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How to Estimate Autoregressive Roots Near Unity

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Author Info
Peter C.B. Phillips () (Cowles Foundation, Yale University)
Hyungsik R. Moon (Dept. Econ, UCLA, Santa Barbara)
Zhijie Xiao (Univ. Illinois at Urbana-Champaign)

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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, 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 localising parameter are obtained for this case as well. Conventional unit root tests are shown to be consistent against local alternatives in the new class.

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File URL: http://cowles.econ.yale.edu/P/cd/d11b/d1191.pdf
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Publisher Info
Paper provided by Cowles Foundation, Yale University in its series Cowles Foundation Discussion Papers with number 1191.

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Length: 39 pages
Date of creation: Aug 1998
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Publication status: Published in Econometric Theory (2001), 17(1): 29-59
Handle: RePEc:cwl:cwldpp:1191

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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Peter C.B. Phillips & Victor Solo, 1989. "Asymptotics for Linear Processes," Cowles Foundation Discussion Papers 932, Cowles Foundation, Yale University. [Downloadable!]
  2. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March. [Downloadable!] (restricted)
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  3. Peter C.B. Phillips & Joon Y. Park, 1986. "Statistical Inference in Regressions with Integrated Processes: Part 1," Cowles Foundation Discussion Papers 811R, Cowles Foundation, Yale University, revised Aug 1987. [Downloadable!]
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  4. Hyungsik R. Moon & Peter C.B. Phillips, 1999. "Estimation of Autoregressive Roots Near Unity Using Panel Data," Cowles Foundation Discussion Papers 1224, Cowles Foundation, Yale University. [Downloadable!]
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  5. Johansen, Soren, 1991. "Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models," Econometrica, Econometric Society, vol. 59(6), pages 1551-80, November. [Downloadable!] (restricted)
  6. Graham Elliott & Thomas J. Rothenberg & James H. Stock, 1992. "Efficient Tests for an Autoregressive Unit Root," NBER Technical Working Papers 0130, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Chevillon, Guillaume, 2007. "Inference in the Presence of Stochastic and Deterministic Trends," ESSEC Working Papers DR 07021, ESSEC Research Center, ESSEC Business School. [Downloadable!]
  2. Hyungsik R. Moon & Peter C.B. Phillips, 1999. "Estimation of Autoregressive Roots Near Unity Using Panel Data," Cowles Foundation Discussion Papers 1224, Cowles Foundation, Yale University. [Downloadable!]
    Other versions:
  3. Charlotte S. Hansen & Bjorn E. Tuypens, 2004. "Long-Run Regressions: Theory and Application to US Asset Markets," Finance 0410018, EconWPA. [Downloadable!]
  4. Issler, João Victor & Lima, Luiz Renato Regis de Oliveira, 2007. "A Panel Data Approach to Economic Forecasting: The Bias-Corrected Average Forecast," Economics Working Papers (Ensaios Economicos da EPGE) 642, Graduate School of Economics, Getulio Vargas Foundation (Brazil). [Downloadable!]
    Other versions:
  5. Hyungsik R. Moon & Peter C.B. Phillips, 1999. "Maximum Likelihood Estimation in Panels with Incidental Trends," Cowles Foundation Discussion Papers 1246, Cowles Foundation, Yale University. [Downloadable!]
    Other versions:
  6. H. Peter Boswijk, 2001. "Block Local to Unity and Continuous Record Asymptotics," Tinbergen Institute Discussion Papers 01-078/4, Tinbergen Institute. [Downloadable!]
  7. Peter C.B. Phillips & Hyungsik R. Moon, 1999. "Nonstationary Panel Data Analysis: An Overview of Some Recent Developments," Cowles Foundation Discussion Papers 1221, Cowles Foundation, Yale University. [Downloadable!]
    Other versions:
  8. Ai Deng, 2005. "Understanding Spurious Regression in Financial Economics," Boston University - Department of Economics - Working Papers Series WP2005-048, Boston University - Department of Economics. [Downloadable!]
  9. Peter C.B. Phillips, 2003. "Laws and Limits of Econometrics," Cowles Foundation Discussion Papers 1397, Cowles Foundation, Yale University. [Downloadable!]
    Other versions:
  10. Erik Hjalmarsson, 2005. "Estimation of average local-to-unity roots in heterogenous panels," International Finance Discussion Papers 852, Board of Governors of the Federal Reserve System (U.S.). [Downloadable!]
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