IDEAS home Printed from https://ideas.repec.org/p/aah/aarhec/2002-16.html
   My bibliography  Save this paper

Local Empirical Spectral Measure of Multivariate Processes with Long Range Dependence

Author

Listed:
  • Nielsen, Morten Oe.

    (Department of Economics, University of Aarhus, Denmark)

Abstract

We derive a functional central limit theorem for the empirical spectral measure or discretely averaged (integrated) periodogram of a multivariate long range dependent stochastic process in a degenerating neighborhood of the origin. We show that, under certain restrictions on the memory parameters, this local empirical spectral measure converges weakly to a Gaussian process with independent increments. Applications to narrow-band frequency domain estimation in time series regression with long range dependence, and to local (to the origin) goodness-of-fit testing are offered.

Suggested Citation

  • Nielsen, Morten Oe., "undated". "Local Empirical Spectral Measure of Multivariate Processes with Long Range Dependence," Economics Working Papers 2002-16, Department of Economics and Business Economics, Aarhus University.
    • Handle: RePEc:aah:aarhec:2002-16
    as

    Download full text from publisher

    File URL: https://repec.econ.au.dk/repec/afn/wp/02/wp02_16.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Tom Engsted & Niels Haldrup & Boriss Siliverstovs, 2004. "Long-run forecasting in multicointegrated systems," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 23(5), pages 315-335.
    2. Nielsen, Morten Orregaard, 2004. "Spectral analysis of fractionally cointegrated systems," Economics Letters, Elsevier, vol. 83(2), pages 225-231, May.
    3. Morten Ørregaard Nielsen, 2005. "Semiparametric Estimation in Time‐Series Regression with Long‐Range Dependence," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(2), pages 279-304, March.
    4. Yoshihiro Yajima, 1989. "A Central Limit Theorem Of Fourier Transforms Of Strongly Dependent Stationary Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 10(4), pages 375-383, July.
    5. Sims,Christopher A. (ed.), 1994. "Advances in Econometrics," Cambridge Books, Cambridge University Press, number 9780521444606, December.
    6. Anna Christina D'Addio & Michael Rosholm, "undated". "Labour Market Transitions of French Youth," Economics Working Papers 2002-14, Department of Economics and Business Economics, Aarhus University.
    7. Marinucci, D & Robinson, Peter M., 1998. "Semiparametric frequency domain analysis of fractional cointegration," LSE Research Online Documents on Economics 2258, London School of Economics and Political Science, LSE Library.
    8. Lobato, I. & Robinson, P. M., 1996. "Averaged periodogram estimation of long memory," Journal of Econometrics, Elsevier, vol. 73(1), pages 303-324, July.
    9. Lobato, Ignacio N., 1999. "A semiparametric two-step estimator in a multivariate long memory model," Journal of Econometrics, Elsevier, vol. 90(1), pages 129-153, May.
    10. C. W. J. Granger & Roselyne Joyeux, 1980. "An Introduction To Long‐Memory Time Series Models And Fractional Differencing," Journal of Time Series Analysis, Wiley Blackwell, vol. 1(1), pages 15-29, January.
    11. Sims,Christopher A. (ed.), 1994. "Advances in Econometrics," Cambridge Books, Cambridge University Press, number 9780521444590, December.
    12. Kokoszka, P. & Mikosch, T., 1997. "The integrated periodogram for long-memory processes with finite or infinite variance," Stochastic Processes and their Applications, Elsevier, vol. 66(1), pages 55-78, February.
    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. Qu, Zhongjun, 2011. "A Test Against Spurious Long Memory," Journal of Business & Economic Statistics, American Statistical Association, vol. 29(3), pages 423-438.
    2. Stefanos Kechagias & Vladas Pipiras, 2015. "Definitions And Representations Of Multivariate Long-Range Dependent Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(1), pages 1-25, January.

