Properties of nonlinear transformations of fractionally integrated processes

Ingolf Dittmann and Clive Granger

No 2000,25, Technical Reports from Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen

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.

Date: 2000
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Related works:
Journal Article: Properties of nonlinear transformations of fractionally integrated processes (2002)
Working Paper: Properties of Nonlinear Transformations of Fractionally Integrated Processes (2000)
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Persistent link: https://EconPapers.repec.org/RePEc:zbw:sfb475:200025

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