IDEAS home Printed from https://ideas.repec.org/a/jof/jforec/v27y2008i8p690-720.html
   My bibliography  Save this article

Asymptotic prediction of mean squared error for long-memory processes with estimated parameters

Author

Listed:
  • Naoya Katayama

    (Faculty of Economics, Kyushu University, Fukuoka, Japan)

Abstract

In this paper we deal with the prediction theory of long-memory time series. The purpose is to derive a general theory of the convergence of moments of the nonlinear least squares estimator so as to evaluate the asymptotic prediction mean squared error (PMSE). The asymptotic PMSE of two predictors is evaluated. The first is defined by the estimator of the differencing parameter, while the second is defined by a fixed differencing parameter: in other words, a parametric predictor of the seasonal autoregressive integrated moving average model. The effects of misspecifying the differencing parameter is a long-memory model are clarified by the asymptotic results relating to the PMSE. The finite sample behaviour of the predictor and the model selection in terms of PMSE of the two predictors are examined using simulation, and the source of any differences in behaviour made clear in terms of asymptotic theory. Copyright © 2008 John Wiley & Sons, Ltd.

Suggested Citation

  • Naoya Katayama, 2008. "Asymptotic prediction of mean squared error for long-memory processes with estimated parameters," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 27(8), pages 690-720.
    • Handle: RePEc:jof:jforec:v:27:y:2008:i:8:p:690-720
    DOI: 10.1002/for.1078
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1002/for.1078
    File Function: Link to full text; subscription required
    Download Restriction: no
    File URL: https://libkey.io/10.1002/for.1078?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Gourieroux,Christian & Monfort,Alain, 1995. "Statistics and Econometric Models," Cambridge Books, Cambridge University Press, number 9780521471626.
    2. Tanaka, Katsuto, 1999. "The Nonstationary Fractional Unit Root," Econometric Theory, Cambridge University Press, vol. 15(4), pages 549-582, August.
    3. Tanaka, Katsuto & Maekawa, Koichi, 1984. "The sampling distributions of the predictor for an autoregressive model under misspecifications," Journal of Econometrics, Elsevier, vol. 25(3), pages 327-351, July.
    4. Hidalgo, J. & Yajima, Y., 2002. "Prediction And Signal Extraction Of Strongly Dependent Processes In The Frequency Domain," Econometric Theory, Cambridge University Press, vol. 18(3), pages 584-624, June.
    5. Taku Yamamoto, 1976. "Asymptotic Mean Square Prediction Error for an Autoregressive Model with Estimated Coefficients," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 25(2), pages 123-127, June.
    6. Chung, Ching-Fan & Baillie, Richard T, 1993. "Small Sample Bias in Conditional Sum-of-Squares Estimators of Fractionally Integrated ARMA Models," Empirical Economics, Springer, vol. 18(4), pages 791-806.
    7. YAMAMOTO, Taku, 1976. "Asymptotic mean square prediction error for an autoregressive model with estimated coefficients," LIDAM Reprints CORE 291, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    8. Katayama, Naoya, 2007. "Seasonally and Fractionally Differenced Time Series," Hitotsubashi Journal of Economics, Hitotsubashi University, vol. 48(1), pages 25-55, June.
    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. Baillie, Richard T. & Kongcharoen, Chaleampong & Kapetanios, George, 2012. "Prediction from ARFIMA models: Comparisons between MLE and semiparametric estimation procedures," International Journal of Forecasting, Elsevier, vol. 28(1), pages 46-53.

    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. 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.
    2. 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.
    3. Dmitri Koulikov, 2002. "Modeling Sequences of Long Memory Positive Weakly Stationary Random Variables," William Davidson Institute Working Papers Series 493, William Davidson Institute at the University of Michigan.
    4. 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.
    5. Greenaway-McGrevy, Ryan, 2015. "Evaluating panel data forecasts under independent realization," Journal of Multivariate Analysis, Elsevier, vol. 136(C), pages 108-125.
    6. Morten Ørregaard Nielsen & Per Houmann Frederiksen, 2005. "Finite Sample Comparison of Parametric, Semiparametric, and Wavelet Estimators of Fractional Integration," Econometric Reviews, Taylor & Francis Journals, vol. 24(4), pages 405-443.
    7. Dolado Juan J. & Gonzalo Jesus & Mayoral Laura, 2008. "Wald Tests of I(1) against I(d) Alternatives: Some New Properties and an Extension to Processes with Trending Components," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 12(4), pages 1-35, December.
    8. Haldrup, Niels & Nielsen, Morten Orregaard, 2007. "Estimation of fractional integration in the presence of data noise," Computational Statistics & Data Analysis, Elsevier, vol. 51(6), pages 3100-3114, March.
    9. Luisa Bisaglia & Silvano Bordignon, 2002. "Mean square prediction error for long-memory processes," Statistical Papers, Springer, vol. 43(2), pages 161-175, April.
    10. Daniel W. Apley & Hyun Cheol Lee, 2010. "The effects of model parameter deviations on the variance of a linearly filtered time series," Naval Research Logistics (NRL), John Wiley & Sons, vol. 57(5), pages 460-471, August.
    11. R. Bhansali, 1996. "Asymptotically efficient autoregressive model selection for multistep prediction," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 48(3), pages 577-602, September.
    12. Baillie, Richard T & Bollerslev, Tim, 1994. "Cointegration, Fractional Cointegration, and Exchange Rate Dynamics," Journal of Finance, American Finance Association, vol. 49(2), pages 737-745, June.
    13. Bo E. Honoré & Luojia Hu, 2023. "The COVID-19 pandemic and Asian American employment," Empirical Economics, Springer, vol. 64(5), pages 2053-2083, May.
    14. Georgiev, Iliyan, 2010. "Model-based asymptotic inference on the effect of infrequent large shocks on cointegrated variables," Journal of Econometrics, Elsevier, vol. 158(1), pages 37-50, September.
    15. Patrick Gagliardini & Christian Gouriéroux, 2011. "Approximate Derivative Pricing for Large Classes of Homogeneous Assets with Systematic Risk," Journal of Financial Econometrics, Oxford University Press, vol. 9(2), pages 237-280, Spring.
    16. Bergman, Mats A. & Johansson, Per & Bergman, M.A., 2002. "Large investments in the pulp and paper industry: a count data regression analysis," Journal of Forest Economics, Elsevier, vol. 8(1), pages 29-52.
    17. Luis Orea & David Roibás & Alan Wall, 2004. "Choosing the Technical Efficiency Orientation to Analyze Firms' Technology: A Model Selection Test Approach," Journal of Productivity Analysis, Springer, vol. 22(1), pages 51-71, July.
    18. Jinquan Liu & Tingguo Zheng & Jianli Sui, 2008. "Dual long memory of inflation and test of the relationship between inflation and inflation uncertainty," Psychometrika, Springer;The Psychometric Society, vol. 3(2), pages 240-254, June.
    19. Gerhard, Frank & Hess, Dieter & Pohlmeier, Winfried, 1998. "What a Difference a Day Makes: On the Common Market Microstructure of Trading Days," CoFE Discussion Papers 98/01, University of Konstanz, Center of Finance and Econometrics (CoFE).
    20. Alexandre Petkovic & David Veredas, 2009. "Aggregation of linear models for panel data," Working Papers ECARES 2009-012, ULB -- Universite Libre de Bruxelles.

    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:jof:jforec:v:27:y:2008:i:8:p:690-720. 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: Wiley-Blackwell Digital Licensing or Christopher F. Baum (email available below). General contact details of provider: http://www3.interscience.wiley.com/cgi-bin/jhome/2966 .

    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.