IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v121y2011i4p813-844.html
   My bibliography  Save this article

Locally stationary long memory estimation

Author

Listed:
  • Roueff, François
  • von Sachs, Rainer

Abstract

There exists a wide literature on parametrically or semi-parametrically modelling strongly dependent time series using a long-memory parameter d, including more recent work on wavelet estimation. As a generalization of these latter approaches, in this work we allow the long-memory parameter d to be varying over time. We adopt a semi-parametric approach in order to avoid fitting a time-varying parametric model, such as tvARFIMA, to the observed data. We study the asymptotic behavior of a local log-regression wavelet estimator of the time-dependent d. Both simulations and a real data example complete our work on providing a fairly general approach.

Suggested Citation

  • Roueff, François & von Sachs, Rainer, 2011. "Locally stationary long memory estimation," Stochastic Processes and their Applications, Elsevier, vol. 121(4), pages 813-844, April.
    • Handle: RePEc:eee:spapps:v:121:y:2011:i:4:p:813-844
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(10)00289-9
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. F. Roueff & M. S. Taqqu, 2009. "Asymptotic normality of wavelet estimators of the memory parameter for linear processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 30(5), pages 534-558, September.
    2. Granger, Clive W. J. & Ding, Zhuanxin, 1996. "Varieties of long memory models," Journal of Econometrics, Elsevier, vol. 73(1), pages 61-77, July.
    3. Dahlhaus, Rainer & Neumann, Michael H., 2001. "Locally adaptive fitting of semiparametric models to nonstationary time series," Stochastic Processes and their Applications, Elsevier, vol. 91(2), pages 277-308, February.
    4. Dahlhaus, Rainer, 2009. "Local inference for locally stationary time series based on the empirical spectral measure," Journal of Econometrics, Elsevier, vol. 151(2), pages 101-112, August.
    5. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2003. "Modeling and Forecasting Realized Volatility," Econometrica, Econometric Society, vol. 71(2), pages 579-625, March.
    6. E. Moulines & F. Roueff & M. S. Taqqu, 2007. "On the Spectral Density of the Wavelet Coefficients of Long‐Memory Time Series with Application to the Log‐Regression Estimation of the Memory Parameter," Journal of Time Series Analysis, Wiley Blackwell, vol. 28(2), pages 155-187, March.
    7. Haldrup, Niels & Nielsen, Morten Orregaard, 2006. "A regime switching long memory model for electricity prices," Journal of Econometrics, Elsevier, vol. 135(1-2), pages 349-376.
    8. Haldrup Niels & Nielsen Morten Ø., 2006. "Directional Congestion and Regime Switching in a Long Memory Model for Electricity Prices," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 10(3), pages 1-24, September.
    9. Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, vol. 1(1), pages 83-106, June.
    10. Roueff, F. & Taqqu, M.S., 2009. "Central limit theorems for arrays of decimated linear processes," Stochastic Processes and their Applications, Elsevier, vol. 119(9), pages 3006-3041, September.
    11. Dahlhaus, R., 1996. "On the Kullback-Leibler information divergence of locally stationary processes," Stochastic Processes and their Applications, Elsevier, vol. 62(1), pages 139-168, March.
    12. Fryzlewicz, Piotr & Sapatinas, Theofanis & Subba Rao, Suhasini, 2008. "Normalized least-squares estimation in time-varying ARCH models," LSE Research Online Documents on Economics 25187, London School of Economics and Political Science, LSE Library.
    13. Faÿ, Gilles & Moulines, Eric & Roueff, François & Taqqu, Murad S., 2009. "Estimators of long-memory: Fourier versus wavelets," Journal of Econometrics, Elsevier, vol. 151(2), pages 159-177, August.
    14. Thomas Mikosch & Catalin Starica, 2004. "Changes of structure in financial time series and the GARCH model," Econometrics 0412003, University Library of Munich, Germany.
    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. Shi, Yanlin & Ho, Kin-Yip, 2015. "Long memory and regime switching: A simulation study on the Markov regime-switching ARFIMA model," Journal of Banking & Finance, Elsevier, vol. 61(S2), pages 189-204.
