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Estimation for Autoregressive Time Series with a Root Near 1

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  • Roy, Anindya
  • Fuller, Wayne A
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    Abstract

    Estimators for the parameters of autoregressive time series are compared, emphasizing processes with a unit root or a root close to 1. The approximate bias of the sum of the autoregressive coefficients is expressed as a function of the test for a unit root. This expression is used to construct an estimator that is nearly unbiased for the parameter of the first-order scalar process. The estimator for the first-order process has a mean squared error that is about 40% of that of ordinary least squares for the process with a unit root and a constant mean, and the mean squared error is smaller than that of ordinary least squares for about half of the parameter space. The maximum loss of efficiency is 6n[superscript -1] in the remainder of the parameter space. The estimation procedure is extended to higher-order processes by modifying the estimator of the sum of the autoregressive coefficients. Limiting results are derived for the autoregressive process with a mean that is a linear trend.

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    Bibliographic Info

    Article provided by American Statistical Association in its journal Journal of Business and Economic Statistics.

    Volume (Year): 19 (2001)
    Issue (Month): 4 (October)
    Pages: 482-93

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    Handle: RePEc:bes:jnlbes:v:19:y:2001:i:4:p:482-93

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    Cited by:
    1. Mohitosh Kejriwal & Claude Lopez, 2010. "Unit Roots, Level Shifts and Trend Breaks in PerCapita Output: A Robust Evaluation," University of Cincinnati, Economics Working Papers Series 2010-02, University of Cincinnati, Department of Economics.
    2. Han, Chirok & Phillips, Peter C. B. & Sul, Donggyu, 2011. "Uniform Asymptotic Normality In Stationary And Unit Root Autoregression," Econometric Theory, Cambridge University Press, vol. 27(06), pages 1117-1151, December.
    3. Marek Jarocinski & Albert Marcet, 2011. "Autoregressions in Small Samples, Priors about Observables and Initial Conditions," CEP Discussion Papers dp1061, Centre for Economic Performance, LSE.
    4. Steve Lawford & Michalis P. Stamatogiannis, 2008. "The Finite-Sample E ects of VAR Dimensions on OLS Bias, OLS Variance, and Minimum MSE Estimators," Working Paper Series 13-08, The Rimini Centre for Economic Analysis, revised Jan 2008.
    5. Hendrik Kaufmannz & Robinson Kruse, 2013. "Bias-corrected estimation in potentially mildly explosive autoregressive models," CREATES Research Papers 2013-10, School of Economics and Management, University of Aarhus.
    6. Michael Wolf & Dan Wunderli, 2012. "Bootstrap joint prediction regions," ECON - Working Papers 064, Department of Economics - University of Zurich, revised May 2013.
    7. Jae Kim & Param Silvapulle & Rob J. Hyndman, 2006. "Half-Life Estimation based on the Bias-Corrected Bootstrap: A Highest Density Region Approach," Monash Econometrics and Business Statistics Working Papers 11/06, Monash University, Department of Econometrics and Business Statistics.

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