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Joint Extremal Behavior of Hidden and Observable Time Series with an Application to GARCH Processes

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Andree Ehlert, Ulf-Rainer Fiebig, Anja Jan{ss}en, Martin Schlather

Probability · Submitted 3 Jul 2011

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We show that under suitable assumptions their concept of a tail chain as a limiting process is also applicable to our setting.

how it is stated · asserted 1.00 read the record →

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arXiv ID1107.0493 (version 3)
Pith IDNBKEFIPU, Pith's permanent record of this paper and its review
CitationAndree Ehlert, Anja Jan{\ss}en, Martin Schlather, Ulf-Rainer Fiebig. "Joint Extremal Behavior of Hidden and Observable Time Series with an Application to GARCH Processes." arXiv:1107.0493 (2011). https://pith.science/paper/NBKEFIPU
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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,842 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.29 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.92 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; .

We study the behavior of a real-valued and unobservable process (Y_t) under an extreme event of a related process (X_t) that is observable. Our analysis is motivated by the well-known GARCH model which represents two such sequences, i.e. the observable log returns of an asset as well as the hidden volatility process. Our results complement the findings of Segers (2007) and Smith (1992) for a single time series. We show that under suitable assumptions their concept of a tail chain as a limiting process is also applicable to our setting. Furthermore, we discuss existence and uniqueness of a limiting process under some weaker assumptions. Finally, we apply our results to the GARCH(1,1) case.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We study the behavior of a real-valued and unobservable process (Y_t) under an extreme event of a related process (X_t) that is observable. contribution 0.91 0.70 0.07 asserted 0.92
s1 Our analysis is motivated by the well-known GARCH model which represents two such sequences, i.e. the observable log returns of an asset as well as the hidden volatility process. background 0.98 0.08 0.04 asserted 1.00
s2 Our results complement the findings of Segers (2007) and Smith (1992) for a single time series. background 0.86 0.19 0.04 asserted 0.98
s3 We show that under suitable assumptions their concept of a tail chain as a limiting process is also applicable to our setting. result 0.90 0.91 0.49 asserted 1.00
s4 Furthermore, we discuss existence and uniqueness of a limiting process under some weaker assumptions. result 0.70 0.92 0.13 asserted 0.91
s5 Finally, we apply our results to the GARCH(1,1) case. contribution 0.71 0.92 0.08 asserted 0.96

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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  • references and citing sentences
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  • T body sentences
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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

We study the behavior of a real-valued and unobservable process (Y_t) under an extreme event of a related process (X_t) that is observable. Our analysis is motivated by the well-known GARCH model which represents two such sequences, i.e. the observable log returns of an asset as well as the hidden volatility process. Our results complement the findings of Segers (2007) and Smith (1992) for a single time series. We show that under suitable assumptions their concept of a tail chain as a limiting process is also applicable to our setting. Furthermore, we discuss existence and uniqueness of a limiting process under some weaker assumptions. Finally, we apply our results to the GARCH(1,1) case.

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