Regularly varying multivariate time series
Extreme values of a stationary, multivariate time series may exhibit dependence across coordinates and over time. The aim of this paper is to offer a new and potentially useful tool called tail process to describe and model such extremes. The key property is the following fact: existence of the tail process is equivalent to multivariate regular variation of finite cuts of the original process. Certain remarkable properties of the tail process are exploited to shed new light on known results on certain point processes of extremes. The theory is shown to be applicable with great ease to stationary solutions of stochastic autoregressive processes with random coefficient matrices, an interesting special case being a recently proposed factor GARCH model. In this class of models, the distribution of the tail process is calculated by a combination of analytical methods and a novel sampling algorithm.
Year of publication: |
2009
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Authors: | Basrak, Bojan ; Segers, Johan |
Published in: |
Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 119.2009, 4, p. 1055-1080
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Publisher: |
Elsevier |
Keywords: | Autoregressive process Clusters of extremes Extremal index Factor GARCH model Heavy tails Mixing Multivariate regular variation Point processes Stable random vector Stationary time series Stochastic recurrence equation Tail process Vague convergence Weak convergence |
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