Nonparametric Estimation and Identification of Nonlinear ARCH Time Series Strong Convergence and Asymptotic Normality: Strong Convergence and Asymptotic Normality
- 11 February 1995
- journal article
- research article
- Published by Cambridge University Press (CUP) in Econometric Theory
- Vol. 11 (2) , 258-289
- https://doi.org/10.1017/s0266466600009166
Abstract
We consider the estimation and identification of the functional structures of nonlinear econometric systems of the ARCH type. We employ nonparametric kernel estimates for the nonlinear functions characterizing the systems, and we establish strong consistency along with sharp rates of convergence under mild regularity conditions. We also prove the asymptotic normality of the estimates.Keywords
This publication has 29 references indexed in Scilit:
- Nonparametric Identification of Nonlinear Time Series: Selecting Significant LagsJournal of the American Statistical Association, 1994
- Multivariate regression estimation with errors-in-variables: Asymptotic normality for mixing processesJournal of Multivariate Analysis, 1992
- Semiparametric ARCH ModelsJournal of Business & Economic Statistics, 1991
- Kernel density estimation on random fieldsJournal of Multivariate Analysis, 1990
- The econometric analysis of models with risk termsJournal of Applied Econometrics, 1988
- The mixing property of bilinear and generalised random coefficient autoregressive modelsStochastic Processes and their Applications, 1986
- Strong uniform convergence rates in robust nonparametric time series analysis and prediction: Kernel regression estimation from dependent observationsStochastic Processes and their Applications, 1986
- Generalized autoregressive conditional heteroskedasticityJournal of Econometrics, 1986
- Weak and strong uniform consistency of kernel regression estimatesProbability Theory and Related Fields, 1982
- Sufficient conditions for ergodicity and recurrence of Markov chains on a general state spaceStochastic Processes and their Applications, 1975