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Regression Theory for Near-Integrated Time Series

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Author Info
Phillips, Peter C B

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Abstract

The concept of a near-integrated vector random process is introduce d, helping the author work towards a general asymptotic theory of regression fo r multiple time series in which some series may be integrated processe s of the ARIMA type, others may be stable ARMA processes with near unit roots, and yet others may be mildly explosive. A limit theory for th e sample moments of such time series is developed using weak convergence. The theory is applied to the study of vector autoregress ions and cointegrating regressions of the type advanced by R. F. Engle and C. W. Granger (1987). A noncentral limiting distribution theory is derived for some recently-proposed multivariate unit root tests. Models with drift and near-integration are also studied. Copyright 1988 by The Econometric Society.

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Publisher Info
Article provided by Econometric Society in its journal Econometrica.

Volume (Year): 56 (1988)
Issue (Month): 5 (September)
Pages: 1021-43
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Handle: RePEc:ecm:emetrp:v:56:y:1988:i:5:p:1021-43

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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. Kramer, Walter, 1984. "On the consequences of trend for simultaneous equation estimation," Economics Letters, Elsevier, vol. 14(1), pages 23-30. [Downloadable!] (restricted)
  2. 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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  3. Peter C.B. Phillips & Pierre Perron, 1986. "Testing for a Unit Root in Time Series Regression," Cowles Foundation Discussion Papers 795R, Cowles Foundation, Yale University, revised Sep 1987. [Downloadable!]
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  4. Phillips, P C B, 1974. "The Estimation of Some Continuous Time Models," Econometrica, Econometric Society, vol. 42(5), pages 803-23, September. [Downloadable!] (restricted)
  5. Peter C.B. Phillips, 1986. "Weak Convergence to the Matrix Stochastic Integral BdB," Cowles Foundation Discussion Papers 796, Cowles Foundation, Yale University. [Downloadable!]
  6. Granger, C. W. J. & Newbold, P., 1974. "Spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 2(2), pages 111-120, July. [Downloadable!] (restricted)
  7. Evans, G B A & Savin, N E, 1981. "Testing for Unit Roots: 1," Econometrica, Econometric Society, vol. 49(3), pages 753-79, May. [Downloadable!] (restricted)
  8. West, Kenneth D, 1988. "Asymptotic Normality, When Regressors Have a Unit Root," Econometrica, Econometric Society, vol. 56(6), pages 1397-1417, November. [Downloadable!] (restricted)
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