Handbook of Computational Econometrics 2009
DOI: 10.1002/9780470748916.ch10
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Concepts of and tools for Nonlinear Time‐Series Modelling

Abstract: Tools and approaches are provided for nonlinear time series modelling in econometrics. A wide range of topics is covered, including probabilistic properties, statistical inference and computational methods. The focus is on the applications but the ideas of the mathematical arguments are also provided. Techniques and concepts are illustrated by various examples, Monte Carlo experiments and a real application. 1

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Cited by 13 publications
(13 citation statements)
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References 150 publications
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“…Considering mainly this approach, several authors have established constraints on the coefficients of different non-linear models under which a stationary solution is reached. In particular, results by Amendola and Francq (2009) for EXPAR(1) models, Pham and Tran (1981) for bilinear models, An and Huang (1996) for non-linear autoregressive models, Chen et al (2011) for GJR-GARCH models, and Fan and Yao ( 2005) for ARCH, GARCH and EGARCH models, ensure stationarity for the specific models forming our simulation scenarios.…”
Section: Clustering Of Conditional Heteroskedastic Modelsmentioning
confidence: 71%
“…Considering mainly this approach, several authors have established constraints on the coefficients of different non-linear models under which a stationary solution is reached. In particular, results by Amendola and Francq (2009) for EXPAR(1) models, Pham and Tran (1981) for bilinear models, An and Huang (1996) for non-linear autoregressive models, Chen et al (2011) for GJR-GARCH models, and Fan and Yao ( 2005) for ARCH, GARCH and EGARCH models, ensure stationarity for the specific models forming our simulation scenarios.…”
Section: Clustering Of Conditional Heteroskedastic Modelsmentioning
confidence: 71%
“…However note that the assumed heteroscedasticity is only conditional while the unconditional variance is still constant in this case. This kind of situation can arise if we (spuriously) assume that the innovations process is driven by a GARCH model or any other model displaying nonlinearities such as models driven by hidden Markov chains or All-Pass models (see Amendola and Francq (2009) (1997)). Denote by m,1 , .…”
Section: Tests Based On the Assumption Of Constant Error Variancementioning
confidence: 99%
“…When the usual stationary assumption is met, it is well known that, in general, considering stochastic volatility for the error process entails second-order dynamics, see, for example, Amendola and Francq (2009). This explains why autocorrelations of the squared residuals are commonly used to detect nonlinear effects.…”
Section: Extending the Scopementioning
confidence: 99%