Stability of Nonlinear AR-GARCH Models
Copyright policy )Stability of Nonlinear AR-GARCH Models
Abstract. This article studies the stability of nonlinear autoregressive models with conditionally heteroskedastic errors. We consider a nonlinear autoregression of order p [AR(p)] with the conditional variance specified as a nonlinear first‐order generalized autoregressive conditional heteroskedasticity [GARCH(1,1)] model. Conditions under which the model is stable in the sense that its Markov chain representation is geometrically ergodic are provided. This implies the existence of an initial distribution such that the process is strictly stationary and β‐mixing. Conditions under which the stationary distribution has finite moments are also given. The results cover several nonlinear specifications recently proposed for both the conditional mean and conditional variance, and only require mild moment conditions.
- University of Helsinki Finland
- Université Catholique de Louvain Belgium
- University of Helsinki
- University of Oxford United Kingdom
- Koç University Turkey
Markovscher Prozess, Heteroskedastizität, Markov chains, ddc:330, ARCH-Modell, nonlinear autoregressive models, geometric ergodicity, -, Nonlinear Autoregression, Generalized Autoregressive Conditional Heteroskedasticity, Nonlinear Time Series Models, Geometric Ergodicity, Mixing, Strict Stationarity, Existence of Moments, Markov Models, Time series, auto-correlation, regression, etc. in statistics (GARCH), generalized autoregressive conditional heteroskedasticity, stationarity, \(\beta\)-mixing, C22, Asymptotic properties of parametric estimators, jel: jel:C10, jel: jel:C22
Markovscher Prozess, Heteroskedastizität, Markov chains, ddc:330, ARCH-Modell, nonlinear autoregressive models, geometric ergodicity, -, Nonlinear Autoregression, Generalized Autoregressive Conditional Heteroskedasticity, Nonlinear Time Series Models, Geometric Ergodicity, Mixing, Strict Stationarity, Existence of Moments, Markov Models, Time series, auto-correlation, regression, etc. in statistics (GARCH), generalized autoregressive conditional heteroskedasticity, stationarity, \(\beta\)-mixing, C22, Asymptotic properties of parametric estimators, jel: jel:C10, jel: jel:C22
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).48 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Top 10% influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Top 10% impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!