Semi-Heavy Tails

Omey, Edward; Gulck, Stefan Van; Vesilo, Rein

doi:10.1007/s10986-018-9417-0

Cited by 14 publications

(8 citation statements)

References 15 publications

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“…where v is a regularly varying function (see e.g. Omeya et al 2018). Recall that a positive function v is regularly varying with index ν if…”

Section: Tempered Stable Autoregressive Processesmentioning

confidence: 99%

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Tempered Stable Autoregressive Models

Niharika¹,

Kumar²

2021

Preprint

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In this article, we introduce and study a one sided tempered stable autoregressive (TAR) process. Under the assumption of stationarity of the model, the marginal probbaility density function of the error term is found. It is shown that the distribution of error is infinitely divisible. Parameter estimation of the introduced TAR process is done by adopting the conditional least square and moments based approach and the performance of the proposed methods is shown on simulated data. Our model generalize the inverse Gaussian and one-sided stable autoregressive models.

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“…where v is a regularly varying function (see e.g. Omeya et al 2018). Recall that a positive function v is regularly varying with index ν if…”

Section: Tempered Stable Autoregressive Processesmentioning

confidence: 99%

“…Semi-heavy tailed pdf are those where tails are heavier than the Gaussian and lighter than the power law, see e.g. Omeya et al (2018). It is well known that series of counts, proportions, binary outcomes or non-negative observations are some examples of non-normal real life time-series data (see Grunwald et al 1996 ).…”

Section: Introductionmentioning

confidence: 99%

Tempered Stable Autoregressive Models

Niharika¹,

Kumar²

2021

Preprint

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“…GH distributions are semi-heavy tailed, that is, the tails are thinner than any power law but heavier than any normal law. For a rigorous definition, see Omey et al (2017). An important consequence is that E(e X ) < ∞ if X follows a semi-heavy-tailed distribution.…”

Section: The Generalized Hyperbolic Modelmentioning

confidence: 99%

What is the best Lévy model for stock indices? A comparative study with a view to time consistency

Massing

2019

Financ Mark Portf Manag

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Lévy models are frequently used for asset log-returns. An important criterion is the distributional assumption on the increments. Candidates include, for example, the generalized hyperbolic, the normal inverse Gaussian, and the (skew) Student-Lévy process. We perform a comparative study for multiple equity indices of different countries using different Lévy models to determine the best fit using the Kolmogorov-Smirnov statistic, the Anderson-Darling statistic, and the Bayesian information criterion as goodness-of-fit measures. We fit Lévy models both to daily and to hourly log-returns. To date, the literature has paid little attention to the question of whether these Lévy models for daily returns also fit well at higher frequencies, that is, intraday returns, and vice versa. Eberlein and Özkan (Quant Finance 3(1):40-50, 2003) called this "time consistency." Our key finding is that there are time inconsistencies. This means that some models that fit well for daily returns, for example, the variance gamma model, fit poorly for hourly returns. We find that the Student-Lévy process is a more appropriate alternative. KeywordsStock index returns • Generalized hyperbolic distribution • Time consistency • Goodness of fit JEL Classification C58 • G15

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“…A number of interesting and important properties of distributions from these classes can be found in the book by Foss et al [19] and in the papers by Albin and Sundén [2], Beck et al [4], Cheng et al [6], Chover et al [8,9], Cline [10,11], Cui et al [12], Embrechts and Goldie [18], Klüppelberg [20], Omey et al [23], Pakes [24,25], Shimura and Watanabe [26], Watanabe [28], Watanabe and Yamamuro [29] and Xu et al [30][31][32], Yang et al [33], among others.…”

Section: Introductionmentioning

confidence: 99%

Randomly stopped minima and maxima with exponential-type distributions

Ragulina

Šiaulys

2019

NAMC

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Let {ξ1, ξ2,...} be a sequence of independent real-valued and possibly nonidentically distributed random variables. Suppose that η is a nonnegative, nondegenerate at 0 and integer-valued random variable, which is independent of {ξ1, ξ2,...}. In this paper, we consider conditions for {ξ1, ξ2,...} and η under which the distributions of the randomly stopped maxima and minima as well as randomly stopped maxima of sums and randomly stopped minima of sums belong to the class of exponential distributions.

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Semi-Heavy Tails

Cited by 14 publications

References 15 publications

Tempered Stable Autoregressive Models

Tempered Stable Autoregressive Models

What is the best Lévy model for stock indices? A comparative study with a view to time consistency

Randomly stopped minima and maxima with exponential-type distributions

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