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Characterizing the degree of stability of non-linear dynamic models

Listed author(s):
  • Bask, Mikael

    ()

    (Department of Economics, Umeå University)

  • de Luna, Xavier

    ()

    (Department of Statistics)

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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Paper provided by Umeå University, Department of Economics in its series Umeå Economic Studies with number 564.

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Length: 22 pages
Date of creation: 01 Nov 2001
Handle: RePEc:hhs:umnees:0564
Contact details of provider: Postal:
Department of Economics, Umeå University, S-901 87 Umeå, Sweden

Phone: 090 - 786 61 42
Fax: 090 - 77 23 02
Web page: http://www.econ.umu.se/
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  1. Plosser, Charles I, 1989. "Understanding Real Business Cycles," Journal of Economic Perspectives, American Economic Association, vol. 3(3), pages 51-77, Summer.
  2. Qiwei Yao & Howell Tong, 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.
  3. White, Halbert & Domowitz, Ian, 1984. "Nonlinear Regression with Dependent Observations," Econometrica, Econometric Society, vol. 52(1), pages 143-161, January.
  4. Bask, Mikael & de Luna, Xavier, 2001. "EMU and the Stability and Volatility of Foreign Exchange: Some Empirical Evidence," Umeå Economic Studies 565, Umeå University, Department of Economics.
  5. Potter, Simon M., 2000. "Nonlinear impulse response functions," Journal of Economic Dynamics and Control, Elsevier, vol. 24(10), pages 1425-1446, September.
  6. 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.
  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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