Hostname: page-component-89b8bd64d-r6c6k Total loading time: 0 Render date: 2026-05-13T18:30:46.310Z Has data issue: false hasContentIssue false
  • English
  • Français

UNIT ROOTS: A SELECTIVE REVIEW OF THE CONTRIBUTIONS OF PETER C. B. PHILLIPS

Published online by Cambridge University Press:  25 February 2014

Zhijie Xiao
Zhijie Xiao*
Affiliation:
Boston College
*
*Address correspondence to Zhijie Xiao, Department of Economics, Boston College, Chestnut Hill, MA 02467; e-mail: xiaoz@bc.edu.
Get access Rights & Permissions [Opens in a new window]

Abstract

Peter C. B. Phillips has made fundamental contributions to unit root econometrics. This paper provides a selective review of Peter’s contribution to unit roots, with a focus on unit root asymptotics, unit root tests, and testing for stationarity against the unit root alternative. The discussion puts a relatively heavier weight on Peter’s most recent work.

Information

Type
ARTICLES
Information
Econometric Theory , Volume 30 , Issue 4 , August 2014 , pp. 775 - 814
Copyright
Copyright © Cambridge University Press 2014 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

REFERENCES

Andrews, D.W.K. & Guggenberger, P. (2008) Asymptotics for stationary very nearly unit root processes. Journal of Time Series Analysis 29(1), 203–210.Google Scholar
Andrews, D.W.K. (1991) Heteroskedasticity and autocorrelation consistent covariance matrix estimation. Econometrica 59, 817–858.Google Scholar
Ayat, L. & Burridge, P. (2000) Unit root tests in the presence of uncertainty about the non-stochastic trend. Journal of Econometrics 95, 71–90.Google Scholar
Bai, J. & Perron, P. (1998) Estimating and testing linear models with multiple structural changes. Econometrica 66(1), 47–78.Google Scholar
Banerjee, A., Dolado, J., Galbraith, J.W., & Hendry, D.F. (1992) Cointegration, Error Correction, and the Econometric Analysis of Non-Stationary Time Series. Oxford University Press.Google Scholar
Beveridge, S. & Nelson, R. (1981) A new approach to decomposition of time series in permanent and transitory components with particular attention to measurement of the ‘business cycle’. Journal of Monetary Economics 7, 151–174.CrossRefGoogle Scholar
Bhargava, A. (1986) On the theory of testing for unit roots in observed time series. Review of Economic Studies 53, 369–384.CrossRefGoogle Scholar
Blough, S.R. (1992) The relationship between power and level for generic unit root tests in finite samples. Journal of Applied Econometrics 7, 295–308.Google Scholar
Campbell, J.Y. & Perron, P. (1991) Pitfalls and opportunities: What macroeconomists should know about unit roots (with discussion). In Blanchard, O.J. & Fischer, S. (eds.), NBER Macroeconomics Annual. MIT Press.Google Scholar
Canjels, N. & Watson, M. (1997) Estimating deterministic trends in the presence of serially correlated errors. Review of Economics and Statistics 79, 184–200.Google Scholar
Chan, N.H. & Wei, C.Z.. (1988) Limiting distributions of least squares estimates of unstable autoregressive processes. Annals of Statistics 16, 367–401.CrossRefGoogle Scholar
Choi, I. & Phillips, P.C.B. (1993) Testing for a unit root by frequency domain regression. Journal of Econometrics 59, 263–286.CrossRefGoogle Scholar
Christiano, L.J. (1992) Searching for a break in GNP. Journal of Business & Economic Statistics 10, 237–250.Google Scholar
Dickey, D.A. & Fuller, W.A. (1979) Distribution of estimators for autoregressive time series with a unit root. Journal of the American Statistical Association 74, 427–431.Google Scholar
Dickey, D.A. & Fuller, W.A. (1981) Likelihood ratio tests for autoregressive time series with a unit root. Econometrica 49, 1057–1072.Google Scholar
Dhrymes, P. (1998) Time Series, Unit Roots and Cointegration. Academic pressGoogle Scholar
Dufour, J. & King, M.L. (1991) Optimal invariant tests for the autocorrelation coefficient in linear regressions with stationary and nonstationary AR(1) errors. Journal of Econometrics 47,115–143.Google Scholar
