The Annals of Statistics

Inference for Unstable Long-Memory Processes with Applications to Fractional Unit Root Autoregressions

Ngai Hang Chan and Norma Terrin

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Abstract

An autoregressive time series is said to be unstable if all of its characteristic roots lie on or outside the unit circle, with at least one on the unit circle. This paper aims at developing asymptotic inferential schemes for an unstable autoregressive model generated by long-memory innovations. This setting allows both nonstationarity and long-memory behavior in the modeling of low-frequency phenomena. In developing these procedures, a novel weak convergence result for a sequence of long-memory random variables to a stochastic integral of fractional Brownian motions is established. Results of this paper can be used to test for unit roots in a fractional AR model.

Article information

Source
Ann. Statist., Volume 23, Number 5 (1995), 1662-1683.

Dates
First available in Project Euclid: 11 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176324318

Digital Object Identifier
doi:10.1214/aos/1176324318

Mathematical Reviews number (MathSciNet)
MR1370302

Zentralblatt MATH identifier
0843.62084

JSTOR
links.jstor.org

Subjects
Primary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]
Secondary: 62E20: Asymptotic distribution theory 60F17: Functional limit theorems; invariance principles

Keywords
Fractional Brownian motion least squares long-range dependence stochastic integral unstable

Citation

Chan, Ngai Hang; Terrin, Norma. Inference for Unstable Long-Memory Processes with Applications to Fractional Unit Root Autoregressions. Ann. Statist. 23 (1995), no. 5, 1662--1683. doi:10.1214/aos/1176324318. https://projecteuclid.org/euclid.aos/1176324318


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