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Characterizing the Degree of Stability of Non-linear Dynamic Models

Author

Listed:
  • Bask Mikael

    (Department of Economics, Umeå University, Sweden)

  • de Luna Xavier

    (Department of Statistics, Umeå University, Sweden)

Abstract

The purpose of this paper is to show how the stability properties of 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, 2002. "Characterizing the Degree of Stability of Non-linear Dynamic Models," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 6(1), pages 1-19, April.
    • Handle: RePEc:bpj:sndecm:v:6:y:2002:i:1:n:3
    DOI: 10.2202/1558-3708.1002
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    References listed on IDEAS

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    1. Potter, Simon M., 2000. "Nonlinear impulse response functions," Journal of Economic Dynamics and Control, Elsevier, vol. 24(10), pages 1425-1446, September.
    2. Plosser, Charles I, 1989. "Understanding Real Business Cycles," Journal of Economic Perspectives, American Economic Association, vol. 3(3), pages 51-77, Summer.
    3. 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.
    4. 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.
    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.
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    Citations

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    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. repec:zbw:bofrdp:2007_020 is not listed on IDEAS
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. Bask, Mikael, 2010. "Measuring potential market risk," Journal of Financial Stability, Elsevier, vol. 6(3), pages 180-186, September.
    10. 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.
    11. repec:zbw:bofrdp:2006_009 is not listed on IDEAS
    12. Bask, Mikael, 2010. "Measuring potential market risk," Journal of Financial Stability, Elsevier, vol. 6(3), pages 180-186, September.
    13. 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.
    14. 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.
    15. 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.
    16. Sekandary, Ghezal & Bask, Mikael, 2023. "Monetary policy uncertainty, monetary policy surprises and stock returns," Journal of Economics and Business, Elsevier, vol. 124(C).

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    More about this item

    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

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