IDEAS home Printed from https://ideas.repec.org/a/eee/econom/v111y2002i1p85-101.html
   My bibliography  Save this article

Median unbiased forecasts for highly persistent autoregressive processes

Author

Listed:
  • 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.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4076(02)00123-9
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    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.
    2. Paul Kabaila, 1993. "On Bootstrap Predictive Inference For Autoregressive Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 14(5), pages 473-484, September.
    3. 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.
    4. 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.
    5. 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.
    6. Stock, James H, 1996. "VAR, Error Correction and Pretest Forecasts at Long Horizons," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 58(4), pages 685-701, November.
    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. Sampson, Michael, 1991. "The Effect of Parameter Uncertainty on Forecast Variances and Confidence Intervals for Unit Root and Trend Stationary Time-Series Models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 6(1), pages 67-76, Jan.-Marc.
    11. Heimann, Günter & Kreiss, Jens-Peter, 1996. "Bootstrapping general first order autoregression," Statistics & Probability Letters, Elsevier, vol. 30(1), pages 87-98, September.
    12. 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(2), pages 238-256, April.
    13. Andrews, Donald W K, 1993. "Exactly Median-Unbiased Estimation of First Order Autoregressive/Unit Root Models," Econometrica, Econometric Society, vol. 61(1), pages 139-165, January.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. Athanasia Gavala & Nikolay Gospodinov & Deming Jiang, 2006. "Forecasting volatility," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 25(6), pages 381-400.
    3. Zi‐Yi Guo, 2021. "Out‐of‐sample performance of bias‐corrected estimators for diffusion processes," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 40(2), pages 243-268, March.
    4. 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.
    5. 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.
    6. Kim, Hyeongwoo & Durmaz, Nazif, 2012. "Bias correction and out-of-sample forecast accuracy," International Journal of Forecasting, Elsevier, vol. 28(3), pages 575-586.
    7. Kruse, Robinson & Kaufmann, Hendrik & Wegener, Christoph, 2018. "Bias-corrected estimation for speculative bubbles in stock prices," Economic Modelling, Elsevier, vol. 73(C), pages 354-364.
    8. Müller, Ulrich K. & Wang, Yulong, 2019. "Nearly weighted risk minimal unbiased estimation," Journal of Econometrics, Elsevier, vol. 209(1), pages 18-34.
    9. 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.
    10. João Henrique Gonçalves Mazzeu & Esther Ruiz & Helena Veiga, 2018. "Uncertainty And Density Forecasts Of Arma Models: Comparison Of Asymptotic, Bayesian, And Bootstrap Procedures," Journal of Economic Surveys, Wiley Blackwell, vol. 32(2), pages 388-419, April.
    11. Simionescu, Mihaela, 2017. "Prediction intervals for inflation and unemployment rate in Romania. A Bayesian approach," GLO Discussion Paper Series 82, Global Labor Organization (GLO).
    12. 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.
    13. 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.
    14. 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.
    15. Fallahi, Firouz, 2017. "Stochastic convergence in per capita energy use in world," Energy Economics, Elsevier, vol. 65(C), pages 228-239.
    16. Eric Beutner & Alexander Heinemann & Stephan Smeekes, 2017. "A Justification of Conditional Confidence Intervals," Papers 1710.00643, arXiv.org, revised Jan 2019.
    17. Stanislav Anatolyev & Nikolay Gospodinov, 2012. "Asymptotics of near unit roots (in Russian)," Quantile, Quantile, issue 10, pages 57-71, December.
    18. Gonçalves Mazzeu, Joao Henrique & Ruiz Ortega, 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Stanislav Anatolyev & Nikolay Gospodinov, 2012. "Asymptotics of near unit roots (in Russian)," Quantile, Quantile, issue 10, pages 57-71, December.
