IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/62552.html
   My bibliography  Save this paper

The Out-of-sample Performance of an Exact Median-Unbiased Estimator for the Near-Unity AR(1) Model

Author

Listed:
  • Medel, Carlos
  • Pincheira, Pablo

Abstract

We analyse the multihorizon forecasting performance of several strategies to estimate the stationary AR(1) model in a near-unity context. We focus on the Andrews' (1993) exact median-unbiased estimator (BC), the OLS estimator, and the driftless random walk (RW). In addition, we explore the forecasting performance of pairwise combinations between these individual strategies. We do this to investigate whether the Andrews' (1993) correction of the OLS downward bias helps in reducing mean squared forecast errors. Via simulations, we find that BC forecasts typically outperform OLS forecasts. When BC is compared to the RW we obtain mixed results, favouring the latter as the persistence of the true process increases. Interestingly, we also find that the combination of BC and RW performs well when the persistence of the process is high.

Suggested Citation

  • Medel, Carlos & Pincheira, Pablo, 2015. "The Out-of-sample Performance of an Exact Median-Unbiased Estimator for the Near-Unity AR(1) Model," MPRA Paper 62552, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:62552
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/62552/1/MPRA_paper_62552.pdf
    File Function: original version
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Kim, Jae H., 2003. "Forecasting autoregressive time series with bias-corrected parameter estimators," International Journal of Forecasting, Elsevier, vol. 19(3), pages 493-502.
    2. So, Beong Soo & Shin, Dong Wan, 1999. "Recursive mean adjustment in time-series inferences," Statistics & Probability Letters, Elsevier, vol. 43(1), pages 65-73, May.
    3. Withers, Christopher S. & Nadarajah, Saralees, 2011. "Estimates of low bias for the multivariate normal," Statistics & Probability Letters, Elsevier, vol. 81(11), pages 1635-1647, November.
    4. Andrews, Donald W K & Chen, Hong-Yuan, 1994. "Approximately Median-Unbiased Estimation of Autoregressive Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(2), pages 187-204, April.
    5. 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.
    6. Maekawa, Koichi, 1987. "Finite Sample Properties of Several Predictors From an Autoregressive Model," Econometric Theory, Cambridge University Press, vol. 3(3), pages 359-370, June.
    7. Gospodinov, Nikolay, 2002. "Median unbiased forecasts for highly persistent autoregressive processes," Journal of Econometrics, Elsevier, vol. 111(1), pages 85-101, November.
    8. Kim, Hyeongwoo & Durmaz, Nazif, 2012. "Bias correction and out-of-sample forecast accuracy," International Journal of Forecasting, Elsevier, vol. 28(3), pages 575-586.
    9. Hansen, Bruce E., 2010. "Averaging estimators for autoregressions with a near unit root," Journal of Econometrics, Elsevier, vol. 158(1), pages 142-155, September.
    10. Yu, Jun, 2012. "Bias in the estimation of the mean reversion parameter in continuous time models," Journal of Econometrics, Elsevier, vol. 169(1), pages 114-122.
    11. Roy, Anindya & Fuller, Wayne A, 2001. "Estimation for Autoregressive Time Series with a Root Near 1," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(4), pages 482-493, October.
    12. Patterson, K. D., 2000. "Bias reduction in autoregressive models," Economics Letters, Elsevier, vol. 68(2), pages 135-141, August.
    13. Orcutt, Guy H & Winokur, Herbert S, Jr, 1969. "First Order Autoregression: Inference, Estimation, and Prediction," Econometrica, Econometric Society, vol. 37(1), pages 1-14, January.
    14. Mark W. Watson & James H. Stock, 2004. "Combination forecasts of output growth in a seven-country data set," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 23(6), pages 405-430.
    15. Pablo Pincheira & Carlos Medel, 2012. "Forecasting Inflation With a Random Walk," Working Papers Central Bank of Chile 669, Central Bank of Chile.
    16. 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.
    17. Anna Mikusheva, 2007. "Uniform Inference in Autoregressive Models," Econometrica, Econometric Society, vol. 75(5), pages 1411-1452, September.
    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. Carlos Medel, 2017. "Forecasting Chilean inflation with the hybrid new keynesian Phillips curve: globalisation, combination, and accuracy," Journal Economía Chilena (The Chilean Economy), Central Bank of Chile, vol. 20(3), pages 004-050, December.
    2. Carlos A. Medel & Michael Pedersen & Pablo M. Pincheira, 2016. "The Elusive Predictive Ability of Global Inflation," International Finance, Wiley Blackwell, vol. 19(2), pages 120-146, June.
    3. Carlos A. Medel, 2016. "Un análisis de la capacidad predictiva del precio del cobre sobre la inflación global," Notas de Investigación Journal Economía Chilena (The Chilean Economy), Central Bank of Chile, vol. 19(2), pages 128-153, August.
    4. Carlos A. Medel, 2018. "Forecasting Inflation with the Hybrid New Keynesian Phillips Curve: A Compact-Scale Global VAR Approach," International Economic Journal, Taylor & Francis Journals, vol. 32(3), pages 331-371, July.
    5. Carlos Medel, 2021. "Forecasting Brazilian Inflation with the Hybrid New Keynesian Phillips Curve: Assessing the Predictive Role of Trading Partners," Working Papers Central Bank of Chile 900, Central Bank of Chile.

