Properties of Nonlinear Transformations of Fractionally Integrated Processes
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||fractional integration, long memory, non-stationarity, nonlinearity|
|Persistent URL||dx.doi.org/10.1016/S0304-4076(02)00089-1, hdl.handle.net/1765/11356|
Dittmann, I., & Granger, C.W.J.. (2002). Properties of Nonlinear Transformations of Fractionally Integrated Processes. Journal of Econometrics, 110(2), 113–133. doi:10.1016/S0304-4076(02)00089-1