IDEAS home Printed from https://ideas.repec.org/p/upf/upfgen/959.html
   My bibliography  Save this paper

Minimum distance estimation of stationary and non-stationary ARFIMA processes

Author

Listed:
  • Laura Mayoral

Abstract

A new parametric minimum distance time-domain estimator for ARFIMA processes is introduced in this paper. The proposed estimator minimizes the sum of squared correlations of residuals obtained after filtering a series through ARFIMA parameters. The estimator is easy to compute and is consistent and asymptotically normally distributed for fractionally integrated (FI) processes with an integration order d strictly greater than -0.75. Therefore, it can be applied to both stationary and non-stationary processes. Deterministic components are also allowed in the DGP. Furthermore, as a by-product, the estimation procedure provides an immediate check on the adequacy of the specified model. This is so because the criterion function, when evaluated at the estimated values, coincides with the Box-Pierce goodness of fit statistic. Empirical applications and Monte-Carlo simulations supporting the analytical results and showing the good performance of the estimator in finite samples are also provided.

Suggested Citation

  • Laura Mayoral, 2006. "Minimum distance estimation of stationary and non-stationary ARFIMA processes," Economics Working Papers 959, Department of Economics and Business, Universitat Pompeu Fabra.
    • Handle: RePEc:upf:upfgen:959
    as

    Download full text from publisher

    File URL: https://econ-papers.upf.edu/papers/959.pdf
    File Function: Whole Paper
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Peter C.B. Phillips, 1999. "Discrete Fourier Transforms of Fractional Processes," Cowles Foundation Discussion Papers 1243, Cowles Foundation for Research in Economics, Yale University.
    2. Hong, Yongmiao, 1996. "Consistent Testing for Serial Correlation of Unknown Form," Econometrica, Econometric Society, vol. 64(4), pages 837-864, July.
    3. Michelacci, Claudio & Zaffaroni, Paolo, 2000. "(Fractional) beta convergence," Journal of Monetary Economics, Elsevier, vol. 45(1), pages 129-153, February.
    4. Tanaka, Katsuto, 1999. "The Nonstationary Fractional Unit Root," Econometric Theory, Cambridge University Press, vol. 15(4), pages 549-582, August.
    5. Baillie, Richard T., 1996. "Long memory processes and fractional integration in econometrics," Journal of Econometrics, Elsevier, vol. 73(1), pages 5-59, July.
    6. Juan J. Dolado & Jesús Gonzalo & Laura Mayoral, 2005. "Testing I(1) against I(d) alternatives in the presence of deteministic components," Economics Working Papers 957, Department of Economics and Business, Universitat Pompeu Fabra.
    7. Chung, C.F. & Schmidt, P., 1994. "The Minimum Distance Estimator for Fractionally Integrated ARMA Models," Papers 9408, Michigan State - Econometrics and Economic Theory.
    8. Sowell, Fallaw, 1990. "The Fractional Unit Root Distribution," Econometrica, Econometric Society, vol. 58(2), pages 495-505, March.
    9. Peter M Robinson & Carlos Velasco, 2000. "Whittle Pseudo-Maximum Likelihood Estimation for Nonstationary Time Series - (Now published in Journal of the American Statistical Association, 95, (2000), pp.1229-1243.)," STICERD - Econometrics Paper Series 391, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    10. Sowell, Fallaw, 1992. "Maximum likelihood estimation of stationary univariate fractionally integrated time series models," Journal of Econometrics, Elsevier, vol. 53(1-3), pages 165-188.
    11. Chen, Willa W. & Deo, Rohit S., 2004. "A Generalized Portmanteau Goodness-Of-Fit Test For Time Series Models," Econometric Theory, Cambridge University Press, vol. 20(2), pages 382-416, April.
    12. Hidalgo, Javier, 1999. "Bootstrap goodness-of-fit tests for farima models," DES - Working Papers. Statistics and Econometrics. WS 6324, Universidad Carlos III de Madrid. Departamento de Estadística.
    13. Tieslau, Margie A. & Schmidt, Peter & Baillie, Richard T., 1996. "A minimum distance estimator for long-memory processes," Journal of Econometrics, Elsevier, vol. 71(1-2), pages 249-264.
    14. Robinson, Peter M. & Velasco, Carlos, 2000. "Whittle pseudo-maximum likelihood estimation for nonstationary time series," LSE Research Online Documents on Economics 2273, London School of Economics and Political Science, LSE Library.
    15. Hosking, Jonathan R. M., 1996. "Asymptotic distributions of the sample mean, autocovariances, and autocorrelations of long-memory time series," Journal of Econometrics, Elsevier, vol. 73(1), pages 261-284, July.
    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. & Kapetanios, George & Papailias, Fotis, 2014. "Bandwidth selection by cross-validation for forecasting long memory financial time series," Journal of Empirical Finance, Elsevier, vol. 29(C), pages 129-143.
    2. Guglielmo Maria Caporale & Luis Gil‐Alana, 2014. "Long‐Run and Cyclical Dynamics in the US Stock Market," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 33(2), pages 147-161, March.
    3. Zevallos, Mauricio & Palma, Wilfredo, 2013. "Minimum distance estimation of ARFIMA processes," Computational Statistics & Data Analysis, Elsevier, vol. 58(C), pages 242-256.
    4. Guglielmo Caporale & Luis Gil-Alana, 2013. "Long memory in US real output per capita," Empirical Economics, Springer, vol. 44(2), pages 591-611, April.
    5. Baillie, Richard T. & Kapetanios, George & Papailias, Fotis, 2014. "Modified information criteria and selection of long memory time series models," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 116-131.
    6. Terence Tai-Leung Chong, 2007. "Estimating the Fractionally Integrated Model with a Break in the Differencing Parameter," Economics Bulletin, AccessEcon, vol. 3(67), pages 1-10.
    7. Juan F. Jimeno & Esther Moral & Lorena Saiz, 2006. "Structural breaks in labor productivity growth: the United States vs. the European Union," Working Papers 0625, Banco de España.
    8. repec:ebl:ecbull:v:3:y:2007:i:67:p:1-10 is not listed on IDEAS
    9. Beran, Jan & Ghosh, Sucharita & Schell, Dieter, 2009. "On least squares estimation for long-memory lattice processes," Journal of Multivariate Analysis, Elsevier, vol. 100(10), pages 2178-2194, November.

