The Annals of Statistics
- Ann. Statist.
- Volume 23, Number 5 (1995), 1662-1683.
Inference for Unstable Long-Memory Processes with Applications to Fractional Unit Root Autoregressions
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.
Ann. Statist., Volume 23, Number 5 (1995), 1662-1683.
First available in Project Euclid: 11 April 2007
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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