The sample autocorrelation function of non-linear time series

By Bojan Basrak. 2000

52 citations recorded by the source corpus.

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Citations in the corpus

The Extremal Dependence Measure and Asymptotic Independence (2004, background): “(1) Normalization of all components by the same function means that marginal distributions are tail equivalent; that is, in Refs.”
On the foundations of multivariate heavy-tail analysis (2004, background): “A different treatment of the polar coordinate transformation is given in [1], [2], [35].”
Tail probabilities for infinite series of regularly varying random vectors (2007, methodology): “For more on multivariate regular variation, we refer to Basrak (2000) and Resnick (1987, 2006).”
Multivariate extremes, aggregation and dependence in elliptical distributions (2002, background): “FIGURE 1: The difference between (6/7r) arcsin(p/2) and (3/7r) arcsin p - (4/7r3)(arcsin p)3 as a function of p for p E [0, 1] (see the counterexample in Section 4).”
Extremal behavior of regularly varying stochastic processes (2005, background): “Before formulating regular variation for stochastic processes with sample paths in D we recall the definition (one of several equivalent definitions) of regular variation for R-valued random vectors (Basrak, 2000; Basrak, Davis and Mikosch, 2002; Lindskog, 2004; Resnick, 1987).”
REGULAR VARIATION FOR MEASURES ON METRIC SPACES (2006, background): “If Vu,S = {x ∈ R : |x| > u, x/|x| ∈ S} for u > 0 and Borel sets S ⊂ {x ∈ R : |x| = 1}, then the collection of such sets satisfying μ(∂Vu,S) = 0 form a convergence determining class (see [3]).”
Characterizations and Examples of Hidden Regular Variation (2004, unknown): “There are equivalent formulations in terms of polar coordinates (cf. Basrak, 2000, Basrak et al., 2002, Resnick, 2002b,c).”
A characterization of multivariate regular variation (2002, background): “Basrak [1] has documented several of these equivalences.”
Asymptotic properties of estimators in a stable Cox–Ingersoll–Ross model (2013, methodology): “2 in Basrak and Segers (2009), the sequence {Ik} is jointly regularly varying with index α.”