    2. 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.
    3. Abderrazak Ben Maatoug & Rim Lamouchi & Russell Davidson & Ibrahim Fatnassi, 2018. "Modelling Foreign Exchange Realized Volatility Using High Frequency Data: Long Memory versus Structural Breaks," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 10(1), pages 1-25, March.
    4. Frömmel, Michael & Han, Xing & Kratochvil, Stepan, 2014. "Modeling the daily electricity price volatility with realized measures," Energy Economics, Elsevier, vol. 44(C), pages 492-502.
    5. Do, Hung Xuan & Brooks, Robert & Treepongkaruna, Sirimon & Wu, Eliza, 2014. "The effects of sovereign rating drifts on financial return distributions: Evidence from the European Union," International Review of Financial Analysis, Elsevier, vol. 34(C), pages 5-20.
    6. Gregory Bauer & Keith Vorkink, 2007. "Multivariate Realized Stock Market Volatility," Staff Working Papers 07-20, Bank of Canada.
    7. Bouezmarni, Taoufik & Rombouts, Jeroen V.K., 2010. "Nonparametric density estimation for positive time series," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 245-261, February.
    8. Geoffrey Ngene & Ann Nduati Mungai & Allen K. Lynch, 2018. "Long-Term Dependency Structure and Structural Breaks: Evidence from the U.S. Sector Returns and Volatility," Review of Pacific Basin Financial Markets and Policies (RPBFMP), World Scientific Publishing Co. Pte. Ltd., vol. 21(02), pages 1-38, June.
    9. Kuswanto, Heri & Sibbertsen, Philipp, 2009. "Testing for Long Memory Against ESTAR Nonlinearities," Hannover Economic Papers (HEP) dp-427, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    10. Robinson Kruse & Christoph Wegener, 2019. "Explosive behaviour and long memory with an application to European bond yield spreads," Scottish Journal of Political Economy, Scottish Economic Society, vol. 66(1), pages 139-153, February.
    11. F. Roueff & M. S. Taqqu, 2009. "Asymptotic normality of wavelet estimators of the memory parameter for linear processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 30(5), pages 534-558, September.
    12. Jensen Mark J., 2016. "Robust estimation of nonstationary, fractionally integrated, autoregressive, stochastic volatility," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 20(4), pages 455-475, September.
    13. David McMillan & Alan Speight, 2006. "Heterogeneous information flows and intra-day volatility dynamics: evidence from the UK FTSE-100 stock index futures market," Applied Financial Economics, Taylor & Francis Journals, vol. 16(13), pages 959-972.
    14. Haldrup, Niels & Nielsen, Frank S. & Nielsen, Morten Ørregaard, 2010. "A vector autoregressive model for electricity prices subject to long memory and regime switching," Energy Economics, Elsevier, vol. 32(5), pages 1044-1058, September.
    15. Choi, Kyongwook & Yu, Wei-Choun & Zivot, Eric, 2010. "Long memory versus structural breaks in modeling and forecasting realized volatility," Journal of International Money and Finance, Elsevier, vol. 29(5), pages 857-875, September.
    16. Eduardo Rossi & Paolo Santucci de Magistris, 2014. "Estimation of Long Memory in Integrated Variance," Econometric Reviews, Taylor & Francis Journals, vol. 33(7), pages 785-814, October.
    17. Niels Haldrup & Robinson Kruse, 2014. "Discriminating between fractional integration and spurious long memory," CREATES Research Papers 2014-19, Department of Economics and Business Economics, Aarhus University.
    18. Haldrup Niels & Nielsen Morten Ø., 2006. "Directional Congestion and Regime Switching in a Long Memory Model for Electricity Prices," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 10(3), pages 1-24, September.
    19. Taylor, Nick, 2017. "Realised variance forecasting under Box-Cox transformations," International Journal of Forecasting, Elsevier, vol. 33(4), pages 770-785.
    20. Scharth, Marcel & Medeiros, Marcelo C., 2009. "Asymmetric effects and long memory in the volatility of Dow Jones stocks," International Journal of Forecasting, Elsevier, vol. 25(2), pages 304-327.

    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:eee:spapps:v:121:y:2011:i:4:p:813-844. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    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.