Titlebook: Heavy-Tailed Time Series; Rafal Kulik,Philippe Soulier Textbook 2020 Springer Science+Business Media, LLC, part of Springer Nature 2020 Ex

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Regularly varying random variablesented here is standard. We will state certain results without proof. See Section . for references. We will apply these results to real-valued random variables with regularly varying tails. We will prove some of the most famous and useful results, such as Potter’s bounds and Breiman’s lemma.

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Concerto

Regular variation of series and random sumsly random and possibly dependent of the summands, to ensure the existence and the regular variation of the sum of the series. This will be the main result of the chapter, Theorem .. We will apply it to series with deterministic weights and random sums. The results of this chapter will be useful to s

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Convergence of clusters statistical point of view, it is important to identify these clusters in order to make inference on the extremal dependence of the time series. A very common statistical practice is, given . successive observations of the said time series, to split them into . blocks of size . (with . and .), compu

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Point process convergenceences. The point process of exceedences records the location and value of the observations over a high threshold. Its convergence to a point process is the main object of this chapter. This convergence in turn will be the starting point of the limit theorems for the partial maxima and partial sum pr

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Estimation for extremally independent time series-dimensional distributions satisfy Definition ., which we restate here under the equivalent formulation from Theorem .. Recall first that we defined the boundedness . on . which consists of sets separated from . and that we say that a Borel measure . on . is .-boundedly finite if and only if . for a

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