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Properties of nonlinear transformations of fractionally integrated processes

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  • Dittmann, Ingolf
  • Granger, Clive W. J.

Abstract

This paper shows that the properties of nonlinear transformations of a fractionally integrated process depend strongly on whether the initial series is stationary or not. Transforming a stationary Gaussian I(d) process with d > 0 leads to a long-memory process with the same or a smaller long-memory parameter depending on the Hermite rank of the transformation. Any nonlinear transformation of an antipersistent Gaussian I(d) process is I(0). For non-stationary I(d) processes, every integer power transformation is non-stationary and exhibits a deterministic trend in mean and in variance. In particular, the square of a non-stationary Gaussian I(d) process still has long memory with parameter d, whereas the square of a stationary Gaussian I(d) process shows less dependence than the initial process. Simulation results for other transformations are also discussed.

Suggested Citation

  • Dittmann, Ingolf & Granger, Clive W. J., 2000. "Properties of nonlinear transformations of fractionally integrated processes," Technical Reports 2000,25, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
  • Handle: RePEc:zbw:sfb475:200025
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    1. Diebold, Francis X. & Inoue, Atsushi, 2001. "Long memory and regime switching," Journal of Econometrics, Elsevier, vol. 105(1), pages 131-159, November.
    2. Granger, Clive W J, 1995. "Modelling Nonlinear Relationships between Extended-Memory Variables," Econometrica, Econometric Society, vol. 63(2), pages 265-279, March.
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