Testing for long memory in the presence of a general trend

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Structural breaks in time series (2013, methodology): “: This rescaled variance statistic was considered by (Giraitis et al., 2001, 2003).”
An Analytical Evaluation of the Log-periodogram Estimate in the Presence of Level Shifts (2006, methodology): “We then evaluate ΛT,j as defined by (8).”
On discriminating between long-range dependence and changes in mean (2006, background): “That research was elaborated on by Giraitis, Kokoszka and Leipus [16] who showed that several statistics akin to the modified R/S statistic of Lo [31] diverge to infinity under either long-range dependence or weak dependence with change-points.”
Empirical Process of the Squared Residuals of an ARCH Sequence (2001, background): “Following Giraitis et al. (2000) we also assume that E" 4 0 <1(1.7) and E" 4 0 1=2 X 1 j p bj < 1:(1.8) If condition (1.8) is satis ed, then the ARCH equations above have a unique strictly stationary solution such that Ey4k <1 and the squares y2k have a Volterra representation y 2 k = 1X l=0 pX…”
Rescaled variance and related tests for long memory in volatility and levels (2003, unknown): “10 of Gourieroux and Monfort (1997). The second example concerns the so-called linear ARCH (∞) or LARCH (∞) process, introduced by Robinson (1991).”