    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. 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.
    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. Martin, Gael M. & Nadarajah, K. & Poskitt, D.S., 2020. "Issues in the estimation of mis-specified models of fractionally integrated processes," Journal of Econometrics, Elsevier, vol. 215(2), pages 559-573.
    4. Laura Mayoral, 2006. "Further Evidence on the Statistical Properties of Real GNP," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 68(s1), pages 901-920, December.
    5. Juan J. Dolado & Jesús Gonzalo & Laura Mayoral, 2005. "What is What? A Simple Time-Domain Test of Long-memory vs. Structural Breaks," Working Papers 258, Barcelona School of Economics.
    6. Cunado, J. & Gil-Alana, L. A. & Perez de Gracia, F., 2004. "Real convergence in Taiwan: a fractionally integrated approach," Journal of Asian Economics, Elsevier, vol. 15(3), pages 529-547, June.
    7. Juan J. Dolado & Jesús Gonzalo & Laura Mayoral, 2005. "Testing I(1) against I(d) alternatives in the presence of deteministic components," Economics Working Papers 957, Department of Economics and Business, Universitat Pompeu Fabra.
    8. Laura Mayoral, 2003. "A New Minimum Distance Estimation Procedure of ARFIMA Processes," Working Papers 100, Barcelona School of Economics.
    9. Banerjee, Anindya & Urga, Giovanni, 2005. "Modelling structural breaks, long memory and stock market volatility: an overview," Journal of Econometrics, Elsevier, vol. 129(1-2), pages 1-34.
    10. Guglielmo Caporale & Luis Gil-Alana, 2013. "Long memory in US real output per capita," Empirical Economics, Springer, vol. 44(2), pages 591-611, April.
    11. Ana Pérez & Esther Ruiz, 2002. "Modelos de memoria larga para series económicas y financieras," Investigaciones Economicas, Fundación SEPI, vol. 26(3), pages 395-445, September.
    12. D. S. Poskitt, 2005. "Autoregressive Approximation in Nonstandard Situations: The Non-Invertible and Fractionally Integrated Cases," Monash Econometrics and Business Statistics Working Papers 16/05, Monash University, Department of Econometrics and Business Statistics.
    13. Juncal Cunado & Luis A. Gil-Alana & Fernando Pérez de Gracia, 2006. "Additional Empirical Evidence on Real Convergence: A Fractionally Integrated Approach," Review of World Economics (Weltwirtschaftliches Archiv), Springer;Institut für Weltwirtschaft (Kiel Institute for the World Economy), vol. 142(1), pages 67-91, April.
    14. Palandri, Alessandro, 2024. "Reconciling interest rates evidence with theory: Rejecting unit roots when the HD(1) is a competing alternative," Journal of Banking & Finance, Elsevier, vol. 161(C).
    15. Laura Mayoral, 2005. "Is the observed persistence spurious? A test for fractional integration versus short memory and structural breaks," Economics Working Papers 956, Department of Economics and Business, Universitat Pompeu Fabra.
    16. John W. Galbraith & Victoria Zinde-Walsh, 2001. "Autoregression-Based Estimators for ARFIMA Models," CIRANO Working Papers 2001s-11, CIRANO.
    17. Pestana Barros, Carlos & Gil-Alana, Luis A. & Payne, James E., 2012. "Evidence of long memory behavior in U.S. renewable energy consumption," Energy Policy, Elsevier, vol. 41(C), pages 822-826.
    18. Li, Jia & Phillips, Peter C. B. & Shi, Shuping & Yu, Jun, 2022. "Weak Identification of Long Memory with Implications for Inference," Economics and Statistics Working Papers 8-2022, Singapore Management University, School of Economics.
    19. Godfrey Madigu & Luis A. Gil‐Alana, 2021. "What do productivity indices tell us? A case study of U.S. industries," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 26(4), pages 4946-4978, October.
    20. Wright, Jonathan H., 1999. "A new estimator of the fractionally integrated stochastic volatility model," Economics Letters, Elsevier, vol. 63(3), pages 295-303, June.

    More about this item

    Keywords

    Fractional integration; nonstationary long-memory time series; minimum distance estimation;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • 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:upf:upfgen:959. 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: the person in charge (email available below). General contact details of provider: http://www.econ.upf.edu/ .

    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.