How to estimate autoregressive roots near unity

Peter C.B. Phillips, Hyungsik Roger Moon, Zhijie Xiao

Research output: Contribution to journalArticle

25 Citations (Scopus)

Abstract

A new model of near integration is formulated in which the local to unity parameter is identifiable and consistently estimable with time series data. The properties of the model are investigated, new functional laws for near integrated time series are obtained that lead to mixed diffusion processes, and consistent estimators of the localizing parameter are constructed. The model provides a more complete interface between I(0) and I(1) models than the traditional local to unity model and leads to autoregressive coefficient estimates with rates of convergence that vary continuously between the O(√n) rate of stationary autoregression, the O(n) rate of unit root regression, and the power rate of explosive autoregression. Models with deterministic trends are also considered, least squares trend regression is shown to be efficient, and consistent estimates of the localizing parameter are obtained for this case also. Conventional unit root tests are shown to be consistent against local alternatives in the new class.

Original languageEnglish
Pages (from-to)29-69
Number of pages41
JournalEconometric Theory
Volume17
Issue number1
DOIs
Publication statusPublished - 2001 Jan 1

Fingerprint

time series
regression
trend
Law
Autoregression
Time series data
Unit root tests
Rate of convergence
Integrated time series
Deterministic trend
Least squares
Diffusion process
Estimator
Coefficients
Local alternatives
Unit root

All Science Journal Classification (ASJC) codes

  • Social Sciences (miscellaneous)
  • Economics and Econometrics

Cite this

Phillips, Peter C.B. ; Moon, Hyungsik Roger ; Xiao, Zhijie. / How to estimate autoregressive roots near unity. In: Econometric Theory. 2001 ; Vol. 17, No. 1. pp. 29-69.
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How to estimate autoregressive roots near unity. / Phillips, Peter C.B.; Moon, Hyungsik Roger; Xiao, Zhijie.

In: Econometric Theory, Vol. 17, No. 1, 01.01.2001, p. 29-69.

Research output: Contribution to journalArticle

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