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A Primer on Unit Root Testing

  • Phillips, Peter C B
  • Xiao, Zhijie

The immense literature and diversity of unit root tests can at times be confusing even to the specialist and presents a truly daunting prospect to the uninitiated. In consequence, much empirical work still makes use of the simplest testing procedures because it is unclear from the literature and from recent reviews which tests if any are superior. This paper presents a survey of unit root theory with an emphasis on testing principles and recent developments. The general framework adopted makes it possible to consider tests of stochastic trends against trend stationarity and trend breaks of a general type. The main tests are listed, and asymptotic distributions are given in a simple form that emphasizes commonalities in the theory. Some simulation results are reported, and an extensive list of references and all annotated bibliography are provided. Copyright 1998 by Blackwell Publishers Ltd

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Article provided by Wiley Blackwell in its journal Journal of Economic Surveys.

Volume (Year): 12 (1998)
Issue (Month): 5 (December)
Pages: 423-69

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Handle: RePEc:bla:jecsur:v:12:y:1998:i:5:p:423-69
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  1. Hylleberg, S. & Engle, R. F. & Granger, C. W. J. & Yoo, B. S., 1990. "Seasonal integration and cointegration," Journal of Econometrics, Elsevier, vol. 44(1-2), pages 215-238.
  2. Hall, Robert E, 1978. "Stochastic Implications of the Life Cycle-Permanent Income Hypothesis: Theory and Evidence," Journal of Political Economy, University of Chicago Press, vol. 86(6), pages 971-87, December.
  3. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
  4. Sims, Christopher A & Stock, James H & Watson, Mark W, 1990. "Inference in Linear Time Series Models with Some Unit Roots," Econometrica, Econometric Society, vol. 58(1), pages 113-44, January.
  5. Peter C.B. Phillips, 1985. "Understanding Spurious Regressions in Econometrics," Cowles Foundation Discussion Papers 757, Cowles Foundation for Research in Economics, Yale University.
  6. repec:cup:etheor:v:10:y:1994:i:3-4:p:774-808 is not listed on IDEAS
  7. Nelson, Charles R. & Plosser, Charles I., 1982. "Trends and random walks in macroeconmic time series : Some evidence and implications," Journal of Monetary Economics, Elsevier, vol. 10(2), pages 139-162.
  8. Jeganathan, P., 1995. "Some Aspects of Asymptotic Theory with Applications to Time Series Models," Econometric Theory, Cambridge University Press, vol. 11(05), pages 818-887, October.
  9. Jeganathan, P., 1991. "On the Asymptotic Behavior of Least-Squares Estimators in AR Time Series with Roots Near the Unit Circle," Econometric Theory, Cambridge University Press, vol. 7(03), pages 269-306, September.
  10. Eugene Canjels & Mark W. Watson, 1994. "Estimating Deterministic Trends in the Presence of Serially Correlated Errors," NBER Technical Working Papers 0165, National Bureau of Economic Research, Inc.
  11. Phillips, P C B, 1991. "To Criticize the Critics: An Objective Bayesian Analysis of Stochastic Trends," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 6(4), pages 333-64, Oct.-Dec..
  12. Diebold, Francis X. & Rudebusch, Glenn D., 1991. "On the power of Dickey-Fuller tests against fractional alternatives," Economics Letters, Elsevier, vol. 35(2), pages 155-160, February.
  13. repec:cup:etheor:v:11:y:1995:i:5:p:818-87 is not listed on IDEAS
  14. Steven N. Durlauf & Peter C.B. Phillips, 1986. "Trends Versus Random Walks in Time Series Analysis," Cowles Foundation Discussion Papers 788, Cowles Foundation for Research in Economics, Yale University.
  15. repec:cup:etheor:v:10:y:1994:i:5:p:917-36 is not listed on IDEAS
  16. G. William Schwert, 1988. "Tests For Unit Roots: A Monte Carlo Investigation," NBER Technical Working Papers 0073, National Bureau of Economic Research, Inc.
  17. DeJong, David N & Whiteman, Charles H, 1991. "The Temporal Stability of Dividends and Stock Prices: Evidence from the Likelihood Function," American Economic Review, American Economic Association, vol. 81(3), pages 600-617, June.
  18. Eric Zivot & Peter C.B. Phillips, 1991. "A Bayesian Analysis of Trend Determination in Economic Time Series," Cowles Foundation Discussion Papers 1002, Cowles Foundation for Research in Economics, Yale University.
  19. Engle, Robert & Granger, Clive, 2015. "Co-integration and error correction: Representation, estimation, and testing," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 39(3), pages 106-135.
  20. Peter C.B. Phillips & Sam Ouliaris, 1987. "Asymptotic Properties of Residual Based Tests for Cointegration," Cowles Foundation Discussion Papers 847R, Cowles Foundation for Research in Economics, Yale University, revised Jul 1988.
  21. repec:cup:etheor:v:10:y:1994:i:3-4:p:764-73 is not listed on IDEAS
