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Characterizing the Degree of Stability of Non-linear Dynamic Models

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  • 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.

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File URL: http://www.degruyter.com/view/j/snde.2002.6.1/snde.2002.6.1.1002/snde.2002.6.1.1002.xml?format=INT
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Bibliographic Info

Article provided by De Gruyter in its journal Studies in Nonlinear Dynamics & Econometrics.

Volume (Year): 6 (2002)
Issue (Month): 1 (April)
Pages: 1-19

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Handle: RePEc:bpj:sndecm:v:6:y:2002:i:1:n:3

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Cited by:
  1. Mototsugu Shintani & Oliver Linton, 2002. "Nonparametric neural network estimation of Lyapunov exponents and a direct test for chaos," LSE Research Online Documents on Economics 2093, London School of Economics and Political Science, LSE Library.
  2. Mikael Bask & Tung Liu & Anna Widerberg, 2006. "The Stability of Electricity Prices: Estimation and Inference of the Lyapunov Exponent," Working Papers 200603, Ball State University, Department of Economics, revised Apr 2006.
  3. Mototsugu Shintani, 2004. "A Dynamic Factor Approach to Nonlinear Stability Analysis," Vanderbilt University Department of Economics Working Papers 0418, Vanderbilt University Department of Economics.
  4. Bask, Mikael, 2010. "Measuring potential market risk," Journal of Financial Stability, Elsevier, vol. 6(3), pages 180-186, September.
  5. Bask, Mikael, 2003. "Chartists and Fundamentalists in the Currency Market and the Volatility of Exchange Rates," UmeÃ¥ Economic Studies 605, Umeå University, Department of Economics.
  6. Bask, Mikael & Widerberg, Anna, 2008. "Market Structure and the Stability and Volatility of Electricity Prices," Working Papers in Economics 327, University of Gothenburg, Department of Economics.
  7. 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.
  8. Mototsugu Shintani, 2003. "A Nonparametric Measure of Convergence Toward Purchasing Power Parity," Levine's Working Paper Archive 506439000000000172, David K. Levine.
  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.

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