Regular variation of GARCH processes

By Bojan Basrak, Richard A. Davis, Thomas Mikosch. 2002

373 citations recorded by the source corpus.

Subfields: Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/ec14d2b27dfcbbde3dfd1dbc81e38a9e031febf2

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Citations in the corpus

Tail Risk of Multivariate Regular Variation (2011, background): “of MRV distributions can be found in [24, 25, 2, 3 ].”
Measures of serial extremal dependence and their estimation (2013, background): “[1] for GARCH(p, q) and the review paper Davis and Mikosch [13].”
Self-weighted and local quasi-maximum likelihood estimators for ARMA-GARCH/IGARCH models (2007, methodology): “When r ¼ s ¼ 1, this tail index was also obtained by Basrak et al. (2002).”
Regularly varying functions (2006, background): “The first three statements can be found in Basrak et al. [1], the last statements are due to Hult and Lindskog [26] .”
Functional large deviations for multivariate regularly varying random walks (2005, background): “random vectors [25], and it occurs in a natural way for the finite-dimensional distributions of the stationary solution to stochastic recurrence equations (see [11, 15]), including ARCH and GARCH processes; see [2] and Section 8.”
A characterization of multivariate regular variation (2002, background): “4, [7] and [15] for some special cases and see [3] for the case of general GARCH processes.”
The tail of the stationary distribution of a random coefficient AR(q) model (2004, methodology): “ V:Rq →[0,∞) be a continuous function such that V(z)=0 for |z|≥1 and R Rq V(z)dz=1. For some ǫ∈(0,1), deﬁne Kǫ ={y∈Rq :|hyi 1|≥ ǫ,|y|≤1/ǫ}, νǫ =ǫ/4 and gǫ(x)= R |y|≤1 χKǫ (x+νǫy)V(y)dy. Then gǫ :Rq → [0,1] iscontinuous, such that g ǫ(x)≤χK ǫ/4 (x) andg(x)=1−gǫ(x)≤χKc 4ǫ (x) for every x∈Rq. We can re”
Statistics of Extremes (2004, background): “Not surprisingly, their extremal properties have been thoroughly investigated (Basrak et al. 2002; Borkovec 2000; Borkovec and Klüppelberg 2003; de Haan et al. 1989; Mikosch and Stărică 2000), even for multivariate versions (Stărică 1999).”
Regularly varying multivariate time series (2007, background): “The following version for multivariate regular variation appears as Proposition A.1 in Basrak et al. (2002b).”
On some nonstationary, nonlinear random processes and their stationary approximations (2006, methodology): “We state below a state-space version of this theorem given in Basrak et al. (2002), Theorem 2.8 and Remark 2.9. Lemma 4.1 (Basrak, Davis and Mikosch (2002)) Suppose the matrices {At} and vectors bt are independent, identically distributed processes, such that E(log ‖At‖spec) < 0 and there exists an ”
Stable limits for sums of dependent infinite variance random variables (2009, background): “[5] shows that (Xt ) is regularly varying with index 2α and P(X > x) = 0.”