Open Access
Translator Disclaimer
December, 1994 Asymptotic Distribution of Statistics in Time Series
F. Gotze, C. Hipp
Ann. Statist. 22(4): 2062-2088 (December, 1994). DOI: 10.1214/aos/1176325772

Abstract

Verifiable conditions are given for the validity of formal Edgeworth expansions for the distribution of sums $X_1 + \cdots + X_n$, where $X_i = F(Z_i, \ldots, Z_{i + p - 1})$ and $Z_1, Z_2, \ldots$ is a strict sense stationary sequence that can be written as $Z_j = g(\varepsilon_{j - k}: k \geq 0)$ with an $\operatorname{iid}$ sequence $(\varepsilon_i)$ of innovations. These models include nonlinear functions of ARMA processes $(Z_i)$ as well as certain nonlinear AR processes. The results apply to many statistics in (nonlinear) time series models.

Citation

Download Citation

F. Gotze. C. Hipp. "Asymptotic Distribution of Statistics in Time Series." Ann. Statist. 22 (4) 2062 - 2088, December, 1994. https://doi.org/10.1214/aos/1176325772

Information

Published: December, 1994
First available in Project Euclid: 11 April 2007

zbMATH: 0827.62015
MathSciNet: MR1329183
Digital Object Identifier: 10.1214/aos/1176325772

Subjects:
Primary: 62E20
Secondary: 60F05

Rights: Copyright © 1994 Institute of Mathematical Statistics

JOURNAL ARTICLE
27 PAGES


SHARE
Vol.22 • No. 4 • December, 1994
Back to Top