The Annals of Statistics

Identification of Nonlinear Time Series from First Order Cumulative Characteristics

Ian W. McKeague and Mei-Jie Zhang

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Abstract

A new approach to the problem of identifying a nonlinear time series model is considered. We argue that cumulative lagged conditional mean and variance functions are the appropriate "signatures" of a nonlinear time series for the purpose of model identification, being analogous to cumulative distribution functions or cumulative hazard functions in iid models. We introduce estimators of the cumulative lagged conditional mean and variance functions and study their asymptotic properties. A goodness-of-fit test for parametric time series models is also developed.

Article information

Source
Ann. Statist., Volume 22, Number 1 (1994), 495-514.

Dates
First available in Project Euclid: 11 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176325381

Digital Object Identifier
doi:10.1214/aos/1176325381

Mathematical Reviews number (MathSciNet)
MR1272096

Zentralblatt MATH identifier
0797.62073

JSTOR
links.jstor.org

Subjects
Primary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]
Secondary: 62G07: Density estimation 62G02 62M02: Markov processes: hypothesis testing

Keywords
Stationary time series Markov processes goodness-of-fit tests martingale central limit theorem nonparametric estimation

Citation

McKeague, Ian W.; Zhang, Mei-Jie. Identification of Nonlinear Time Series from First Order Cumulative Characteristics. Ann. Statist. 22 (1994), no. 1, 495--514. doi:10.1214/aos/1176325381. https://projecteuclid.org/euclid.aos/1176325381


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