Authors: Dittmann, Ingolf
Granger, Clive W. J.
Title: Properties of Nonlinear Transformations of Fractionally Integrated Processes
Language (ISO): en
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.
URI: http://hdl.handle.net/2003/5030
http://dx.doi.org/10.17877/DE290R-5480
Issue Date: 2000
Publisher: Universitätsbibliothek Dortmund
Appears in Collections:Sonderforschungsbereich (SFB) 475

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