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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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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!]
    Other versions:
  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!]
    Other versions:
  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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(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. Nelson C. Mark & Donggyu Sul, 2004. "The Use of Predictive Regressions at Alternative Horizons in Finance and Economics," Finance 0409032, EconWPA. [Downloadable!]
    Other versions:
  2. Erik Hjalmarsson, 2006. "New methods for inference in long-run predictive regressions," International Finance Discussion Papers 853, Board of Governors of the Federal Reserve System (U.S.). [Downloadable!]
  3. Lucas, Andr‚, 1997. "Strategic and tactical asset allocation and the effect of long-run equilibrium relations," Serie Research Memoranda 0042, Free University Amsterdam, Faculty of Economics, Business Administration and Econometrics. [Downloadable!]
  4. Guillaume Chevillon, 2004. "`Weak` trends for inference and forecasting in finite samples," Economics Series Working Papers 210, University of Oxford, Department of Economics. [Downloadable!]
    Other versions:
  5. Erik Hjalmarsson & Par Osterholm, 2007. "A residual-based cointegration test for near unit root variables," International Finance Discussion Papers 907, Board of Governors of the Federal Reserve System (U.S.). [Downloadable!]
  6. Daniel B. Nelson, 1994. "Asymptotic Filtering Theory for Multivariate ARCH Models," NBER Technical Working Papers 0162, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  7. Elena Pesavento, 2005. "Residuals Bases Tests for the Null of No Cointegration: an Analytical Comparison," Emory Economics 0503, Department of Economics, Emory University (Atlanta). [Downloadable!]
  8. Peter C.B. Phillips & Tassos Magadalinos, 2005. "Limit Theory for Moderate Deviations from a Unit Root under Weak Dependence," Cowles Foundation Discussion Papers 1517, Cowles Foundation, Yale University. [Downloadable!]
  9. Erik Hjalmarsson & Pär Österholm, 2007. "Testing for Cointegration Using the Johansen Methodology when Variables are Near-Integrated," IMF Working Papers 07/141, International Monetary Fund. [Downloadable!]
    Other versions:
  10. Maurice Obstfeld & Jay C.Shambaugh & Alan M.Taylor, 2003. "The Trilemma in History:Tradeoffs among Exchange Rates, Monetary Policies,and Capital Mobility," DNB Staff Reports (discontinued) 94, Netherlands Central Bank. [Downloadable!]
    Other versions:
  11. Mototsugu Shintani, 2000. "A Simple Cointegrating Rank Test Without Vector Autoregression," Working Papers 0044, Department of Economics, Vanderbilt University. [Downloadable!]
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  12. Rossen Valkanov, 1999. "The Term Structure with Highly Persistent Interest Rates," University of California at Los Angeles, Anderson Graduate School of Management 1099, Anderson Graduate School of Management, UCLA. [Downloadable!]
  13. Andrew W. Lo & A. Craig MacKinlay, 1989. "Stock Market Prices Do Not Follow Random Walks: Evidence From a Simple Specification Test," NBER Working Papers 2168, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
    Other versions:
  14. Boswijk, H. Peter & Lucas, Andr‚ & Taylor, Nick, 1998. "A comparison of parametric, semi-nonparametric, adaptive and nonparametric tests," Serie Research Memoranda 0062, Free University Amsterdam, Faculty of Economics, Business Administration and Econometrics. [Downloadable!]
  15. Cosme Vodounou, 1998. "Inférence fondée sur les statistiques des rendements de long terme," CIRANO Working Papers 98s-20, CIRANO. [Downloadable!]
  16. H. Peter Boswijk & Andre Lucas & Nick Taylor, 1999. "A Comparison of Parametric, Semi-nonparametric, Adaptive, and Nonparametric Cointegration Tests," Tinbergen Institute Discussion Papers 99-012/4, Tinbergen Institute. [Downloadable!]
  17. Hjalmarsson, Erik, 2005. "On the Predictability of Global Stock Returns," Working Papers in Economics 161, Göteborg University, Department of Economics. [Downloadable!]
  18. David Hendry, 1995. "On the interactions of unit roots and exogeneity," Economics Papers 7., Economics Group, Nuffield College, University of Oxford. [Downloadable!]
    Other versions:
  19. Leon, Costas, 2006. "The Taylor rule: can it be supported by the data?," MPRA Paper 1650, University Library of Munich, Germany. [Downloadable!]
  20. Mukhtar M. Ali, 1996. "Distribution of the Least Squares Estimator in a First-Order Autoregressive Model," Econometrics 9610004, EconWPA. [Downloadable!]
  21. Clifford A. Ball, Antonio Roma, 1998. "Detecting mean reversion within reflecting barriers: application to the European Exchange Rate Mechanism," Applied Mathematical Finance, Taylor and Francis Journals, vol. 5(1), pages 1-15, March. [Downloadable!] (restricted)
  22. Österholm, Pär, 2003. "The Taylor Rule: A Spurious Regression?," Working Paper Series 2003:20, Uppsala University, Department of Economics. [Downloadable!]
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