    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. Kim, Hyeongwoo & Durmaz, Nazif, 2012. "Bias correction and out-of-sample forecast accuracy," International Journal of Forecasting, Elsevier, vol. 28(3), pages 575-586.
    2. 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.
    3. Carlos Medel, 2017. "Forecasting Chilean inflation with the hybrid new keynesian Phillips curve: globalisation, combination, and accuracy," Journal Economía Chilena (The Chilean Economy), Central Bank of Chile, vol. 20(3), pages 004-050, December.
    4. Müller, Ulrich K. & Wang, Yulong, 2019. "Nearly weighted risk minimal unbiased estimation," Journal of Econometrics, Elsevier, vol. 209(1), pages 18-34.
    5. Giorgio Canarella & Rangan Gupta & Stephen M. Miller & Stephen K. Pollard, 2019. "Unemployment rate hysteresis and the great recession: exploring the metropolitan evidence," Empirical Economics, Springer, vol. 56(1), pages 61-79, January.
    6. 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.
    7. K. D. Patterson, 2007. "Bias Reduction through First-order Mean Correction, Bootstrapping and Recursive Mean Adjustment," Journal of Applied Statistics, Taylor & Francis Journals, vol. 34(1), pages 23-45.
    8. Carlos A. Medel, 2018. "Forecasting Inflation with the Hybrid New Keynesian Phillips Curve: A Compact-Scale Global VAR Approach," International Economic Journal, Taylor & Francis Journals, vol. 32(3), pages 331-371, July.
    9. Kim, Jae H., 2003. "Forecasting autoregressive time series with bias-corrected parameter estimators," International Journal of Forecasting, Elsevier, vol. 19(3), pages 493-502.
    10. 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.
    11. Sigrunn H. Sørbye & Pedro G. Nicolau & Håvard Rue, 2022. "Finite-sample properties of estimators for first and second order autoregressive processes," Statistical Inference for Stochastic Processes, Springer, vol. 25(3), pages 577-598, October.
    12. Kruse, Yves Robinson & Kaufmann, Hendrik, 2015. "Bias-corrected estimation in mildly explosive autoregressions," VfS Annual Conference 2015 (Muenster): Economic Development - Theory and Policy 112897, Verein für Socialpolitik / German Economic Association.
    13. Mohitosh Kejriwal & Xuewen Yu, 2019. "Generalized Forecasr Averaging in Autoregressions with a Near Unit Root," Purdue University Economics Working Papers 1318, Purdue University, Department of Economics.
    14. 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.
    15. Marcet, Albert & Jarociński, Marek, 2010. "Autoregressions in small samples, priors about observables and initial conditions," Working Paper Series 1263, European Central Bank.
    16. Falk, Barry & Roy, Anindya, 2005. "Forecasting using the trend model with autoregressive errors," International Journal of Forecasting, Elsevier, vol. 21(2), pages 291-302.
    17. Kim, Hyeongwoo & Stern, Liliana V. & Stern, Michael L., 2010. "Half-life bias correction and the G7 stock markets," Economics Letters, Elsevier, vol. 109(1), pages 1-3, October.
    18. Stanislav Anatolyev & Nikolay Gospodinov, 2012. "Asymptotics of near unit roots (in Russian)," Quantile, Quantile, issue 10, pages 57-71, December.
    19. 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.
    20. Tom Engsted & Thomas Q. Pedersen, 2014. "Bias-Correction in Vector Autoregressive Models: A Simulation Study," Econometrics, MDPI, vol. 2(1), pages 1-27, March.

    More about this item

    Keywords

    Near-unity autoregression; median-unbiased estimation; unbiasedness; unit root model; forecasting; forecast combinations;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:pra:mprapa:62552. 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: Joachim Winter (email available below). General contact details of provider: https://edirc.repec.org/data/vfmunde.html .

    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.