  22. Peter C.B. Phillips & Chin Chin Lee, 1996. "Efficiency Gains from Quasi-Differencing Under Nonstationarity," Cowles Foundation Discussion Papers 1134, Cowles Foundation for Research in Economics, Yale University.
  23. Dufour, J.M. & King, M.L., 1989. "Optimal Invariant Tests for the Autocorrelation Coefficient in Linear Regressions with Stationary and Nonstationary Ar(1) Errors," Cahiers de recherche 8921, Universite de Montreal, Departement de sciences economiques.
  24. Osborn, Denise R & Smith, Jeremy P, 1989. "The Performance of Periodic Autoregressive Models in Forecasting Seasonal U. K. Consumption," Journal of Business & Economic Statistics, American Statistical Association, vol. 7(1), pages 117-27, January.
  25. Gil-Alana, L. A. & Robinson, P. M., 1997. "Testing of unit root and other nonstationary hypotheses in macroeconomic time series," Journal of Econometrics, Elsevier, vol. 80(2), pages 241-268, October.
  26. Philip Hans Franses & Michael McAleer, 1998. "Cointegration Analysis of Seasonal Time Series," Journal of Economic Surveys, Wiley Blackwell, vol. 12(5), pages 651-678, December.
  27. Eric Zivot & Donald W.K. Andrews, 1990. "Further Evidence on the Great Crash, the Oil Price Shock, and the Unit Root Hypothesis," Cowles Foundation Discussion Papers 944, Cowles Foundation for Research in Economics, Yale University.
  28. 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.
  29. Perron, Pierre, 1989. "The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis," Econometrica, Econometric Society, vol. 57(6), pages 1361-1401, November.
  30. Meese, Richard A & Singleton, Kenneth J, 1982. " On Unit Roots and the Empirical Modeling of Exchange Rates," Journal of Finance, American Finance Association, vol. 37(4), pages 1029-35, September.
  31. Blough, Stephen R, 1992. "The Relationship between Power and Level for Generic Unit Root Tests in Finite Samples," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 7(3), pages 295-308, July-Sept.
  32. Leybourne, S J & McCabe, B P M, 1994. "A Consistent Test for a Unit Root," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(2), pages 157-66, April.
  33. Denis Kwiatkowski & Peter C.B. Phillips & Peter Schmidt, 1991. "Testing the Null Hypothesis of Stationarity Against the Alternative of a Unit Root: How Sure Are We That Economic Time Series Have a Unit Root?," Cowles Foundation Discussion Papers 979, Cowles Foundation for Research in Economics, Yale University.
  34. M. N. Hasan & R. W. Koenker, 1997. "Robust Rank Tests of the Unit Root Hypothesis," Econometrica, Econometric Society, vol. 65(1), pages 133-162, January.
  35. Kim, Jae-Young, 1994. "Bayesian Asymptotic Theory in a Time Series Model with a Possible Nonstationary Process," Econometric Theory, Cambridge University Press, vol. 10(3-4), pages 764-773, August.
  36. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-58, May.
  37. Chao, John C. & Phillips, Peter C. B., 1999. "Model selection in partially nonstationary vector autoregressive processes with reduced rank structure," Journal of Econometrics, Elsevier, vol. 91(2), pages 227-271, August.
  38. Perron, Pierre, 1988. "Trends and random walks in macroeconomic time series : Further evidence from a new approach," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 297-332.
  39. Phillips, Peter C.B. & Ploberger, Werner, 1994. "Posterior Odds Testing for a Unit Root with Data-Based Model Selection," Econometric Theory, Cambridge University Press, vol. 10(3-4), pages 774-808, August.
  40. Phillips, Peter C B & Ploberger, Werner, 1996. "An Asymptotic Theory of Bayesian Inference for Time Series," Econometrica, Econometric Society, vol. 64(2), pages 381-412, March.
  41. Dickey, David A & Fuller, Wayne A, 1981. "Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root," Econometrica, Econometric Society, vol. 49(4), pages 1057-72, June.
  42. Baillie, Richard T. & Bollerslev, Tim & Mikkelsen, Hans Ole, 1996. "Fractionally integrated generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 74(1), pages 3-30, September.
  43. Robin L. Lumsdaine & David H. Papell, 1997. "Multiple Trend Breaks And The Unit-Root Hypothesis," The Review of Economics and Statistics, MIT Press, vol. 79(2), pages 212-218, May.
  44. Park, Joon Y. & Sung, Jaewhan, 1994. "Testing for Unit Roots in Models with Structural Change," Econometric Theory, Cambridge University Press, vol. 10(05), pages 917-936, December.
  45. Osborn, Denise R, et al, 1988. "Seasonality and the Order of Integration for Consumption," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 50(4), pages 361-77, November.
  46. DeJong, David N. & Nankervis, John C. & Savin, N. E. & Whiteman, Charles H., 1992. "The power problems of unit root test in time series with autoregressive errors," Journal of Econometrics, Elsevier, vol. 53(1-3), pages 323-343.
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