Elliot, G., Rothenberg, T.J., & Stock, J.H. (1996) Efficient tests for an autoregressive unit root. Econometrca 64, 813–836.CrossRefGoogle Scholar
Engle, R.F. & Granger, C.W.J. (1987) Cointegration and error correction: Representation, estimation and testing. Econometrica 55, 251–276.CrossRefGoogle Scholar
Faust, J. (1996) Near observational equivalence and theoretical size problems with unit root tests. Econometric Theory 12, 724–731.Google Scholar
Fuller, W.A. (1976) Introduction to Statistical Time Series. Wiley.Google Scholar
Fuller, W.A. (1996) Introduction to Statistical Time Series. Wiley.Google Scholar
Giraitis, L. & Phillips, P.C.B. (2006) Uniform limit theory for stationary autoregression. Journal of Time Series Analysis 27(1), 51–60.Google Scholar
Grenander, U. & Rosenblatt, M. (1957) Statistical Analysis of Stationary Time Series. John Wiley.CrossRefGoogle Scholar
Hall, P. & Heyde, C.C. (1980) Martingale Limit Theory and its Applications. Academic Press.Google Scholar
Hansen, B. (1995) Rethinking the univariate approach to unit root tests: How to use covariates to increase power. Econometric Theory 11, 1148–1171.Google Scholar
Hansen, B. (2000) Testing for structural change in conditional models. Journal of Econometrics 97, 93–115.CrossRefGoogle Scholar
Hansen, B. (2001) The new econometrics of structural change: Dating changes in U.S. labor productivity. Journal of Economic Perspectives 15, 117–128.CrossRefGoogle Scholar
Hansen, B. & Caner, M. (2001) Threshold autoregression with a unit root. Econometrica 69, 1555–1596.Google Scholar
Harris, D., Leybourne, S., & McCabe, B. (2007) Modified KPSS tests for near integration. Econometric Theory 23, 355–363.CrossRefGoogle Scholar
Harvey, D.I., Leybourne, S.J., & Taylor, A.M.R. (2008) Unit root testing in practice: Dealing with uncertainty over the trend and initial conditions. Econometric Theory 25, 587.Google Scholar
Hasan, M.N. & Koenker, R.W. (1997) Robust rank tests of the unit root hypothesis. Econometrica 65, 133–161.CrossRefGoogle Scholar
Hercé, M. (1996) Asymptotic theory od LAD estimation in a unit root process with finite variance errors. Econometric Theory 12, 129–153.Google Scholar
Ibragimov, R., & Phillips, P.C.B. (2008) Regression asymptotics using martingale convergence methods. Econometric Theory 24(4), 888–947.CrossRefGoogle Scholar
Jacod, J. & Shiryaev, A.N. (2003) Limit Theorems for Stochastic Processes. Springer-Verlag.Google Scholar
Juhl, T. (2008) A nonparametric test of the predictive regression model, mimeo.Google Scholar
Juhl, T. & Xiao, Z. (2003) Power functions and envelopes for unit root tests. Econometric Theory 19, 240–253.CrossRefGoogle Scholar
Kapetanois, G. (2005) Unit root testing against the alternative hypothesis up to m structural breaks. Journal of Time Series Analysis 26, 123–133.Google Scholar
Knight, K. (1989) Limit theory for autoregressive-parameter estimates in an infinite-variance random walk. The Canadian Journal of Statistics 17, 261–278.Google Scholar
Knight, K. (1998) Asymptotics for L1 regression estimates under general conditions. Annals of Statistics 26, 755–770.Google Scholar
King, M.L. (1988) Towards a theory of point optimal testing. Econometric Reviews 6, 169–218.Google Scholar
Koenker, R. & Xiao, Z. (2004) Unit root quantile autoregression. Journal of American Statistical Association 99, 467.Google Scholar
Kwiatkowski, D., Phillips, P.C.B., Schmidt, P., & Shin, Y. (1992) 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? Journal of Econometrics 54, 159–178.Google Scholar
Lai, T.L. & Wei, C.Z. (1982) Least squares estimation in stochastic regresssion models with applications to identification and control of dynamic systems. Annals of Statistics 10, 154–166.Google Scholar
Lee, J. & Strazicich, M.C. (2003) Minimum Lagrange multiplier unit root test with two structural breaks. Review of Economics and Statistics 85(4), 1082–1089.Google Scholar
Leybourne, S.J. & McCabe, B.P.M. (1994) A consistent test for a unit root. Journal of Business and Economic Statistics 12, 157–166.Google Scholar
