An efficient locally asymptotic parametric test in nonlinear heteroscedastic time series models

Estimation in a class of nonlinear heteroscedastic time series models

Abstract: Parameter estimation in a class of heteroscedastic time series models is investigated. The existence of conditional least-squares and conditional likelihood estimators is proved. Their consistency and their asymptotic normality are established. Kernel estimators of the noise’s density and its derivatives are defined and shown to be uniformly consistent. A simulation experiment conduct...

Locally asymptotically optimal tests for nonlinear time-series models

Based on the local asymptotic normality (LAN) of the log-likelihood ratio statistic, we proposed some distribution-free tests for examining simultaneously hypotheses about the conditional mean and the conditional variance functions in time series models. Our results are established under stationarity and ergodicity conditions with unspecified "innovation" densities under the null hypothesis as ...

Estimating the error distribution in multivariate heteroscedastic time series models

Copulas have attracted considerable interest for modelling multivariate observations and for stress testing in quantitative finance. In this paper, a semiparametric method is studied for estimating the copula parameter and the joint distribution of the error term in a class of multivariate time series models when the marginal distributions of the errors are unknown. The proposed method first ob...

Asymptotic Spectral Theory for Nonlinear Time Series

We consider asymptotic problems in spectral analysis of stationary causal processes. Limiting distributions of periodograms and smoothed periodogram spectral density estimates are obtained and applications to the spectral domain bootstrap are given. Instead of the commonly used strong mixing conditions, in our asymptotic spectral theory we impose conditions only involving (conditional) moments,...

Nonlinear Time Series: Nonparametric and Parametric Methods