Characterizing the degree of stability of non-linear dynamic models

Mikael Bask and Xavier de Luna ()
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Xavier de Luna: Department of Statistics, Postal: S 901 87 Umeå, Sweden

No 564, Umeå Economic Studies from Umeå University, Department of Economics

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.

Keywords: Autoregression; Exchange rates; Exogenous shocks; Lyapunov exponents; Persistence; Time series. (search for similar items in EconPapers)
JEL-codes: C13 C22 C50 (search for similar items in EconPapers)
Pages: 22 pages
Date: 2001-11-01
New Economics Papers: this item is included in nep-ets and nep-ifn
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Journal Article: Characterizing the Degree of Stability of Non-linear Dynamic Models (2002)
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Persistent link: https://EconPapers.repec.org/RePEc:hhs:umnees:0564

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