IDEAS home Printed from https://ideas.repec.org/a/eee/ecolet/v144y2016icp80-84.html
   My bibliography  Save this article

Inference on the long-memory properties of time series with non-stationary volatility

Author

Listed:
  • Demetrescu, Matei
  • Sibbertsen, Philipp

Abstract

Time-varying volatility is often present in time series data and can have adverse effects when inferring about the persistence properties of examined series. This note analyzes the effects of such nonstationarity on periodogram-based inference for the fractional integration parameter. Based on asymptotic arguments and Monte Carlo simulations, we show that the log-periodogram regression estimator remains consistent, but has asymptotic distribution whose variance depends on the variation of the volatility of the series.

Suggested Citation

  • Demetrescu, Matei & Sibbertsen, Philipp, 2016. "Inference on the long-memory properties of time series with non-stationary volatility," Economics Letters, Elsevier, vol. 144(C), pages 80-84.
    • Handle: RePEc:eee:ecolet:v:144:y:2016:i:c:p:80-84
    DOI: 10.1016/j.econlet.2016.04.034
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0165176516301446
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.econlet.2016.04.034?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
    ---><---

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

    Other versions of this item:

    References listed on IDEAS

    as
    1. Cavaliere, Giuseppe & Rahbek, Anders & Taylor, A.M. Robert, 2010. "Testing for co-integration in vector autoregressions with non-stationary volatility," Journal of Econometrics, Elsevier, vol. 158(1), pages 7-24, September.
    2. Giuseppe Cavaliere & A. M. Robert Taylor, 2008. "Time‐Transformed Unit Root Tests for Models with Non‐Stationary Volatility," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(2), pages 300-330, March.
    3. Velasco, Carlos, 2000. "Non-Gaussian Log-Periodogram Regression," Econometric Theory, Cambridge University Press, vol. 16(1), pages 44-79, February.
    4. 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.
    5. Cavaliere, Giuseppe & Taylor, A.M. Robert, 2005. "Stationarity Tests Under Time-Varying Second Moments," Econometric Theory, Cambridge University Press, vol. 21(6), pages 1112-1129, December.
    6. Clifford M. Hurvich & Rohit Deo & Julia Brodsky, 1998. "The mean squared error of Geweke and Porter‐Hudak's estimator of the memory parameter of a long‐memory time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 19(1), pages 19-46, January.
    7. Kew, Hsein & Harris, David, 2009. "Heteroskedasticity-Robust Testing For A Fractional Unit Root," Econometric Theory, Cambridge University Press, vol. 25(6), pages 1734-1753, December.
    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. Matei Demetrescu & Christoph Hanck & Robinson Kruse, 2016. "Fixed-b Inference in the Presence of Time-Varying Volatility," CREATES Research Papers 2016-01, Department of Economics and Business Economics, Aarhus University.
    2. Eroğlu, Burak Alparslan & Yiğit, Taner, 2016. "A nonparametric unit root test under nonstationary volatility," Economics Letters, Elsevier, vol. 140(C), pages 6-10.
    3. Hanck, Christoph & Demetrescu, Matei & Kruse, Robinson, 2015. "Fixed-b Asymptotics for t-Statistics in the Presence of Time-Varying Volatility," VfS Annual Conference 2015 (Muenster): Economic Development - Theory and Policy 112916, Verein für Socialpolitik / German Economic Association.

    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. 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.
    2. 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.
    3. Javier Hualde & Morten {O}rregaard Nielsen, 2022. "Fractional integration and cointegration," Papers 2211.10235, arXiv.org.
    4. Chang Sik Kim & Peter C.B. Phillips, 2006. "Log Periodogram Regression: The Nonstationary Case," Cowles Foundation Discussion Papers 1587, Cowles Foundation for Research in Economics, Yale University.
    5. Arteche, J., 2006. "Semiparametric estimation in perturbed long memory series," Computational Statistics & Data Analysis, Elsevier, vol. 51(4), pages 2118-2141, December.
    6. Boswijk, H. Peter & Cavaliere, Giuseppe & Georgiev, Iliyan & Rahbek, Anders, 2021. "Bootstrapping non-stationary stochastic volatility," Journal of Econometrics, Elsevier, vol. 224(1), pages 161-180.
    7. Mccloskey, Adam & Perron, Pierre, 2013. "Memory Parameter Estimation In The Presence Of Level Shifts And Deterministic Trends," Econometric Theory, Cambridge University Press, vol. 29(6), pages 1196-1237, December.
    8. Renzo Pardo Figueroa & Gabriel Rodríguez, 2014. "Distinguishing between True and Spurious Long Memory in the Volatility of Stock Market Returns in Latin America," Documentos de Trabajo / Working Papers 2014-395, Departamento de Economía - Pontificia Universidad Católica del Perú.
    9. Guglielmo Caporale & Luis Gil-Alana, 2013. "Long memory in US real output per capita," Empirical Economics, Springer, vol. 44(2), pages 591-611, April.
    10. Matei Demetrescu & Christoph Hanck & Robinson Kruse, 2016. "Fixed-b Inference in the Presence of Time-Varying Volatility," CREATES Research Papers 2016-01, Department of Economics and Business Economics, Aarhus University.
    11. La Spada Gabriele & Lillo Fabrizio, 2014. "The effect of round-off error on long memory processes," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 18(4), pages 1-38, September.
    12. J. Arteche, 2012. "Semiparametric Inference in Correlated Long Memory Signal Plus Noise Models," Econometric Reviews, Taylor & Francis Journals, vol. 31(4), pages 440-474.
    13. Hassler, U. & Marmol, F. & Velasco, C., 2006. "Residual log-periodogram inference for long-run relationships," Journal of Econometrics, Elsevier, vol. 130(1), pages 165-207, January.
    14. Carlos Barros & Guglielmo Maria Caporale & Luis Gil-Alana, 2014. "Long Memory in Angolan Macroeconomic Series: Mean Reversion versus Explosive Behaviour," African Development Review, African Development Bank, vol. 26(1), pages 59-73.
    15. Christoph Hanck & Robert Czudaj, 2015. "Nonstationary-volatility robust panel unit root tests and the great moderation," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 99(2), pages 161-187, April.
    16. Cavaliere, Giuseppe & Rahbek, Anders & Taylor, A.M. Robert, 2010. "Testing for co-integration in vector autoregressions with non-stationary volatility," Journal of Econometrics, Elsevier, vol. 158(1), pages 7-24, September.
    17. H. Peter Boswijk & Giuseppe Cavaliere & Luca De Angelis & A. M. Robert Taylor, 2023. "Adaptive information-based methods for determining the co-integration rank in heteroskedastic VAR models," Econometric Reviews, Taylor & Francis Journals, vol. 42(9-10), pages 725-757, November.
    18. Matei Demetrescu & Christoph Hanck, 2013. "Nonlinear IV panel unit root testing under structural breaks in the error variance," Statistical Papers, Springer, vol. 54(4), pages 1043-1066, November.
    19. Hsieh, Meng-Chen & Hurvich, Clifford M. & Soulier, Philippe, 2007. "Asymptotics for duration-driven long range dependent processes," Journal of Econometrics, Elsevier, vol. 141(2), pages 913-949, December.

    More about this item

    Keywords

    Time-varying variance; Heteroskedasticity; Persistence; Fractional integration; Modulated process;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

    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:eee:ecolet:v:144:y:2016:i:c:p:80-84. 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/locate/ecolet .

    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.