Median unbiased forecasts for highly persistent autoregressive processes
AbstractThis 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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Bibliographic InfoArticle provided by Elsevier in its journal Journal of Econometrics.
Volume (Year): 111 (2002)
Issue (Month): 1 (November)
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Web page: http://www.elsevier.com/locate/jeconom
Other versions of this item:
- Nikolay Gospodinov, 1999. "Median Unbiased Forecasts for Highly Persistent Autoregressive Processes," Computing in Economics and Finance 1999 533, Society for Computational Economics.
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.:
- 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.
- 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.
- Peter C.B. Phillips, 1995.
"Impulse Response and Forecast Error Variance Asymptotics in Nonstationary VAR's,"
Cowles Foundation Discussion Papers
1102, Cowles Foundation for Research in Economics, Yale University.
- 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.
- Russell Davidson & James G. MacKinnon, 2001.
"Bootstrap Tests: How Many Bootstraps?,"
1036, Queen's University, Department of Economics.
- 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.
- 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.
- 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.
- Hansen,B.E., 1998.
"The grid bootstrap and the autoregressive model,"
26, Wisconsin Madison - Social Systems.
- Heimann, Günter & Kreiss, Jens-Peter, 1996. "Bootstrapping general first order autoregression," Statistics & Probability Letters, Elsevier, vol. 30(1), pages 87-98, September.
- 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.
- Hyeongwoo Kim & Nazif Durmaz, 2010.
"Bias Correction and Out-of-Sample Forecast Accuracy,"
Auburn Economics Working Paper Series
auwp2010-02, Department of Economics, Auburn University.
- Kim, Hyeongwoo & Durmaz, Nazif, 2012. "Bias correction and out-of-sample forecast accuracy," International Journal of Forecasting, Elsevier, vol. 28(3), pages 575-586.
- Kim, Hyeongwoo & Durmaz, Nazif, 2009. "Bias Correction and Out-of-Sample Forecast Accuracy," MPRA Paper 16780, University Library of Munich, Germany.
- Clements, Michael P. & Kim, Jae H., 2007. "Bootstrap prediction intervals for autoregressive time series," Computational Statistics & Data Analysis, Elsevier, vol. 51(7), pages 3580-3594, April.
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