IDEAS home Printed from https://ideas.repec.org/p/cwl/cwldpp/975.html
   My bibliography  Save this paper

Exactly Unbiased Estimation of First Order Autoregressive-Unit Root Models

Author

Abstract

This paper is concerned with the estimation of first-order autoregressive/unit root models with independent identically distributed normal errors. The models considered include those without an intercept, those with an intercept, and those with an intercept and time trend. The autoregressive (AR) parameter alpha is allowed to lie in the interval (-1,1], which includes the case of a unit root. Exactly median-unbiased estimators of the AR parameter alpha are proposed. Exact confidence intervals for this parameter are introduced. Corresponding exactly median-unbiased estimators and exact confidence intervals are also provided for the impulse response function and the cumulative impulse response. An unbiased model selection procedure is discussed. The procedures that are introduced are applied to several data series including real exchange rates, the velocity of money, and industrial production.

Suggested Citation

  • Donald W.K. Andrews, 1991. "Exactly Unbiased Estimation of First Order Autoregressive-Unit Root Models," Cowles Foundation Discussion Papers 975, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:975
    Note: CFP 832.
    as

    Download full text from publisher

    File URL: https://cowles.yale.edu/sites/default/files/files/pub/d09/d0975.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Sims, Christopher A., 1988. "Bayesian skepticism on unit root econometrics," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 463-474.
    2. Sims, Christopher A & Uhlig, Harald, 1991. "Understanding Unit Rooters: A Helicopter Tour," Econometrica, Econometric Society, vol. 59(6), pages 1591-1599, November.
    3. Andrews, Donald W K, 1989. "Power in Econometric Applications," Econometrica, Econometric Society, vol. 57(5), pages 1059-1090, September.
    4. Alok Bhargava, 1986. "On the Theory of Testing for Unit Roots in Observed Time Series," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(3), pages 369-384.
    5. Rudebusch, Glenn D, 1992. "Trends and Random Walks in Macroeconomic Time Series: A Re-examination," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 33(3), pages 661-680, August.
    6. Schotman, Peter & van Dijk, Herman K., 1991. "A Bayesian analysis of the unit root in real exchange rates," Journal of Econometrics, Elsevier, vol. 49(1-2), pages 195-238.
    7. Stock, James H., 1991. "Confidence intervals for the largest autoregressive root in U.S. macroeconomic time series," Journal of Monetary Economics, Elsevier, vol. 28(3), pages 435-459, December.
    8. Orcutt, Guy H & Winokur, Herbert S, Jr, 1969. "First Order Autoregression: Inference, Estimation, and Prediction," Econometrica, Econometric Society, vol. 37(1), pages 1-14, January.
    9. 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.
    10. DeJong, David N. & Whiteman, Charles H., 1991. "Reconsidering 'trends and random walks in macroeconomic time series'," Journal of Monetary Economics, Elsevier, vol. 28(2), pages 221-254, October.
    11. Phillips, Peter C B, 1977. "Approximations to Some Finite Sample Distributions Associated with a First-Order Stochastic Difference Equation," Econometrica, Econometric Society, vol. 45(2), pages 463-485, March.
    12. Donald W.K. Andrews & Peter C.B. Phillips, 1986. "Best Median Unbiased Estimation in Linear Regression with Bounded Asymmetric Loss Functions," Cowles Foundation Discussion Papers 786, Cowles Foundation for Research in Economics, Yale University.
    13. Evans, G B A & Savin, N E, 1981. "Testing for Unit Roots: 1," Econometrica, Econometric Society, vol. 49(3), pages 753-779, May.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Christopher A. Sims, 1993. "A Nine-Variable Probabilistic Macroeconomic Forecasting Model," NBER Chapters, in: Business Cycles, Indicators, and Forecasting, pages 179-212, National Bureau of Economic Research, Inc.
    2. Donald W.K. Andrews & Hong-Yuan Chen, 1992. "Approximately Median-Unbiased Estimation of Autoregressive Models with Applications to U.S. Macroeconomic and Financial Time Series," Cowles Foundation Discussion Papers 1026, Cowles Foundation for Research in Economics, Yale University.
    3. Stock, James H., 1991. "Confidence intervals for the largest autoregressive root in U.S. macroeconomic time series," Journal of Monetary Economics, Elsevier, vol. 28(3), pages 435-459, December.
    4. Peter C.B.Phillips & Donggyu Sul, 2002. "Dynamic Panel Estimation and Homogeneity Testing Under Cross Section Dependence," Cowles Foundation Discussion Papers 1362, Cowles Foundation for Research in Economics, Yale University.
    5. Klaus Neusser, 1993. "Dynamics of Total Factor Productivities," Revue Économique, Programme National Persée, vol. 44(2), pages 389-418.