Lumsdaine, R.L. & Papell, D.H. (1997) Multiple trend breaks and the unit root hypothesis. Review of Economics and Statistics 79, 212–218.CrossRefGoogle Scholar
Müller, U.K. (2008). The impossibility of consistent discrimination between I(0) and I(1) processes. Econometric Theory 24, 616–630.CrossRefGoogle Scholar
Müller, U.K. & Elliott, G.. (2003) Tests for unit roots and the initial condition. Econometrica 71, 1269–1286.Google Scholar
Nelson, C.R. & Plosser, C. (1982) Trends and random walks in macro-economic time series: some evidence and implications. Journal of Monetary Economics 10, 139–162.Google Scholar
Ouliaris, S., Park, J.Y., & Phillips, P.C.B. (1989) Testing for a unit root in the presence of a maintained trend. In Raj, B. (ed.), Advances in Econometrics and Modelling, pp. 7–28. Kluwer.CrossRefGoogle Scholar
Ouliaris, S. & Phillips, P.C.B. (1994) Coint 2.0. Aptech Systems.Google Scholar
Park, J.Y. & Sung, J. (1994) Testing for unit roots in models with structural change. Econometric Theory 10, 917–936.Google Scholar
Park, J. & Phillips, P.C.B. (1998) Nonstationary density estimation and kernel autoregression, CFDP 1181, Yale University.Google Scholar
Park, J. & Phillips, P.C.B. (1999) Asymptotics for nonlinear transformations of integrated time series. Econometric Theory 15(3), 269–298.Google Scholar
Perron, P. (1989) The great crash, the oil price shock and the unit root hypothesis. Econometrica 57, 1361–1401.Google Scholar
Perron, P. & Ng, S.. (1996) Useful modifications to some unit root tests with dependent errors and their local asymptotic properties. Review of Economic Studies 63, 435–463.Google Scholar
Phillips, P.C.B. (1986) Understanding spurious regressions in econometrics. Journal of Econometrics 33(3), 311–340.Google Scholar
Phillips, P.C.B. (1987a) Time series regression with a unit root. Econometrica 55, 277–302.Google Scholar
Phillips, P.C.B. (1987b) Towards a unified asymptotic theory of autoregression. Biometrika 74,535–547.Google Scholar
Phillips, P.C.B. (1988) Regression theory for near-integrated time series. Econometrica 56(5), 1021–1044.Google Scholar
Phillips, P.C.B. (1991) A shortcut to LAD estimator asymptotics. Econometric Theory 7.CrossRefGoogle Scholar
Phillips, P.C.B. (1995a) Robust nonstationary regression. Econometric Theory 12(5), 912–951.Google Scholar
Phillips, P.C.B. (1995b) Fully modified least squares and vector autoregression. Econometrica 63(5), 1023–1078.CrossRefGoogle Scholar
Phillips, P.C.B. (1998) New tools for understanding spurious regression. Econometrica 66(6), 1299–1326.Google Scholar
Phillips, Peter C.B., & Park, Joon Y. (1998) Nonstationary Density Estimation and kernel Autoregression. Cowles Foundation.Google Scholar
Phillips, P.C.B. (2002) The invalidity of critical values of tests for unit roots against trend alternatives. Journal of Econometrics 111, 323–353.Google Scholar
Phillips, P.C.B. (2005) Some themes in modern econometrics. Lecture Notes, Singapore Management University.Google Scholar
Phillips, P.C.B. & Hansen, B.E. (1990) Statistical inference in instrumental variable regressions with I(1) processes. Review of Economic Studies 57, 99–125.Google Scholar
Phillips, P.C.B. & Lee, C.C. (1996) Efficiency gains from quasi-differencing under nonstationarity. In Robinson, P.M. & Rosenblatt, M. (eds.), Athens Conference on Applied Probability and Time Series: Essays in Memory of E.J. Hannan. Springer–Verlag.Google Scholar
Phillips, P.C.B. & Magdalinos, T. (2006) Limit theory for moderate deivations from unity under weak dependence. In Phillips, G.D.A. & Tzavalis, E. (eds.), The Refinement of Econometric Estimation and Test Procedures: Finite Sample and Asymptotic Analysis. Cambridge University Press, forthcoming.Google Scholar
Phillips, P.C.B. & Magdalinos, T. (2007) Limit theory for moderate deviations from a unit root. Journal of Econometrics 136, 115–130.Google Scholar
