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Higher order asymptotic theory for time series analysis
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A survey of the first-order asymptotic theory for time series analysis can be found in this article, along with a survey of higher-order theory for gussian arma processes.Abstract:
A survey of the first-order asymptotic theory for time series analysis higher order asymptotic theory for gussian arma processes validity of Edgeworth expansions in time series analysis higher order asymptotic sufficiency, asymptotic ancillarity in time series analysis higher order investigations for testing theory in time series analysis higher order asymptotic theory for multivariate time series some practical examples.read more
Citations
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Local asymptotic normality of multivariate ARMA processes with a linear trend
Bernard Garel,Marc Hallin +1 more
TL;DR: In this paper, the local asymptotic normality (LAN) property for multivariate ARMA models with a linear trend was established for general linear models with ARMA error term.
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Edgeworth expansions for spectral density estimates and studentized sample mean
Peter M. Robinson,Carlos Velasco +1 more
TL;DR: In this article, the authors establish valid Edgeworth expansions for the distribution of smoothed nonparametric spectral estimates, and of studentized versions of linear statistics such as the same mean.
Journal ArticleDOI
Sharp large deviations for gaussian quadratic forms with applications
TL;DR: In this article, a sharp large deviation principle for Hermitian quadratic forms of stationary Gaussian processes was established under regularity assumptions, and several examples of application such as the Neyman-Pearson likelihood ratio test, the sum of squares, and the Yule-Walker estimator of the parameter of a stable autoregressive Gaussian process were provided.
Journal ArticleDOI
An Asymptotic Expansion in the GARCH(l, 1) Model
TL;DR: This article developed order T−1 asymptotic expansions for the quasi-maximum likelihood estimator (QMLE) and a two-step approximate QMLE in the GARCH(l,l) model.
Journal ArticleDOI
Partial mixing and Edgeworth expansion
TL;DR: In this paper, the Malliavin calculus for jump processes is generalized to continuous-time conditional ∈-Markov processes, and the support theorem is used to verify the non-degeneracy condition.
References
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Posted ContentDOI
Local asymptotic normality of multivariate ARMA processes with a linear trend
Bernard Garel,Marc Hallin +1 more
TL;DR: In this paper, the local asymptotic normality (LAN) property for multivariate ARMA models with a linear trend was established for general linear models with ARMA error term.
Journal ArticleDOI
Sharp large deviations for gaussian quadratic forms with applications
TL;DR: In this article, a sharp large deviation principle for Hermitian quadratic forms of stationary Gaussian processes was established under regularity assumptions, and several examples of application such as the Neyman-Pearson likelihood ratio test, the sum of squares, and the Yule-Walker estimator of the parameter of a stable autoregressive Gaussian process were provided.
Journal ArticleDOI
Partial mixing and Edgeworth expansion
TL;DR: In this paper, the Malliavin calculus for jump processes is generalized to continuous-time conditional ∈-Markov processes, and the support theorem is used to verify the non-degeneracy condition.
Journal Article
Higher order cumulants of random vectors and applications to statistical inference and time series
TL;DR: In this paper, a unified and comprehensive approach that is useful in deriving expressions for higher order cumulants of random vectors is presented, based on expanding the characteristic functions and cumulant generating functions in terms of the Kronecker products of di¤erential operators.
Journal ArticleDOI
Asymptotic expansion of Bayes estimators for small diffusions
TL;DR: In this article, the authors derived asymptotic expansion of the distribution of the Bayes estimators for small diffusions using the Malliavin calculus and proved the second order efficiency of the estimator.