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October, 1995 Inference for Unstable Long-Memory Processes with Applications to Fractional Unit Root Autoregressions
Ngai Hang Chan, Norma Terrin
Ann. Statist. 23(5): 1662-1683 (October, 1995). DOI: 10.1214/aos/1176324318

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.

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Ngai Hang Chan. Norma Terrin. "Inference for Unstable Long-Memory Processes with Applications to Fractional Unit Root Autoregressions." Ann. Statist. 23 (5) 1662 - 1683, October, 1995. https://doi.org/10.1214/aos/1176324318

Information

Published: October, 1995
First available in Project Euclid: 11 April 2007

zbMATH: 0843.62084
MathSciNet: MR1370302
Digital Object Identifier: 10.1214/aos/1176324318

Subjects:
Primary: 62M10
Secondary: 60F17, 62E20

Rights: Copyright © 1995 Institute of Mathematical Statistics

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Vol.23 • No. 5 • October, 1995
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