2017/04/20 by Anja Janßen, Janßen, Anja
Economics, Econometrics and Finance · #60G10 #60G55 #60G70 #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.1704.06179
openalex publication_date 2017/04/20 · openalex created_date 2022/08/16 · openalex updated_date 2026/07/28
A regularly varying time series as introduced in Basrak and Segers (2009) is\na (multivariate) time series such that all finite dimensional distributions are\nmultivariate regularly varying. The extremal behavior of such a process can\nthen be described by the index of regular variation and the so-called spectral\ntail process, which is the limiting distribution of the rescaled process, given\nan extreme event at time 0. As shown in Basrak and Segers (2009), the\nstationarity of the underlying time series implies a certain structure of the\nspectral tail process, informally known as the "time change formula". In this\narticle, we show that on the other hand, every process which satisfies this\nproperty is in fact the spectral tail process of an underlying stationary\nmax-stable process. The spectral tail process and the corresponding max-stable\nprocess then provide two complementary views on the extremal behavior of a\nmultivariate regularly varying stationary time series.\n