 Properties of Nonlinear Transformations of Fractionally Integrated ProcessesIngolf Dittmann and Clive Granger University of California at San Diego, Economics Working Paper Series from Department of Economics, UC San Diego 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. Keywords: nonlinear transformations; frationally integrated process (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:cdl:ucsdec:qt0kk9x0mc Access Statistics for this paper More papers in University of California at San Diego, Economics Working Paper Series from Department of Economics, UC San Diego Contact information at EDIRC. |
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