Montag, 18. Oktober 2021, 16:45 - 17:45 iCal

ISOR Colloquium

"The joint limit distribution of partial maxima and partial sums of a heavy-tailed time series"

Speaker: Thomas Mikosch (University of Copenhagen)

HS 7 OMP1 (#1.303)
Oskar-Morgenstern-Platz 1, 1090 Wien


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 infinite variance. Then, roughly speaking, the maximum of a given sample and the sum have the same magnitude.

We will consider the infinite 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 difference 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)


The talk also can be joined online via ZOOM:

Meeting room opens at: October 18, 2021 4.30 pm Vienna

Meeting ID: 928 1821 6086

Password: 156890

Zur Webseite der Veranstaltung


Institut für Statistik und Operations Research


Sabine Sobotka-Tompits, BA
Fakultät für Wirtschaftswissenschaften
Institut für Statistik und Operations Research
+43 1 4277 38631