The Annals of Statistics

Asymptotic Distribution of Statistics in Time Series

F. Gotze and C. Hipp

Full-text: Open access

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.

Article information

Source
Ann. Statist., Volume 22, Number 4 (1994), 2062-2088.

Dates
First available in Project Euclid: 11 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176325772

Digital Object Identifier
doi:10.1214/aos/1176325772

Mathematical Reviews number (MathSciNet)
MR1329183

Zentralblatt MATH identifier
0827.62015

JSTOR
links.jstor.org

Subjects
Primary: 62E20: Asymptotic distribution theory
Secondary: 60F05: Central limit and other weak theorems

Keywords
Edgeworth expansions statistics in time series models

Citation

Gotze, F.; Hipp, C. Asymptotic Distribution of Statistics in Time Series. Ann. Statist. 22 (1994), no. 4, 2062--2088. doi:10.1214/aos/1176325772. https://projecteuclid.org/euclid.aos/1176325772


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