Are Correlations Constant Over Time? Application of the CC-TRIGt-test to Return Series from Different Asset Classes.

A new test for constant correlation is proposed. Based on the bivariate Student-t distribution, this test is derived as Lagrange multiplier (LM) test. Whereas most of the traditional tests (e.g. Jennrich, 1970, Tang, 1995 and Goetzmann, Li & Rouwenhorst, 2005) specify the unknown correlations as piecewise constant, our model-setup for the correlation coefficient is based on trigonometric functions. Applying this test to assets from different financial markets (stocks, exchange rates, metals) there is empirical evidence that many of the correlations vary over time.Lagrange multiplier test, constant correlation, trigonometric functions.

Generalized Tukey-type distributions with application to financial and teletraffic data

Constructing skew and heavy-tailed distributions by transforming a standard normal variable goes back to Tukey (1977) and was extended and formalized by Hoaglin (1983) and Martinez & Iglewicz (1984). Applications of Tukey's GH distribution family - which are composed by a skewness transformation G and a kurtosis transformation H - can be found, for instance, in financial, environmental or medical statistics. Recently, alternative transformations emerged in the literature. Rayner & MacGillivray (2002b) discuss the GK distributions, where Tukey's H-transformation is replaced by another kurtosis transformation K. Similarly, Fischer & Klein (2004) advocate the J-transformation which also produces heavy tails but - in contrast to Tukey's H-transformation - still guarantees the existence of all moments. Within this work we present a very general kurtosis transformation which nests H-, K- and J-transformation and, hence, permits to discriminate between them. Applications to financial and teletraffic data are given. --

Testing for constant correlation by means of trigonometric functions

A new test for constant correlation is proposed. The TC-test is derived as Lagrange multiplier (LM) test. Whereas most of the traditional tests (e.g. Jennrich, 1970, Tang, 1995 and Goetzmann, Li & Rouwenhorst, 2005) specify the unknown correlations as piecewise constant, our model-setup for the correlation coefficient is based on trigonometric functions. The simulation results demonstrate that the TC-test guarantees correct empirical size, is powerful against many alternatives and able to detect structural breaks in correlations. Finally, application of the TC-test to foreign exchange rate data over the period of 15 years is given. --

Skew generalized secant hyperbolic distributions: unconditional and conditional fit to asset returns

A generalization of the hyperbolic secant distribution which allows both for skewness and for leptokurtosis was given by Morris (1982). Recently, Vaughan (2002) proposed another flexible generalization of the hyperbolic secant distribution which has a lot of nice properties but is not able to allow for skewness. For this reason, Fischer and Vaughan (2002) additionally introduced a skewness parameter by means of splitting the scale parameter and showed that most of the nice properties are preserved. We briefly review both classes of distributions and apply them to financial return data. By means of the Nikkei225 data, it will be shown that this class of distributions - the socalled skew generalized secant hyperbolic distribution - provides an excellent fit in the context of unconditional and conditional return models. --SGSH distribution,NEF-GHS distribution,skewness,GARCH,APARCH

The L-distribution and skew generalizations

Leptokurtic or platykurtic distributions can, for example, be generated by applying certain non-linear transformations to a Gaussian random variable. Within this work we focus on the class of so-called power transformations which are determined by their generator function. Examples are the H-transformation of Tukey (1960), the J-transformation of Fischer and Klein (2004) and the L-transformation which is derived from Johnson's inverse hyperbolic sine transformation. It is shown that generator functions themselves which meet certain requirements can be used to construct both probability densities and cumulative distribution functions. For the J-transformation, we recover the logistic distribution. Using the L-transformation, a new class of densities is derived, discussed and generalized. --Power kurtosis transformation,leptokurtosis,(skew) L-distribution

A note on the construction of generalized Tukey-type transformations

One possibility to construct heavy tail distributions is to directly manipulate a standard Gaussian random variable by means of transformations which satisfy certain conditions. This approach dates back to Tukey (1960) who introduces the popular H-transformation. Alternatively, the K-transformation of MacGillivray & Cannon (1997) or the J-transformation of Fischer & Klein (2004) may be used. Recently, Klein & Fischer (2006) proposed a very general power kurtosis transformation which includes the above-mentioned transformations as special cases. Unfortunately, their transformation requires an infinite number of unknown parameters to be estimated. In contrast, we introduce a very simple method to construct êexible kurtosis transformations. In particular, manageable superstructures are suggested in order to statistically discriminate between H-, J-and K-distributions (associated to H-, J- and K-transformations). --Generalized kurtosis transformation,H-transformation

The L-distribution and skew generalizations

Leptokurtic or platykurtic distributions can, for example, be generated by applying certain non-linear transformations to a Gaussian random variable. Within this work we focus on the class of so-called power transformations which are determined by their generator function. Examples are the H-transformation of Tukey (1960), the J-transformation of Fischer and Klein (2004) and the L-transformation which is derived from Johnson's inverse hyperbolic sine transformation. It is shown that generator functions themselves which meet certain requirements can be used to construct both probability densities and cumulative distribution functions. For the J-transformation, we recover the logistic distribution. Using the L-transformation, a new class of densities is derived, discussed and generalized. --Power kurtosis transformation,leptokurtosis,(skew) L-distribution

Consequences of simultaneous chiral symmetry breaking and deconfinement for the isospin symmetric phase diagram

The thermodynamic bag model (tdBag) has been applied widely to model quark matter properties in both heavy-ion and astrophysics communities. Several fundamental physics aspects are missing in tdBag, e.g., dynamical chiral symmetry breaking (D$\chi$SB) and repulsions due to the vector interaction are both included explicitly in the novel vBag quark matter model of Kl\"ahn and Fischer (2015) (Astrophys. J. 810, 134 (2015)). An important feature of vBag is the simultaneous D$\chi$SB and deconfinement, where the latter links vBag to a given hadronic model for the construction of the phase transition. In this article we discuss the extension to finite temperatures and the resulting phase diagram for the isospin symmetric medium.Comment: 6 pages, 2 figures, Contribution to the Topical Issue Exploring strongly interacting matter at high densities - NICA White Paper edited by David Blaschke et a