1 Department of Mathematical Sciences, Faculty of Science, Københavns Universitet2 Department of Mathematical Sciences, Faculty of Science, Københavns Universitet
We introduce the cluster index of a multivariate stationary sequence and characterize the index in terms of the spectral tail process. This index plays a major role in limit theory for partial sums of sequences. We illustrate the use of the cluster index by characterizing infinite variance stable limit distributions and precise large deviation results for sums of multivariate functions acting on a stationary Markov chain under a drift condition.
Probability Theory and Related Fields, 2014, Vol 159, p. 157-196