Properties of Nonlinear Transformations of Fractionally Integrated Processes

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A jump diffusion model for VIX volatility options and futures (2010, background): “One must view this evidence with caution since long-memory tests are sensitive to a variety of factors such as structural breaks, outliers, regime switching and nonlinear transformations (see, for example, Diebold and Inoue, 2001; Engle and Smith, 1999; Dittmann and Granger, 2002).”
Asymptotic Properties of GARCH-X Processes (2015, background): “j=0 (d+ j) (d) (j + 1) vt j : (4)Dittmann and Granger (2002) investigated the properties of nonlinear transformations of fractionally integrated processess even if they did not consider asymptotic limts of partial sums of those series. They prove that the the Hermite polynomials of a stationary Gaus”
An empirical investigation of the usefulness of ARFIMA models for predicting macroeconomic and financial time series (2006, background): “…(1980), Granger and Joyeux (1980), Hosking (1981), Geweke and Porter-Hudak (1983), Lo (1991), Sowell (1992a,b), Ding, Granger and Engle (1993), Cheung and Diebold (1994), Robinson (1995), Engle and Smith (1999), Diebold and Inoue (2001), Breitung and Hassler (2002), and Dittman and Granger (2002).”
Long Memory and the Relation between Implied and Realized Volatility (2006, background): “yt = α+ βxt + εt (23) with εt = −βuBS t + δt+ et, where uBS t is a measurement error, et is a forecast error and δt is a linear function of the de-meaned time-varying volatility risk premium.”