: Some empirical evidence," Chaos, Solitons & Fractals, Elsevier, vol. 25(3), pages 737-750.
    3. Wolff Rodney & Yao Qiwei & Tong Howell, 2004. "Statistical Tests for Lyapunov Exponents of Deterministic Systems," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 8(2), pages 1-19, May.
    4. El-Gamal, Mahmoud A. & Ryu, Deockhyun, 2006. "Short-memory and the PPP hypothesis," Journal of Economic Dynamics and Control, Elsevier, vol. 30(3), pages 361-391, March.
    5. Shintani, Mototsugu, 2008. "A dynamic factor approach to nonlinear stability analysis," Journal of Economic Dynamics and Control, Elsevier, vol. 32(9), pages 2788-2808, September.
    6. Bask, Mikael & Liu, Tung & Widerberg, Anna, 2007. "The stability of electricity prices: Estimation and inference of the Lyapunov exponents," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 376(C), pages 565-572.
    7. Bask, Mikael & Liu, Tung & Widerberg, Anna, 2007. "The stability of electricity prices: Estimation and inference of the Lyapunov exponents," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 376(C), pages 565-572.
    8. repec:zbw:bofrdp:2006_009 is not listed on IDEAS
    9. Mikael Bask & Anna Widerberg, 2012. "Actual and potential market risks during the stock market turmoil 2007--2008," Applied Financial Economics, Taylor & Francis Journals, vol. 22(5), pages 339-349, March.
    10. van Dijk, Dick & Hans Franses, Philip & Peter Boswijk, H., 2007. "Absorption of shocks in nonlinear autoregressive models," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4206-4226, May.
    11. Blomberg, S. Brock & Hess, Gregory D., 2003. "Is the political business cycle for real?," Journal of Public Economics, Elsevier, vol. 87(5-6), pages 1091-1121, May.
    12. Vlieghe, Gertjan W, 2007. "Imperfect credit markets: implications for monetary policy," MPRA Paper 12957, University Library of Munich, Germany.
    13. J.P.G. Reijnders, 2007. "Impulse or propagation? How the tides turned in Business Cycle Theory," Working Papers 07-07, Utrecht School of Economics.
    14. Park, Joon Y. & Whang, Yoon-Jae, 2012. "Random walk or chaos: A formal test on the Lyapunov exponent," Journal of Econometrics, Elsevier, vol. 169(1), pages 61-74.
    15. Marvin Goodfriend, 2004. "Monetary policy in the new neoclassical synthesis : a primer," Economic Quarterly, Federal Reserve Bank of Richmond, vol. 90(Sum), pages 21-45.
    16. Davide Viviano & Jelena Bradic, 2019. "Synthetic learner: model-free inference on treatments over time," Papers 1904.01490, arXiv.org, revised Aug 2022.
    17. Nadiezhda de la Uz, 2002. "La hipótesis de martingala en el mercado bursátil mexicano," Estudios Económicos, El Colegio de México, Centro de Estudios Económicos, vol. 17(1), pages 91-127.
    18. Mr. Kangni R Kpodar & Ms. Stefania Fabrizio & Kodjovi M. Eklou, 2019. "Export Competitiveness - Fuel Price Nexus in Developing Countries: Real or False Concern?," IMF Working Papers 2019/025, International Monetary Fund.
    19. Niels Lundtorp Olsen & Alessia Pini & Simone Vantini, 2021. "False discovery rate for functional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(3), pages 784-809, September.
    20. Georgios Chortareas & George Kapetanios, 2013. "How Puzzling Is The Ppp Puzzle? An Alternative Half‐Life Measure Of Convergence To Ppp," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 28(3), pages 435-457, April.
    21. Verbrugge, Randal & Zaman, Saeed, 2023. "The hard road to a soft landing: Evidence from a (modestly) nonlinear structural model," Energy Economics, Elsevier, vol. 123(C).

    More about this item

    Keywords

    Autoregression; Exchange rates; Exogenous shocks; Lyapunov exponents; Persistence; Time series.;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C50 - Mathematical and Quantitative Methods - - Econometric Modeling - - - General

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:hhs:umnees:0564. 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: David Skog (email available below). General contact details of provider: https://edirc.repec.org/data/inumuse.html .

    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.