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On the Stationarity of First-order Nonlinear Time Series Models: Some Developments
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May 18, 2004
In the present paper we consider the general class of first-order nonlinear models. The main contributions concern primerly a generalization of the conditions for geometric ergodicity presented in Ferrante et al. (2003). The obtained result is then applied to two classes of first-order nonlinear models not previously addressed. Secondly we apply to general firstorder nonlinear models some recently developed conditions for the existence of the invariant measure of a Markov process. For this class of nonlinear models we also prove that the usual drift-condition for geometric ergodicity for Markov chains still holds even in the presence of an alternative assumption than T-continuity.
Published Online: 2004-5-18
©2011 Walter de Gruyter GmbH & Co. KG, Berlin/Boston
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Articles in the same Issue
- Article
- Introduction
- Extensions of the Forward Search to Time Series
- Analyzing Financial Time Series through Robust Estimators
- Clusters of Extreme Observations and Extremal Index Estimate in GARCH Processes
- Estimating Stochastic Volatility Models: A Comparison of Two Importance Samplers
- MCMC Bayesian Estimation of a Skew-GED Stochastic Volatility Model
- GARCH-type Models with Generalized Secant Hyperbolic Innovations
- Mixture Processes for Financial Intradaily Durations
- Constructing Non-linear Gaussian Time Series by Means of a Simplified State Space Representation
- Statistical Tests for Lyapunov Exponents of Deterministic Systems
- Assessing Chaos in Time Series: Statistical Aspects and Perspectives
- On the Stationarity of First-order Nonlinear Time Series Models: Some Developments
- Experimental Design for Time-Dependent Models with Correlated Observations
- Inference and Forecasting for ARFIMA Models With an Application to US and UK Inflation
- Stability and Consistency of Seasonally Adjusted Aggregates and Their Component Patterns
- Seasonal Specific Structural Time Series
- Relationship between Local and Global Nonparametric Estimators Measures of Fitting and Smoothing