    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. Christensen, Bent Jesper & Nielsen, Morten Orregaard, 2006. "Asymptotic normality of narrow-band least squares in the stationary fractional cointegration model and volatility forecasting," Journal of Econometrics, Elsevier, vol. 133(1), pages 343-371, July.
    2. Gilles de Truchis & Elena Ivona Dumitrescu, 2019. "Narrow-band Weighted Nonlinear Least Squares Estimation of Unbalanced Cointegration Systems," EconomiX Working Papers 2019-14, University of Paris Nanterre, EconomiX.
    3. Pierre Perron & Zhongjun Qu, 2007. "An Analytical Evaluation of the Log-periodogram Estimate in the Presence of Level Shifts," Boston University - Department of Economics - Working Papers Series wp2007-044, Boston University - Department of Economics.
    4. Giraitis, Liudas & Robinson, Peter M., 1998. "Variance-type estimation of long memory," LSE Research Online Documents on Economics 2327, London School of Economics and Political Science, LSE Library.
    5. Lu, Yang K. & Perron, Pierre, 2010. "Modeling and forecasting stock return volatility using a random level shift model," Journal of Empirical Finance, Elsevier, vol. 17(1), pages 138-156, January.
    6. Jamdee, Sutthisit & Los, Cornelis A., 2007. "Long memory options: LM evidence and simulations," Research in International Business and Finance, Elsevier, vol. 21(2), pages 260-280, June.
    7. Javier Hualde & Morten {O}rregaard Nielsen, 2022. "Fractional integration and cointegration," Papers 2211.10235, arXiv.org.
    8. Kyaw, NyoNyo A. & Los, Cornelis A. & Zong, Sijing, 2006. "Persistence characteristics of Latin American financial markets," Journal of Multinational Financial Management, Elsevier, vol. 16(3), pages 269-290, July.
    9. TEYSSIERE, Gilles, 2003. "Interaction models for common long-range dependence in asset price volatilities," LIDAM Discussion Papers CORE 2003026, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    10. Hidalgo, J. & Kreiss, J.-P., 2006. "Bootstrap specification tests for linear covariance stationary processes," Journal of Econometrics, Elsevier, vol. 133(2), pages 807-839, August.
    11. Christian Leschinski & Michelle Voges & Philipp Sibbertsen, 2021. "A comparison of semiparametric tests for fractional cointegration," Statistical Papers, Springer, vol. 62(4), pages 1997-2030, August.
    12. Perron, Pierre & Qu, Zhongjun, 2010. "Long-Memory and Level Shifts in the Volatility of Stock Market Return Indices," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(2), pages 275-290.
    13. Franses,Philip Hans & Dijk,Dick van & Opschoor,Anne, 2014. "Time Series Models for Business and Economic Forecasting," Cambridge Books, Cambridge University Press, number 9780521520911, December.
    14. Morten Ørregaard Nielsen, 2005. "Semiparametric Estimation in Time‐Series Regression with Long‐Range Dependence," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(2), pages 279-304, March.
    15. Michelacci, Claudio, 2004. "Cross-sectional heterogeneity and the persistence of aggregate fluctuations," Journal of Monetary Economics, Elsevier, vol. 51(7), pages 1321-1352, October.
    16. George Kapetanios & Zacharias Psaradakis, 2007. "Semiparametric Sieve-Type GLS Inference in Regressions with Long-Range Dependence," Working Papers 587, Queen Mary University of London, School of Economics and Finance.
    17. Jonathan Wright, 2002. "Log-Periodogram Estimation Of Long Memory Volatility Dependencies With Conditionally Heavy Tailed Returns," Econometric Reviews, Taylor & Francis Journals, vol. 21(4), pages 397-417.
    18. Morten Oerregaard Nielsen, "undated". "Local Whittle Analysis of Stationary Fractional Cointegration," Economics Working Papers 2002-8, Department of Economics and Business Economics, Aarhus University.
    19. Pierre Perron & Zhongjun Qu, 2006. "An Analytical Evaluation of the Log-periodogram Estimate in the Presence of Level Shifts and its Implications for Stock Returns Volatility," Boston University - Department of Economics - Working Papers Series WP2006-016, Boston University - Department of Economics.
    20. Bent Jesper Christensen & Morten Ørregaard Nielsen, 2007. "The Effect of Long Memory in Volatility on Stock Market Fluctuations," The Review of Economics and Statistics, MIT Press, vol. 89(4), pages 684-700, November.

    More about this item

    Keywords

    Brownian Motion; Fractional ARIMA; Functional Central Limit Theorem; Goodness-of-fit Test; Integrated Periodogram; Long Memory; Narrow-band Frequency Domain Least Squares;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

    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:aah:aarhec:2002-16. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: . General contact details of provider: http://www.econ.au.dk/afn/ .

    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: (email available below). General contact details of provider: http://www.econ.au.dk/afn/ .

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.