Tukey-Type Distributions in the Context of Financial Data

Fischer, Matthias; Horn, Armin; Klein, Ingo

doi:10.1080/03610920500476382

Cited by 19 publications

(10 citation statements)

References 15 publications

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“…We mention, the family of the -Stable distributions (Rachev and Mittnik, 2000), the skew t-Student distribution (Jones and Faddy, 2003;Theodossiou, 1998), the normal inverse Gaussian (BarndorffNielsen, 1997), the power exponential distribution (Töyli et al, 2002), the betatype distributions (McDonald and Xu, 1995), the Tukey-type distributions (Fischer et al, 2007), and many others discussed, for instance, in Kleiber and Kotz (2003). The choice among these is usually a matter of analytical and numerical tractability.…”

Section: Characteristics Of the Marginal Distributionsmentioning

confidence: 98%

Statistical Modeling of Temporal Dependence in Financial Data via a Copula Function

Domma

Giordano

Perri

2009

Communications in Statistics - Simulation and Computation

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In financial analysis it is useful to study the dependence between two or more time series as well as the temporal dependence in a univariate time series. This article is concerned with the statistical modeling of the dependence structure in a univariate financial time series using the concept of copula. We treat the series of financial returns as a first order Markov process. The Archimedean two-parameter BB7 copula is adopted to describe the underlying dependence structure between two consecutive returns, while the log-Dagum distribution is employed to model the margins marked by skewness and kurtosis. A simulation study is carried out to evaluate the performance of the maximum likelihood estimates. Furthermore, we apply the model to the daily returns of four stocks and, finally, we illustrate how its fitting to data can be improved when the dependence between consecutive returns is described through a copula function.

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Section: Characteristics Of the Marginal Distributionsmentioning

confidence: 98%

Statistical Modeling of Temporal Dependence in Financial Data via a Copula Function

Domma

Giordano

Perri

2009

Communications in Statistics - Simulation and Computation

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“…On the other hand, in symmetric cases, g ‐and‐ h and sinh‐arcsinh distributions have interestingly different tail behaviour. For variations on the g ‐and‐ h approach, see Rayner & MacGillivray , Fischer et al , and the many references therein. For other transformation forms applied to g = φ , see Shore .…”

Section: The Menu: Four (Or Five) Main Familiesmentioning

confidence: 99%

On Families of Distributions with Shape Parameters

Jones

2014

Int Statistical Rev

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Univariate continuous distributions are one of the fundamental components on which statistical modelling, ancient and modern, frequentist and Bayesian, multi-dimensional and complex, is based. In this article, I review and compare some of the main general techniques for providing families of typically unimodal distributions on R with one or two, or possibly even three, shape parameters, controlling skewness and/or tailweight, in addition to their all-important location and scale parameters. One important and useful family is comprised of the 'skew-symmetric' distributions brought to prominence by Azzalini. As these are covered in considerable detail elsewhere in the literature, I focus more on their complements and competitors. Principal among these are distributions formed by transforming random variables, by what I call 'transformation of scale'-including two-piece distributions-and by probability integral transformation of nonuniform random variables. I also treat briefly the issues of multi-variate extension, of distributions on subsets of R and of distributions on the circle. The review and comparison is not comprehensive, necessarily being selective and therefore somewhat personal.

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“…Other examples --which are heavy-tailed but guarantee the existence of all moments of the transformed distributions --are the K-transformation of MacGillivray and Cannon (1997) and the J-transformation of Fischer and Klein (2004). For application of such 'Tukey-type distributions' to financial return data we refer to Fischer et al (2006).…”

Section: Introductionmentioning

confidence: 97%