0, it can only be partly eliminated because the second-order bias term due to the initial values can only be diminished by increasing N."> 0, it can only be partly eliminated because the second-order bias term due to the initial values can only be diminished by increasing N.">
[go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/p/qed/wpaper/1300.html
   My bibliography  Save this paper

The Role Of Initial Values In Conditional Sum-of-squares Estimation Of Nonstationary Fractional Time Series Models

Author

Listed:
  • Morten Ø. Nielsen

    (Queen's University and CREATES)

  • S Johansen

    (University of Copenhagen and CREATES)

Abstract
In this paper we analyze the influence of observed and unobserved initial values on the bias of the conditional maximum likelihood or conditional sum-of-squares (CSS, or least squares) estimator of the fractional parameter, d, in a nonstationary fractional time series model. The CSS estimator is popular in empirical work due, at least in part, to its simplicity and its feasibility, even in very complicated nonstationary models.We consider a process, X_t, for which data exist from some point in time, which we call -N_0+1, but we only start observing it at a later time, t=1. The parameter (d,?,?²) is estimated by CSS based on the model ?_0^d (X_t-?)=?_t, t=N+1,…,N+T, conditional on X_1,…,X_N. We derive an expression for the second-order bias of d as a function of the initial values, X_t, t=-N_0+1,…,N, and we investigate the effect on the bias of setting aside the first N observations as initial values. We compare d with an estimator, d_c, derived similarly but by choosing ?=C. We find, both theoretically and using a data set on voting behavior, that in many cases, the estimation of the parameter ? picks up the effect of the initial values even for the choice N=0.If N_0=0, we show that the second-order bias can be completely eliminated by a simple bias correction. If, on the other hand, N_0>0, it can only be partly eliminated because the second-order bias term due to the initial values can only be diminished by increasing N.

Suggested Citation

  • Morten Ø. Nielsen & S Johansen, 2012. "The Role Of Initial Values In Conditional Sum-of-squares Estimation Of Nonstationary Fractional Time Series Models," Working Paper 1300, Economics Department, Queen's University.
    • Handle: RePEc:qed:wpaper:1300
    as

    Download full text from publisher

    File URL: https://www.econ.queensu.ca/sites/econ.queensu.ca/files/qed_wp_1300.pdf
    File Function: First version 2012
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Søren Johansen & Morten Ørregaard Nielsen, 2012. "Likelihood Inference for a Fractionally Cointegrated Vector Autoregressive Model," Econometrica, Econometric Society, vol. 80(6), pages 2667-2732, November.
    2. Morten Ørregaard Nielsen, 2015. "Asymptotics for the Conditional-Sum-of-Squares Estimator in Multivariate Fractional Time-Series Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(2), pages 154-188, March.
    3. Rolf Tschernig & Enzo Weber & Roland Weigand, 2013. "Long-Run Identification in a Fractionally Integrated System," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(4), pages 438-450, October.
    4. Johansen, Søren & Nielsen, Morten Ørregaard, 2010. "Likelihood inference for a nonstationary fractional autoregressive model," Journal of Econometrics, Elsevier, vol. 158(1), pages 51-66, September.
    5. Andrews, Donald W.K. & Lieberman, Offer & Marmer, Vadim, 2006. "Higher-order improvements of the parametric bootstrap for long-memory Gaussian processes," Journal of Econometrics, Elsevier, vol. 133(2), pages 673-702, August.
    6. Johansen, SØren, 2008. "A Representation Theory For A Class Of Vector Autoregressive Models For Fractional Processes," Econometric Theory, Cambridge University Press, vol. 24(3), pages 651-676, June.
    7. Juan J. Dolado & Jesus Gonzalo & Laura Mayoral, 2002. "A Fractional Dickey-Fuller Test for Unit Roots," Econometrica, Econometric Society, vol. 70(5), pages 1963-2006, September.
    8. David Byers & James Davidson & David Peel, 1997. "Modelling Political Popularity: an Analysis of Long‐range Dependence in Opinion Poll Series," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 160(3), pages 471-490, September.
    9. Eduardo Rossi & Paolo Santucci de Magistris, 2013. "A No‐Arbitrage Fractional Cointegration Model for Futures and Spot Daily Ranges," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 33(1), pages 77-102, January.
    Full references (including those not matched with items on IDEAS)

