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Approximately Median-Unbiased Estimation of Autoregressive Models with Applications to U.S. Macroeconomic and Financial Time Series

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Abstract

This paper introduces approximately median-unbiased estimators for univariate AR(p) models with time trends. Confidence intervals also are considered. The methods are applied to the Nelson-Plosser macroeconomic data series, the extended Nelson-Plosser macroeconomic data series, and some annual stock dividend and price series. The results show that most of the series exhibit substantially greater persistence than least squares estimates and some Bayesian estimates suggest. For example, for the extended Nelson-Plosser data set, eight of the fourteen series are estimated to have a unit root, while six are estimated to be trend stationary. In contrast, the least squares estimates indicate trend stationarity for all of the series.

Suggested Citation

  • 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.
    • Handle: RePEc:cwl:cwldpp:1026
    Note: CFP 867.
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    References listed on IDEAS

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    1. Peter C.B. Phillips & Werner Ploberger, 1991. "Time Series Modelling with a Bayesian Frame of Reference: 1. Concepts and Illustrations," Cowles Foundation Discussion Papers 980, Cowles Foundation for Research in Economics, Yale University.
    2. Phillips, P C B, 1991. "Bayesian Routes and Unit Roots: De Rebus Prioribus Semper Est Disputandum," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 6(4), pages 435-473, Oct.-Dec..
    3. 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 333-364, Oct.-Dec..
    4. 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.
    5. 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.
    6. 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.
    7. Andrews, Donald W K, 1993. "Exactly Median-Unbiased Estimation of First Order Autoregressive/Unit Root Models," Econometrica, Econometric Society, vol. 61(1), pages 139-165, January.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
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    Cited by:

    1. Rodolfo Cermeño, 2007. "Median-Unbiased Estimation in Panel Data: Methodology and Applications to the GDP Convergence and Purchasing Power Parity Hypotheses," Working papers DTE 407, CIDE, División de Economía.
    2. Elliott, Graham & Stock, James H., 2001. "Confidence intervals for autoregressive coefficients near one," Journal of Econometrics, Elsevier, vol. 103(1-2), pages 155-181, July.

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