IDEAS home Printed from
   My bibliography  Save this article

Apparent Long Memory In Time Series As An Artifact Of A Time-Varying Mean: Considering Alternatives To The Fractionally Integrated Model


  • Ashley, Richard A.
  • Patterson, Douglas M.


Structural breaks and switching processes are known to induce apparent long memory in a time series. Here we show that any significant time variation in the mean renders the sample correlogram (and related spectral estimates) inconsistent. In particular, smooth time variation in the mean—i.e., even a weak trend, either stochastic or deterministic—induces apparent long memory. This apparent long memory can be eliminated by either high-pass filtering or by detrending. Here we demonstrate the effectiveness in this regard of nonlinear detrending via penalized-spline nonparametric regression. A time-varying mean can be of economic interest in its own right. This suggests that isolating out and separately examining both a local mean (i.e., a nonlinear trend or the realization of a stochastic trend) and deviations from it is preferable as a modeling strategy to simply estimating a fractionally integrated model. We illustrate the superiority of this strategy using stock return volatility data.

Suggested Citation

  • Ashley, Richard A. & Patterson, Douglas M., 2010. "Apparent Long Memory In Time Series As An Artifact Of A Time-Varying Mean: Considering Alternatives To The Fractionally Integrated Model," Macroeconomic Dynamics, Cambridge University Press, vol. 14(S1), pages 59-87, May.
  • Handle: RePEc:cup:macdyn:v:14:y:2010:i:s1:p:59-87_99

    Download full text from publisher

    File URL:
    File Function: link to article abstract page
    Download Restriction: no


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    Cited by:

    1. Douglas Patterson & Melvin Hinich & Denisa Roberts, 2018. "A Second Order Cumulant Spectrum Based Test for Strict Stationarity," Papers 1801.06727,
    2. Thanasis Stengos & Ege Yazgan & Harun Ozkan, 2016. "Persistence in Convergence: Some further results," Working Papers 1605, University of Guelph, Department of Economics and Finance.
    3. Thanasis Stengos & M. Ege Yazgan & Harun Özkan, 2018. "Persistence In Convergence And Club Formation," Bulletin of Economic Research, Wiley Blackwell, vol. 70(2), pages 119-138, April.
    4. Yazgan, M. Ege & Özkan, Harun, 2015. "Detecting structural changes using wavelets," Finance Research Letters, Elsevier, vol. 12(C), pages 23-37.
    5. Ye, Haichun & Ashley, Richard & Guerard, John, 2015. "Comparing the effectiveness of traditional vs. mechanized identification methods in post-sample forecasting for a macroeconomic Granger causality analysis," International Journal of Forecasting, Elsevier, vol. 31(2), pages 488-500.

    More about this item


    Access and download statistics


    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:cup:macdyn:v:14:y:2010:i:s1:p:59-87_99. 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: (Keith Waters). General contact details of provider: .

    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.

    We have no references for this item. You can help adding them by using 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.

    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.