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Download the Paper (249 K, PDF file) - April 1, 2000 Tell a colleague about it. Printing Tips: Select 'print as image' in the Acrobat print dialog if you have trouble printing.

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:
Ingolf Dittmann and Clive W.J. Granger, "Properties of Nonlinear Transformations of Fractionally Integrated Processes" (April 1, 2000). Department of Economics, UCSD. Paper 2000-07.
http://repositories.cdlib.org/ucsdecon/2000-07