Phillips, P.C.B., Moon, R.H., & Xiao, Z. (2001) How to estimate autoregressive roots near unity. Econometric Theory 17(1), 29–69.Google Scholar
Phillips, P.C.B. & Ouliaris, S. (1990) Asymptotic properties of residual based tests for cointegration. Econometrica 58, 165–194.Google Scholar
Phillips, P.C.B., & Perron, P. (1988) Testing for unit roots in time series regression. Biometrika 75, 335–346.CrossRefGoogle Scholar
Phillips, P.C.B. & Ploberger, W. (1994) Posterior odds testing for a unit root with data-based model selection. Econometric Theory 10, 774–808.Google Scholar
Phillips, P.C.B. & Ploberger, W.. (1996) An asymptotic theory of Bayesian inference for time series. Econometrica 64, 381–412.Google Scholar
Phillips, P.C.B. & Solo, V. (1992) Asymptotics for linear processes. Annals of Statistics 20, 971–1001.Google Scholar
Pollard, D. (1991) Asymptotics for least absolute deviation regression estimators. Econometric Theory 7, 186–199.Google Scholar
Pötscher, B.M. (2002) Lower risk bounds and properties of confidence sets for ill-posted estimation problems with applications to spectral density and persistency estimation, unit roots and estimation of long memory parameters. Econometrica 70, 1035–1068.Google Scholar
Rothenberg, T. & Stock, J. (1997) Inference in a nearly integrated autoregressive model with nonnormal innovations. Journal of Econometrics 80, 269–286.CrossRefGoogle Scholar
Said, S.E. & Dickey, D.A. (1984) Testing for unit roots in autoregressive-moving average models of unknown order. Biometrika 71, 599–608.CrossRefGoogle Scholar
Sargan, J.D. & Bhargava, A. (1983) Testing residuals from least squares regression for being generated by the Gaussian random walk. Econometrica 51, 153–174.Google Scholar
Schmidt, P. & Phillips, P.C.B. (1992) Testing for a unit root in the presence of deterministic trends. Oxford Bulletin of Economics and Statistics 54, 257–288.Google Scholar
Shimotsu, K. & Phillips, P.C.B. (2005) Exact local whittle estimation of fractional integration. The Annals of Statistics 33(4), 1890–1933.Google Scholar
Shin, Y. (1994) A residual based test of the null of cointegration against the alternative of no cointegration. Econometric Theory 10, 91–115.Google Scholar
Stock, J.H. (1995) Unit roots, structural breaks and trends. In Engle, R.F. & McFadden, D. (eds.), Handbook of Econometrics, vol. 4, pp. 2739–2841. North–Holland.Google Scholar
Sul, D., Phillips, P.C.B., & Choi, C. (2005) Prewhitening Bias in HAC estimation. Oxford Bulletinof Economics and Statistics 67(4), 517–546.Google Scholar
Tanaka, K. (1996) Time Series Analysis: Nonstationary and Noninvertible Distribution Theory. Wiley.Google Scholar
Wang, Q. & Phillips, P.C.B. (2006) Asymptotic Theory for Local Time Density Estimation and Nonparametric Cointegrating Regression CFDP 1594.Google Scholar
White, J.S. (1958) The limiting distribution of the serial correlation coefficient in the explosive case. The Annals of Mathematical Statistics 29, 1188–1197.Google Scholar
Xiao, Z. (1998) A Note on Bandwidth Selection in Hypothesis Tests with Integrated Time Series, mimeo, University of Illinois.Google Scholar
Xiao, Z. (2001a) Testing the null hypothesis of stationarity against an autoregressive unit root alternative. Journal of Time Series Analysis 22(1), 87–105.Google Scholar
Xiao, Z. (2001b) Likelihood based inference in trending time series with a root near unity. Econometric Theory 17, 1082–1112.CrossRefGoogle Scholar
Xiao, Z. (2003) Bandwidth selection in testing for long range dependence. Economics Letters 78(1), 33–39.Google Scholar
Xiao, Z. & Phillips, P.C.B. (1998) An ADF coefficient test for ARMA models with unknown orders. The Econometrics Journal 1, 27–43.Google Scholar
Xiao, Z. & Phillips, P.C.B. (2002) A CUSUM test for cointegration using regression residuals. Journal of Econometrics 108, 43–61.Google Scholar
Zivot, E. & Andrews, D.W.K. (1992) Further evidence on the great crash, the oil price shock, and the unit root hypothesis. Journal of Business and Economic Statistics 10, 251–270.Google Scholar