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Characterizing the degree of stability of non-linear dynamic models

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Author Info
Bask, Mikael () (Department of Economics, Umeå University)
de Luna, Xavier () (Department of Statistics)

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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.

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Publisher Info
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
Date of revision:
Handle: RePEc:hhs:umnees:0564

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Postal: Department of Economics, Umeå University, S-901 87 Umeå, Sweden
Phone: 090 - 786 61 42
Fax: 090 - 77 23 02
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Web page: http://www.econ.umu.se/
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Related research
Keywords: Autoregression; Exchange rates; Exogenous shocks; Lyapunov exponents; Persistence; Time series.;

Other versions of this item:

Find related papers by JEL classification:
C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Estimation
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions
C50 - Mathematical and Quantitative Methods - - Econometric Modeling - - - General

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  1. Mototsugu Shintani, 2004. "A Dynamic Factor Approach to Nonlinear Stability Analysis," Working Papers 0418, Department of Economics, Vanderbilt University. [Downloadable!]
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  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. [Downloadable!]
    Other versions:
  3. Mototsugu Shintani & Oliver Linton, 2003. "Nonparametric Neural Network Estimation of Lyapunov Exponents and a Direct Test for Chaos," Working Papers 0309, Department of Economics, Vanderbilt University. [Downloadable!]
    Other versions:
  4. Mototsugu Shintani, 2002. "A Nonparametric Measure of Convergence Toward Purchasing Power Parity," Working Papers 0219, Department of Economics, Vanderbilt University, revised Jul 2004. [Downloadable!]
    Other versions:
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