    2. Müller, Ulrich K. & Wang, Yulong, 2019. "Nearly weighted risk minimal unbiased estimation," Journal of Econometrics, Elsevier, vol. 209(1), pages 18-34.
    3. Elena Pesavento & Barbara Rossi, 2006. "Small‐sample confidence intervals for multivariate impulse response functions at long horizons," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(8), pages 1135-1155, December.
    4. John L. Turner, 2004. "Local to unity, long-horizon forecasting thresholds for model selection in the AR(1)," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 23(7), pages 513-539.
    5. Tae‐Hwan Kim & Stephen J. Leybourne & Paul Newbold, 2004. "Asymptotic mean‐squared forecast error when an autoregression with linear trend is fitted to data generated by an I(0) or I(1) process," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(4), pages 583-602, July.
    6. Helmut Lütkepohl, 2010. "Forecasting Aggregated Time Series Variables: A Survey," OECD Journal: Journal of Business Cycle Measurement and Analysis, OECD Publishing, Centre for International Research on Economic Tendency Surveys, vol. 2010(2), pages 1-26.
    7. Barbara Rossi, 2007. "Expectations hypotheses tests at Long Horizons," Econometrics Journal, Royal Economic Society, vol. 10(3), pages 554-579, November.
    8. Rossi, Barbara, 2005. "Confidence Intervals for Half-Life Deviations From Purchasing Power Parity," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 432-442, October.
    9. Donald W. K. Andrews & Patrik Guggenberger, 2014. "A Conditional-Heteroskedasticity-Robust Confidence Interval for the Autoregressive Parameter," The Review of Economics and Statistics, MIT Press, vol. 96(2), pages 376-381, May.
    10. Jonathan H. Wright, 2000. "Exact confidence intervals for impulse responses in a Gaussian vector autoregression," International Finance Discussion Papers 682, Board of Governors of the Federal Reserve System (U.S.).
    11. Andrews, Donald W.K. & Guggenberger, Patrik, 2012. "Asymptotics for LS, GLS, and feasible GLS statistics in an AR(1) model with conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 169(2), pages 196-210.
    12. Valkanov, Rossen, 1999. "The Term Structure with Highly Persistent Interest Rates," University of California at Los Angeles, Anderson Graduate School of Management qt8x91m4hg, Anderson Graduate School of Management, UCLA.
    13. Murray, Christian J. & Papell, David H., 2002. "The purchasing power parity persistence paradigm," Journal of International Economics, Elsevier, vol. 56(1), pages 1-19, January.
    14. Guillaume Chevillon, 2017. "Robust cointegration testing in the presence of weak trends, with an application to the human origin of global warming," Econometric Reviews, Taylor & Francis Journals, vol. 36(5), pages 514-545, May.
    15. Chevillon, Guillaume, 2017. "Robustness of Multistep Forecasts and Predictive Regressions at Intermediate and Long Horizons," ESSEC Working Papers WP1710, ESSEC Research Center, ESSEC Business School.
    16. Giuseppe Cavaliere & Heino Bohn Nielsen & Anders Rahbek, 2017. "On the Consistency of Bootstrap Testing for a Parameter on the Boundary of the Parameter Space," Journal of Time Series Analysis, Wiley Blackwell, vol. 38(4), pages 513-534, July.
    17. Elliott, Graham & Stock, James H., 2001. "Confidence intervals for autoregressive coefficients near one," Journal of Econometrics, Elsevier, vol. 103(1-2), pages 155-181, July.
    18. repec:hal:journl:hal-00914830 is not listed on IDEAS
    19. Serena Ng & Timothy Vogelsang, 1999. "Forecasting Dynamic Time Series in the Presence of Deterministic Components," Boston College Working Papers in Economics 445, Boston College Department of Economics.
    20. Liyu Dou & Ulrich K. Müller, 2021. "Generalized Local‐to‐Unity Models," Econometrica, Econometric Society, vol. 89(4), pages 1825-1854, July.
    21. Pesavento, Elena & Rossi, Barbara, 2007. "Impulse response confidence intervals for persistent data: What have we learned?," Journal of Economic Dynamics and Control, Elsevier, vol. 31(7), pages 2398-2412, July.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:econom:v:111:y:2002:i:1:p:85-101. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jeconom .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.