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A study of fractionally integrated time series using descriptive methods

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  • Steven P. Clark
  • T. Daniel Coggin
Abstract
We demonstrate the use of some descriptive methods for nonstationary time series to better understand the sample path behaviours of fractionally integrated processes for a range of different fractional orders of integration. We are particularly interested in better understanding the behaviours of $$I(d)$$I(d) series when $$d \in [1/2,1)$$d∈[1/2,1) . In fact, we will point out that there is considerable disagreement in the literature when it comes to describing such processes, and we show that descriptive methods can be useful tools for better understanding their sample path properties. We also present an empirical example to compare conclusions from some of the descriptive methods and inference from two state-of-the-art estimators for fractional orders of integration.

Suggested Citation

  • Steven P. Clark & T. Daniel Coggin, 2018. "A study of fractionally integrated time series using descriptive methods," Applied Economics, Taylor & Francis Journals, vol. 50(2), pages 172-186, January.
    • Handle: RePEc:taf:applec:v:50:y:2018:i:2:p:172-186
    DOI: 10.1080/00036846.2017.1321839
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    References listed on IDEAS

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    1. Gil-Alana, L. A. & Robinson, P. M., 1997. "Testing of unit root and other nonstationary hypotheses in macroeconomic time series," Journal of Econometrics, Elsevier, vol. 80(2), pages 241-268, October.
    2. Peter C.B. Phillips & Joon Y. Park, 1998. "Nonstationary Density Estimation and Kernel Autoregression," Cowles Foundation Discussion Papers 1181, Cowles Foundation for Research in Economics, Yale University.
    3. Peter C. B. Phillips, 2001. "Descriptive econometrics for non-stationary time series with empirical illustrations," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 16(3), pages 389-413.
    4. Marinucci, D. & Robinson, P. M., 2000. "Weak convergence of multivariate fractional processes," Stochastic Processes and their Applications, Elsevier, vol. 86(1), pages 103-120, March.
    5. Shimotsu, Katsumi & Phillips, Peter C.B., 2006. "Local Whittle estimation of fractional integration and some of its variants," Journal of Econometrics, Elsevier, vol. 130(2), pages 209-233, February.
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