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Median unbiased forecasts for highly persistent autoregressive processes

  • Gospodinov, Nikolay

This paper considers the construction of median unbiased forecasts for near-integrated AR( p ) processes. It is well known that the OLS estimation in AR models produces downward biased parameter estimates. When the largest AR root is near unity, the multi-step forecast iteration leads to severe underprediction of the future value of the conditional mean. The paper derives the appropriately scaled limiting representation of the deviation of the forecast value from the true conditional mean. The asymmetry of this asymptotic representation suggests that the median unbiasedness would be a better criterion in evaluating the properties of the forecast point estimates. Furthermore, the dependence of the limiting distribution on the local-to-unity parameter precludes the use of the standard asymptotic and bootstrap methods for correcting for the bias. For this purpose, we develop a computationally convenient method that generates bootstrap samples backward in time (conditional on the last p observations) and approximates the median function of the predictive distribution on a grid of strategically chosen points around the OLS forecast. Inverting this median function yields median unbiased forecasts. The numerical results demonstrate the impartiality property of the grid MU forecasts and their good accuracy in comparison to several widely used forecasting techniques.

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Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 111 (2002)
Issue (Month): 1 (November)
Pages: 85-101

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Handle: RePEc:eee:econom:v:111:y:2002:i:1:p:85-101
Contact details of provider: Web page: http://www.elsevier.com/locate/jeconom

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  1. Albert, James H & Chib, Siddhartha, 1993. "Bayes Inference via Gibbs Sampling of Autoregressive Time Series Subject to Markov Mean and Variance Shifts," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(1), pages 1-15, January.
  2. Heimann, Günter & Kreiss, Jens-Peter, 1996. "Bootstrapping general first order autoregression," Statistics & Probability Letters, Elsevier, vol. 30(1), pages 87-98, September.
  3. Bruce E. Hansen, 1999. "The Grid Bootstrap And The Autoregressive Model," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 594-607, November.
  4. Phillips, Peter C. B., 1998. "Impulse response and forecast error variance asymptotics in nonstationary VARs," Journal of Econometrics, Elsevier, vol. 83(1-2), pages 21-56.
  5. Kemp, Gordon C.R., 1999. "The Behavior Of Forecast Errors From A Nearly Integrated Ar(1) Model As Both Sample Size And Forecast Horizon Become Large," Econometric Theory, Cambridge University Press, vol. 15(02), pages 238-256, April.
  6. Andrews, Donald W K, 1993. "Exactly Median-Unbiased Estimation of First Order Autoregressive/Unit Root Models," Econometrica, Econometric Society, vol. 61(1), pages 139-65, January.
  7. Russell Davidson & James MacKinnon, 2000. "Bootstrap tests: how many bootstraps?," Econometric Reviews, Taylor & Francis Journals, vol. 19(1), pages 55-68.
  8. 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.
  9. Donald W. K. Andrews & Moshe Buchinsky, 2000. "A Three-Step Method for Choosing the Number of Bootstrap Repetitions," Econometrica, Econometric Society, vol. 68(1), pages 23-52, January.
  10. Phillips, Peter C. B., 1979. "The sampling distribution of forecasts from a first-order autoregression," Journal of Econometrics, Elsevier, vol. 9(3), pages 241-261, February.
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