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How To Estimate Autoregressive Roots Near Unity

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  • Phillips, Peter C.B.
  • Moon, Hyungsik Roger
  • Xiao, Zhijie

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.
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Phillips, Peter C.B. & Moon, Hyungsik Roger & Xiao, Zhijie, 2001. "How To Estimate Autoregressive Roots Near Unity," Econometric Theory, Cambridge University Press, vol. 17(01), pages 29-69, February.
  • Handle: RePEc:cup:etheor:v:17:y:2001:i:01:p:29-69_17
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    References listed on IDEAS

    as
    1. Moon, Hyungsik R. & Phillips, Peter C.B., 2000. "Estimation Of Autoregressive Roots Near Unity Using Panel Data," Econometric Theory, Cambridge University Press, vol. 16(06), pages 927-997, December.
    2. Perron, Pierre & Rodriguez, Gabriel, 2003. "GLS detrending, efficient unit root tests and structural change," Journal of Econometrics, Elsevier, vol. 115(1), pages 1-27, July.
    3. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    4. Park, Joon Y. & Phillips, Peter C.B., 1988. "Statistical Inference in Regressions with Integrated Processes: Part 1," Econometric Theory, Cambridge University Press, vol. 4(03), pages 468-497, December.
    5. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    6. Peter C.B. Phillips & Victor Solo, 1989. "Asymptotics for Linear Processes," Cowles Foundation Discussion Papers 932, Cowles Foundation for Research in Economics, Yale University.
    7. Johansen, Soren, 1991. "Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models," Econometrica, Econometric Society, vol. 59(6), pages 1551-1580, November.
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    Cited by:

    1. Moon, Hyungsik R. & Phillips, Peter C.B., 2000. "Estimation Of Autoregressive Roots Near Unity Using Panel Data," Econometric Theory, Cambridge University Press, vol. 16(06), pages 927-997, December.
    2. repec:eee:econom:v:201:y:2017:i:2:p:400-416 is not listed on IDEAS
    3. Chevillon, Guillaume, 2007. "Inference in the Presence of Stochastic and Deterministic Trends," ESSEC Working Papers DR 07021, ESSEC Research Center, ESSEC Business School.
    4. Sophocles N. Brissimis & Petros M. Migiakis, 2016. "Inflation persistence, learning dynamics and the rationality of inflation expectations," Empirical Economics, Springer, vol. 51(3), pages 963-979, November.
    5. Peter Phillips & Hyungsik Moon, 2000. "Nonstationary panel data analysis: an overview of some recent developments," Econometric Reviews, Taylor & Francis Journals, vol. 19(3), pages 263-286.
    6. Charlotte S. Hansen & Bjorn E. Tuypens, 2004. "Long-Run Regressions: Theory and Application to US Asset Markets," Finance 0410018, EconWPA.
    7. Moon, Hyungsik R & Phillips, Peter C B, 1999. " Maximum Likelihood Estimation in Panels with Incidental Trends," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 61(0), pages 711-747, Special I.
    8. repec:eee:intfin:v:50:y:2017:i:c:p:36-51 is not listed on IDEAS
    9. Baharumshah, Ahmad Zubaidi & Soon, Siew-Voon & Hamzah, Nor Aishah, 2013. "Parity reversion in real interest rate in the Asian countries: Further evidence based on local-persistent model," Economic Modelling, Elsevier, vol. 35(C), pages 634-642.
    10. H. Peter Boswijk, 2001. "Block Local to Unity and Continuous Record Asymptotics," Tinbergen Institute Discussion Papers 01-078/4, Tinbergen Institute.
    11. Kim, Soyoung & Lima, Luiz Renato, 2010. "Local persistence and the PPP hypothesis," Journal of International Money and Finance, Elsevier, vol. 29(3), pages 555-569, April.
    12. Issler, João Victor & Lima, Luiz Renato, 2009. "A panel data approach to economic forecasting: The bias-corrected average forecast," Journal of Econometrics, Elsevier, vol. 152(2), pages 153-164, October.
    13. Peter C. B. Phillips, 2003. "Laws and Limits of Econometrics," Economic Journal, Royal Economic Society, vol. 113(486), pages 26-52, March.
    14. Frühwirth, Manfred & Sögner, Leopold, 2015. "Weather and SAD related mood effects on the financial market," The Quarterly Review of Economics and Finance, Elsevier, vol. 57(C), pages 11-31.
    15. Baharumshah, Ahmad Zubaidi & Soon, Siew-Voon & Lau, Evan, 2017. "Fiscal sustainability in an emerging market economy: When does public debt turn bad?," Journal of Policy Modeling, Elsevier, vol. 39(1), pages 99-113.
    16. Dimitris A. Georgoutsos & Petros Migiakis, 2010. "European sovereign bond spreads: monetary unification, market conditions and financial integration," Working Papers 115, Bank of Greece.
    17. 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.).
    18. Baharumshah, Ahmad Zubaidi & Soon, Siew-Voon & Boršič, Darja, 2013. "Real interest parity in Central and Eastern European countries: Evidence on integration into EU and the US markets," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 25(C), pages 163-180.
    19. Lima, Luiz Renato & Xiao, Zhijie, 2007. "Do shocks last forever? Local persistency in economic time series," Journal of Macroeconomics, Elsevier, vol. 29(1), pages 103-122, March.

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