    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. Søren Johansen & Morten Ørregaard Nielsen, 2012. "The role of initial values in nonstationary fractional time series models," Discussion Papers 12-18, University of Copenhagen. Department of Economics.
    2. Javier Haulde & Morten Ørregaard Nielsen, 2022. "Fractional integration and cointegration," CREATES Research Papers 2022-02, Department of Economics and Business Economics, Aarhus University.
    3. Federico Carlini & Paolo Santucci de Magistris, 2019. "Resuscitating the co-fractional model of Granger (1986)," Discussion Papers 19/01, University of Nottingham, Granger Centre for Time Series Econometrics.
    4. Morten Ørregaard Nielsen & Sergei S. Shibaev, 2015. "Forecasting daily political opinion polls using the fractionally cointegrated VAR model," Working Paper 1340, Economics Department, Queen's University.
    5. Maggie E. C. Jones & Morten Ørregaard Nielsen & Michał Ksawery Popiel, 2014. "A fractionally cointegrated VAR analysis of economic voting and political support," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 47(4), pages 1078-1130, November.
    6. Alexander Boca Saravia & Gabriel Rodríguez, 2022. "Presidential approval in Peru: an empirical analysis using a fractionally cointegrated VAR," Economic Change and Restructuring, Springer, vol. 55(3), pages 1973-2010, August.
    7. Federico Carlini & Paolo Santucci de Magistris, 2019. "Resuscitating the co-fractional model of Granger (1986)," CREATES Research Papers 2019-02, Department of Economics and Business Economics, Aarhus University.
    8. Tobias Hartl & Rolf Tschernig & Enzo Weber, 2020. "Fractional trends in unobserved components models," Papers 2005.03988, arXiv.org, revised May 2020.
    9. Cavaliere, Giuseppe & Nielsen, Morten Ørregaard & Taylor, A.M. Robert, 2015. "Bootstrap score tests for fractional integration in heteroskedastic ARFIMA models, with an application to price dynamics in commodity spot and futures markets," Journal of Econometrics, Elsevier, vol. 187(2), pages 557-579.
    10. Søren Johansen & Morten Ørregaard Nielsen, 2018. "Testing the CVAR in the Fractional CVAR Model," Journal of Time Series Analysis, Wiley Blackwell, vol. 39(6), pages 836-849, November.
    11. Cavaliere, Giuseppe & Nielsen, Morten Ørregaard & Taylor, A.M. Robert, 2017. "Quasi-maximum likelihood estimation and bootstrap inference in fractional time series models with heteroskedasticity of unknown form," Journal of Econometrics, Elsevier, vol. 198(1), pages 165-188.
    12. Pérez-Rodríguez, Jorge V. & Andrada-Félix, Julián & Rachinger, Heiko, 2021. "Testing the forward volatility unbiasedness hypothesis in exchange rates under long-range dependence," The North American Journal of Economics and Finance, Elsevier, vol. 57(C).
    13. Leandro Maciel, 2020. "Technical analysis based on high and low stock prices forecasts: evidence for Brazil using a fractionally cointegrated VAR model," Empirical Economics, Springer, vol. 58(4), pages 1513-1540, April.
    14. Sepideh Dolatabadi & Paresh Kumar Narayan & Morten Ørregaard Nielsen & Ke Xu, 2018. "Economic significance of commodity return forecasts from the fractionally cointegrated VAR model," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 38(2), pages 219-242, February.
    15. Abbritti, Mirko & Carcel, Hector & Gil-Alana, Luis & Moreno, Antonio, 2023. "Term premium in a fractionally cointegrated yield curve," Journal of Banking & Finance, Elsevier, vol. 149(C).
    16. Stoupos, Nikolaos & Kiohos, Apostolos, 2022. "Euro area stock markets integration: Empirical evidence after the end of 2010 debt crisis," Finance Research Letters, Elsevier, vol. 46(PB).
    17. Monge, Manuel & Claudio-Quiroga, Gloria & Poza, Carlos, 2024. "Chinese economic behavior in times of covid-19. A new leading economic indicator based on Google trends," International Economics, Elsevier, vol. 177(C).
    18. Yuliya Lovcha & Alejandro Perez-Laborda, 2017. "Structural shocks and dynamic elasticities in a long memory model of the US gasoline retail market," Empirical Economics, Springer, vol. 53(2), pages 405-422, September.
    19. Guglielmo Maria Caporale & Luis A. Gil-Alana, 2020. "Modelling Loans to Non-Financial Corporations within the Eurozone: A Long-Memory Approach," CESifo Working Paper Series 8674, CESifo.
    20. Samet Gunay, 2018. "Fractionally Cointegrated Vector Autoregression Model: Evaluation of High/Low and Close/Open Spreads for Precious Metals," SAGE Open, , vol. 8(4), pages 21582440188, November.

    More about this item

    Keywords

    fractional integration; conditional inference; bias; Asymptotic expansion; initial values; likelihood inference;
    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

    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:qed:wpaper:1300. 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: Mark Babcock (email available below). General contact details of provider: https://edirc.repec.org/data/qedquca.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.