    6. Chortareas, Georgios & Kapetanios, George, 2009. "Getting PPP right: Identifying mean-reverting real exchange rates in panels," Journal of Banking & Finance, Elsevier, vol. 33(2), pages 390-404, February.
    7. Ray C. Fair, 1992. "Estimates of the Bias of Lagged Dependent Variable Coefficient Estimates in Macroeconomic Equations," Cowles Foundation Discussion Papers 1005, Cowles Foundation for Research in Economics, Yale University.
    8. Chortareas, Georgios & Kapetanios, George, 2009. "Getting PPP right: Identifying mean-reverting real exchange rates in panels," Journal of Banking & Finance, Elsevier, vol. 33(2), pages 390-404, February.
    9. Chen, Shyh-Wei & Shen, Chung-Hua, 2015. "Revisiting the Feldstein–Horioka puzzle with regime switching: New evidence from European countries," Economic Modelling, Elsevier, vol. 49(C), pages 260-269.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Marcet, Albert & Jarociński, Marek, 2010. "Autoregressions in small samples, priors about observables and initial conditions," Working Paper Series 1263, European Central Bank.
    3. Chaturvedi, Anoop & Kumar, Jitendra, 2005. "Bayesian unit root test for model with maintained trend," Statistics & Probability Letters, Elsevier, vol. 74(2), pages 109-115, September.
    4. Francis W. Ahking, 2002. "Is the Bayesian Approach Necessarily Better than the Classical Approach in Unit-Root Test?," Working papers 2002-18, University of Connecticut, Department of Economics.
    5. Marriott, John & Newbold, Paul, 2000. "The strength of evidence for unit autoregressive roots and structural breaks: A Bayesian perspective," Journal of Econometrics, Elsevier, vol. 98(1), pages 1-25, September.
    6. Koop, Gary & Steel, Mark F J, 1994. "A Decision-Theoretic Analysis of the Unit-Root Hypothesis Using Mixtures of Elliptical Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(1), pages 95-107, January.
    7. Magris Martin & Iosifidis Alexandros, 2021. "Approximate Bayes factors for unit root testing," Papers 2102.10048, arXiv.org, revised Feb 2021.
    8. Loukia Meligkotsidou & Elias Tzavalis & Ioannis D. Vrontos, 2004. "A Bayesian Analysis of Unit Roots and Structural Breaks in the Level and the Error Variance of Autoregressive Models," Working Papers 514, Queen Mary University of London, School of Economics and Finance.
    9. Jae H. Kim & In Choi, 2017. "Unit Roots in Economic and Financial Time Series: A Re-Evaluation at the Decision-Based Significance Levels," Econometrics, MDPI, vol. 5(3), pages 1-23, September.
    10. Donald W.K. Andrews & Hong-Yuan Chen, 1992. "Approximately Median-Unbiased Estimation of Autoregressive Models with Applications to U.S. Macroeconomic and Financial Time Series," Cowles Foundation Discussion Papers 1026, Cowles Foundation for Research in Economics, Yale University.
    11. Geweke, John, 1994. "Priors for Macroeconomic Time Series and Their Application," Econometric Theory, Cambridge University Press, vol. 10(3-4), pages 609-632, August.
    12. Razvan Pascalau, 2010. "Unit root tests with smooth breaks: an application to the Nelson-Plosser data set," Applied Economics Letters, Taylor & Francis Journals, vol. 17(6), pages 565-570.
    13. Philip A. Shively, 2001. "Trend-stationary GNP: evidence from a new exact pointwise most powerful invariant unit root test," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 16(4), pages 537-551.
    14. Vosseler, Alexander, 2016. "Bayesian model selection for unit root testing with multiple structural breaks," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 616-630.
    15. Falk, Barry, 1999. "Fitting autoregressive trend stationary models with finite samples," International Journal of Forecasting, Elsevier, vol. 15(1), pages 11-25, February.
    16. N. Vijayamohanan Pillai, 2010. "Electricity Demand Analysis and Forecasting- The Tradition is Questioned," Working Papers id:2966, eSocialSciences.
    17. Charley Xia and William Griffiths, 2012. "Bayesian Unit Root Testing: The Effect Of Choice Of Prior On Test Outcomes," Department of Economics - Working Papers Series 1152, The University of Melbourne.
    18. Lieberman, Offer & Phillips, Peter C.B., 2020. "Hybrid stochastic local unit roots," Journal of Econometrics, Elsevier, vol. 215(1), pages 257-285.
    19. Müller, Ulrich K. & Wang, Yulong, 2019. "Nearly weighted risk minimal unbiased estimation," Journal of Econometrics, Elsevier, vol. 209(1), pages 18-34.
    20. Kleijn, R.H. & van Dijk, H.K., 2001. "A Bayesian analysis of the PPP puzzle using an unobserved components model," Econometric Institute Research Papers EI 2001-35, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.

    More about this item

    Keywords

    Autoregressive process; confidence interval; time trend; model selection; unit roots;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:cwl:cwldpp:975. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Brittany Ladd (email available below). General contact details of provider: https://edirc.repec.org/data/cowleus.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.