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Median unbiased forecasts for highly persistent autoregressive processes

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  • Gospodinov, Nikolay

Abstract

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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  • Gospodinov, Nikolay, 2002. "Median unbiased forecasts for highly persistent autoregressive processes," Journal of Econometrics, Elsevier, vol. 111(1), pages 85-101, November.
  • Handle: RePEc:eee:econom:v:111:y:2002:i:1:p:85-101
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    1. 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.
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    7. Heimann, Günter & Kreiss, Jens-Peter, 1996. "Bootstrapping general first order autoregression," Statistics & Probability Letters, Elsevier, vol. 30(1), pages 87-98, September.
    8. 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.
    9. 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.
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    Cited by:

    1. Fallahi, Firouz & Voia, Marcel-Cristian, 2015. "Convergence and persistence in per capita energy use among OECD countries: Revisited using confidence intervals," Energy Economics, Elsevier, vol. 52(PA), pages 246-253.
    2. Mihaela Simionescu, 2014. "Forecast Intervals for Inflation Rate and Unemployment Rate in Romania," Acta Universitatis Danubius. OEconomica, Danubius University of Galati, issue 10(5), pages 39-51, October.
    3. Fallahi, Firouz & Karimi, Mohammad & Voia, Marcel-Cristian, 2016. "Persistence in world energy consumption: Evidence from subsampling confidence intervals," Energy Economics, Elsevier, vol. 57(C), pages 175-183.
    4. Athanasia Gavala & Nikolay Gospodinov & Deming Jiang, 2006. "Forecasting volatility," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 25(6), pages 381-400.
    5. repec:eee:eneeco:v:65:y:2017:i:c:p:228-239 is not listed on IDEAS
    6. Simionescu, Mihaela, 2014. "New Strategies to Improve the Accuracy of Predictions based on Monte Carlo and Bootstrap Simulations: An Application to Bulgarian and Romanian Inflation || Nuevas estrategias para mejorar la exactitud," Revista de Métodos Cuantitativos para la Economía y la Empresa = Journal of Quantitative Methods for Economics and Business Administration, Universidad Pablo de Olavide, Department of Quantitative Methods for Economics and Business Administration, vol. 18(1), pages 112-129, December.
    7. Eric Beutner & Alexander Heinemann & Stephan Smeekes, 2017. "A Justification of Conditional Confidence Intervals," Papers 1710.00643, arXiv.org.
    8. Mihaela Simionescu, 2015. "A New Technique based on Simulations for Improving the Inflation Rate Forecasts in Romania," Working Papers of Institute for Economic Forecasting 150206, Institute for Economic Forecasting.
    9. 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.
    10. Kim, Hyeongwoo & Durmaz, Nazif, 2012. "Bias correction and out-of-sample forecast accuracy," International Journal of Forecasting, Elsevier, vol. 28(3), pages 575-586.
    11. 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.
    12. Simionescu, Mihaela, 2017. "Prediction intervals for inflation and unemployment rate in Romania. A Bayesian approach," GLO Discussion Paper Series 82, Global Labor Organization (GLO).
    13. Gonçalves Mazzeu, Joao Henrique & Ruiz, Esther & Veiga, Helena, 2015. "Model uncertainty and the forecast accuracy of ARMA models: A survey," DES - Working Papers. Statistics and Econometrics. WS ws1508, Universidad Carlos III de Madrid. Departamento de Estadística.

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