The limits of the ratio of partial maxima and partial sums of an iid real-valued sequence have been studied since the 1959s. The limit theory is well understand since the 1980s; see for example the monograph by Bingham, Goldie, Teugels (1987). This theory is most interesting if the marginal distribution has in nite variance. Then, roughly speaking, the maximum of a given sample and the sum have the same magnitude.
We will consider the in nite variance case and assume stationarity of the underlying sequence. We will exploit regular variation calculus for stationary sequences. It is useful for describing clusters of extremes. These represent the main di erence to the iid case. We provide results about the joint convergence of maxima and sums and, in turn, derive limit theory for their ratios. We also touch on related problems on self-normalization of partial sums such as present in sample autovoriances or
studentized sums.
Jointly with Olivier Wintenberger (Paris)
Personal Website of Thomas Mikosch
The talk also can be joined online via our ZOOM MEETING
Meeting room opens at: October 18, 2021 4.30 pm Vienna
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