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October 2007 Asymptotic theory of least squares estimators for nearly unstable processes under strong dependence
Boris Buchmann, Ngai Hang Chan
Ann. Statist. 35(5): 2001-2017 (October 2007). DOI: 10.1214/009053607000000136


This paper considers the effect of least squares procedures for nearly unstable linear time series with strongly dependent innovations. Under a general framework and appropriate scaling, it is shown that ordinary least squares procedures converge to functionals of fractional Ornstein–Uhlenbeck processes. We use fractional integrated noise as an example to illustrate the important ideas. In this case, the functionals bear only formal analogy to those in the classical framework with uncorrelated innovations, with Wiener processes being replaced by fractional Brownian motions. It is also shown that limit theorems for the functionals involve nonstandard scaling and nonstandard limiting distributions. Results of this paper shed light on the asymptotic behavior of nearly unstable long-memory processes.


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Boris Buchmann. Ngai Hang Chan. "Asymptotic theory of least squares estimators for nearly unstable processes under strong dependence." Ann. Statist. 35 (5) 2001 - 2017, October 2007.


Published: October 2007
First available in Project Euclid: 7 November 2007

zbMATH: 1126.62069
MathSciNet: MR2363961
Digital Object Identifier: 10.1214/009053607000000136

Primary: 62E20, 62M10
Secondary: 60F17

Rights: Copyright © 2007 Institute of Mathematical Statistics


Vol.35 • No. 5 • October 2007
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