Asymptotic distribution of statistics in time series

DOI10.1214/aos/1176325772zbMath0827.62015OpenAlexW1995039079MaRDI QIDQ1896252

Friedrich Götze, Christian Hipp

Publication date: 21 August 1995

Published in: The Annals of Statistics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aos/1176325772

zbMATH Keywords

time seriesformal Edgeworth expansionsnonlinear AR processesnonlinear functions of ARMA processesstrict sense stationary sequence

Mathematics Subject Classification ID

Time series, auto-correlation, regression, etc. in statistics (GARCH) (62M10) Asymptotic distribution theory in statistics (62E20) Central limit and other weak theorems (60F05)

Related Items

Consistency of the jackknife-after-bootstrap variance estimator for the bootstrap quantiles of a Studentized statistic ⋮ Bootstrap refinements for QML estimators of the GARCH(1,1) parameters ⋮ On geometric ergodicity of nonlinear autoregressive models ⋮ Edgeworth expansions for Studentized statistics under weak dependence ⋮ Asymptotic expansions for sums of block-variables under weak dependence ⋮ Bootstrap Methods for Time Series ⋮ RESIDUAL-BASED GARCH BOOTSTRAP AND SECOND ORDER ASYMPTOTIC REFINEMENT ⋮ High order asymptotic expansion for Wiener functionals ⋮ Edgeworth expansions for volatility models ⋮ Asymptotic expansion and estimates of Wiener functionals ⋮ Valid locally uniform Edgeworth expansions for a class of weakly dependent processes or sequences of smooth transformations ⋮ A higher-order correct fast moving-average bootstrap for dependent data ⋮ Edgeworth expansions for linear statistics of possibly long-range-dependent linear processes. ⋮ Valid asymptotic expansions for the maximum likelihood estimators of the parameter of a stationary, Gaussian, strongly dependent process ⋮ Nonparametric estimation of infinite order regression and its application to the risk-return tradeoff ⋮ Asymptotic spectral theory for nonlinear time series ⋮ Asymptotic expansion of Skorohod integrals ⋮ Malliavin calculus and martingale expansion ⋮ Berry-Esseen theorems under weak dependence ⋮ VALID EDGEWORTH EXPANSIONS FOR THE WHITTLE MAXIMUM LIKELIHOOD ESTIMATOR FOR STATIONARY LONG-MEMORY GAUSSIAN TIME SERIES ⋮ Stochastic Model Reduction for Slow-Fast Systems with Moderate Time Scale Separation ⋮ Edgeworth expansions for slow–fast systems with finite time-scale separation ⋮ Sharp connections between Berry-Esseen characteristics and Edgeworth expansions for stationary processes ⋮ On the validity of Edgeworth expansions and moment approximations for three indirect inference estimators ⋮ Edgeworth and Moment Approximations: The Case of MM and QML Estimators for the MA(1) Models ⋮ On the bootstrap for Moran's \(I\) test for spatial dependence ⋮ Parametric first-order Edgeworth expansion for Markov additive functionals. Application to \(M\)-estimations