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

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

Abstract

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
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    Cited by:

    1. Douglas Patterson & Melvin Hinich & Denisa Roberts, 2018. "A Second Order Cumulant Spectrum Based Test for Strict Stationarity," Papers 1801.06727, arXiv.org.
    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.

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