Exactly Unbiased Estimation of First Order Autoregressive-Unit Root Models
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.
|Date of creation:||Apr 1991|
|Publication status:||Published in Econometrica (January 1993), 61(1): 139-165|
|Contact details of provider:|| Postal: Yale University, Box 208281, New Haven, CT 06520-8281 USA|
Phone: (203) 432-3702
Fax: (203) 432-6167
Web page: http://cowles.yale.edu/
More information through EDIRC
|Order Information:|| Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA|
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Sims, Christopher A & Uhlig, Harald, 1991.
"Understanding Unit Rooters: A Helicopter Tour,"
Econometric Society, vol. 59(6), pages 1591-1599, November.
- Christopher A. Sims & Harald Uhlig, 1988. "Understanding unit rooters: a helicopter tour," Discussion Paper / Institute for Empirical Macroeconomics 4, Federal Reserve Bank of Minneapolis.
- Christopher A. Sims, 1988.
"Bayesian skepticism on unit root econometrics,"
Discussion Paper / Institute for Empirical Macroeconomics
3, Federal Reserve Bank of Minneapolis.
- Tom Doan, "undated". "BAYESTST: RATS procedure to perform Bayesian Unit Root test," Statistical Software Components RTS00014, Boston College Department of Economics.
- 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.
- 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.
- Glenn D. Rudebusch, 1990.
"Trends and random walks in macroeconomic time series: a re-examination,"
Working Paper Series / Economic Activity Section
105, Board of Governors of the Federal Reserve System (U.S.).
- 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.
- Glenn D. Rudebusch, 1990. "Trends and random walks in macroeconomic time series: a re-examination," Finance and Economics Discussion Series 139, Board of Governors of the Federal Reserve System (U.S.).
- 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.
- Evans, G B A & Savin, N E, 1981. "Testing for Unit Roots: 1," Econometrica, Econometric Society, vol. 49(3), pages 753-779, May.
- 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.
- James H. Stock, 1991. "Confidence Intervals for the Largest Autoresgressive Root in U.S. Macroeconomic Time Series," NBER Technical Working Papers 0105, National Bureau of Economic Research, Inc.
- 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.
- Donald W.K. Andrews, 1986.
"Power in Econometric Applications,"
Cowles Foundation Discussion Papers
800, Cowles Foundation for Research in Economics, Yale University.
- 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.
- Alok Bhargava, 1986. "On the Theory of Testing for Unit Roots in Observed Time Series," Review of Economic Studies, Oxford University Press, vol. 53(3), pages 369-384.