Electronic Journal of Statistics

Stability and asymptotics for autoregressive processes

Likai Chen and Wei Biao Wu

Full-text: Open access

Abstract

The paper studies infinite order autoregressive models for both temporal and spatial processes. We present sufficient conditions for the existence of stationary distributions. To understand the underlying dynamics and to capture the dependence structure, we introduce functional dependence measures and relate them with Lipschitz coefficients of the data-generating mechanisms. Our stability result allows both short- and long-range dependence. With functional dependence measures, we can establish an asymptotic theory for the underlying processes.

Article information

Source
Electron. J. Statist., Volume 10, Number 2 (2016), 3723-3751.

Dates
Received: July 2016
First available in Project Euclid: 6 December 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1480993452

Digital Object Identifier
doi:10.1214/16-EJS1213

Mathematical Reviews number (MathSciNet)
MR3579674

Zentralblatt MATH identifier
1353.62093

Subjects
Primary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84] 62E20: Asymptotic distribution theory

Keywords
Autoregressive models Markov process nonlinear time series stationarity functional dependence measure invariance principle

Citation

Chen, Likai; Wu, Wei Biao. Stability and asymptotics for autoregressive processes. Electron. J. Statist. 10 (2016), no. 2, 3723--3751. doi:10.1214/16-EJS1213. https://projecteuclid.org/euclid.ejs/1480993452


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