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Averaging estimators for autoregressions with a near unit root

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  • Hansen, Bruce E.

Abstract

This paper uses local-to-unity theory to evaluate the asymptotic mean-squared error (AMSE) and forecast expected squared error from least-squares estimation of an autoregressive model with a root close to unity. We investigate unconstrained estimation, estimation imposing the unit root constraint, pre-test estimation, model selection estimation, and model average estimation. We find that the asymptotic risk depends only on the local-to-unity parameter, facilitating simple graphical comparisons. Our results strongly caution against pre-testing. Strong evidence supports averaging based on Mallows weights. In particular, our Mallows averaging method has uniformly and substantially smaller risk than the conventional unconstrained estimator, and this holds for autoregressive roots far from unity. Our averaging estimator is a new approach to forecast combination.

Suggested Citation

  • Hansen, Bruce E., 2010. "Averaging estimators for autoregressions with a near unit root," Journal of Econometrics, Elsevier, vol. 158(1), pages 142-155, September.
  • Handle: RePEc:eee:econom:v:158:y:2010:i:1:p:142-155
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    Citations

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    Cited by:

    1. Tu, Yundong & Yi, Yanping, 2017. "Forecasting cointegrated nonstationary time series with time-varying variance," Journal of Econometrics, Elsevier, vol. 196(1), pages 83-98.
    2. Liu, Chu-An, 2012. "A plug-in averaging estimator for regressions with heteroskedastic errors," MPRA Paper 41414, University Library of Munich, Germany.
    3. Antonio Diez de los Rios & Maral Shamloo, 2017. "Quantitative Easing and Long-Term Yields in Small Open Economies," Staff Working Papers 17-26, Bank of Canada.
    4. Carlos A. Medel & Pablo M. Pincheira, 2016. "The out-of-sample performance of an exact median-unbiased estimator for the near-unity AR(1) model," Applied Economics Letters, Taylor & Francis Journals, vol. 23(2), pages 126-131, February.
    5. J. Isaac Miller, 2014. "Mixed-frequency Cointegrating Regressions with Parsimonious Distributed Lag Structures," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 12(3), pages 584-614.
    6. Zhang, Xinyu & Ullah, Aman & Zhao, Shangwei, 2016. "On the dominance of Mallows model averaging estimator over ordinary least squares estimator," Economics Letters, Elsevier, vol. 142(C), pages 69-73.
    7. Liu, Chu-An, 2015. "Distribution theory of the least squares averaging estimator," Journal of Econometrics, Elsevier, vol. 186(1), pages 142-159.
    8. Lu, Xun & Su, Liangjun, 2015. "Jackknife model averaging for quantile regressions," Journal of Econometrics, Elsevier, vol. 188(1), pages 40-58.
    9. Bruce E. Hansen & Jeffrey S. Racine, 2018. "Bootstrap Model Averaging Unit Root Inference," Department of Economics Working Papers 2018-09, McMaster University.
    10. Jardet, Caroline & Monfort, Alain & Pegoraro, Fulvio, 2013. "No-arbitrage Near-Cointegrated VAR(p) term structure models, term premia and GDP growth," Journal of Banking & Finance, Elsevier, vol. 37(2), pages 389-402.
    11. Gildas Lamé, 2013. "Was there a "Greenspan conundrum" in the Euro Area ?," Working Papers 2013-07, Center for Research in Economics and Statistics.

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