Tail probabilities for infinite series of regularly varying random vectors

By Henrik Hult, Gennady Samorodnitsky. 2007

61 citations recorded by the source corpus.

A random vector X with representation X = Sigma(j >= 0)A(j)Z(j) is considered. Here, (Z(j)) is a sequence of independent and identically distributed random vectors and (A(j)) is a sequence of random matrices, 'predictable' with respect to the sequence (Z(j)). The distribution of Z(1) is assumed to be multivariate regular varying. Moment conditions on the matrices (A(j)) are determined under which the distribution of X is regularly varying and, in fact, 'inherits' its regular variation from that of the (Z(j))'s. We compute the associated limiting measure. Examples include linear processes, random coefficient linear processes such as stochastic recurrence equations, random sums and stochastic integrals.

Subfields: Finance, Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/a750631c7770506952c0aecb319a6df13aa7fcfd

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Citations in the corpus

Regularly varying multivariate time series (2007, background): “Multivariate regular variation is a property shared by many interesting processes: linear processes with heavy-tailed innovations (Resnick and Willekens, 1991; Hult and Samorodnitsky, 2007), stationary solutions to stochastic recurrence equations with ARCH(1) and GARCH(1,1) processes as special case”