Augmented GARCH sequences: Dependence structure and asymptotics

The augmented GARCH model is a unification of numerous extensions of the popular and widely used ARCH process. It was introduced by Duan and besides ordinary (linear) GARCH processes, it contains exponential GARCH, power GARCH, threshold GARCH, asymmetric GARCH, etc. In this paper, we study the probabilistic structure of augmented $\mathrm {GARCH}(1,1)$ sequences and the asymptotic distribution of various functionals of the process occurring in problems of statistical inference. Instead of using the Markov structure of the model and implied mixing properties, we utilize independence properties of perturbed GARCH sequences to directly reduce their asymptotic behavior to the case of independent random variables. This method applies for a very large class of functionals and eliminates the fairly restrictive moment and smoothness conditions assumed in the earlier theory. In particular, we derive functional CLTs for powers of the augmented GARCH variables, derive the error rate in the CLT and obtain asymptotic results for their empirical processes under nearly optimal conditions.Comment: Published in at http://dx.doi.org/10.3150/07-BEJ120 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Eleven Years of QCD at LEP

Studies of hadronic final states of $e^+e^-$ annihilations, observed at the Large Electron Positron Collider LEP at CERN, are reviewed. The topics included cover measurements of $\alpha_s$, hadronic event shapes and hadronisation studies, tests of asymptotic freedom and of the non-Abelian gauge structure of QCD, differences between quark and gluon jets, tests of power corrections and selected results of two-photon scattering processes. The improvements obtained at LEP are demonstrated by comparing to results from the pre-LEP era. This article consists of a reproduction of slides presented at the LEPFest in October 2000, supplemented by a short descriptive text and a list of relevant references.Comment: 10 pages of text plus reproduction of 27 transparencies presented at the LEPFest at CERN, October 2000. To be published in Eur. Phys. Jour (direct) C; a higher resolution version of the viewgraphs can be obtained from: http://www.mppmu.mpg.de/~bethke/LEPQCDtalk-higres.pd

αs\alpha_s at Zinnowitz 2004

A review of measurements of $\alpha_s$ is given, representing the status of April 2004. The results prove the energy dependence of $\alpha_s$ and are in excellent agreement with the expectations of Quantum Chromodynamics, QCD. Evolving all results to the rest energy of the $Z^0$ boson, the world average of $\alpha_s(M_Z)$ is determined from measurements which are based on QCD calculations in complete NNLO perturbation theory, giving $\alpha_s(M_Z) = 0.1182 \pm 0.0027 .$Comment: 8 pages, 4 figures, talk presented at the workshop Loops and Legs in Quantum Field Theory, April 2004, Zinnowitz (Germany

Media Philosophy— A Reasonable Programme?

It is beyond any doubt that media have an enormous impact on our media-culture societies. Media in?uence our perception and our knowledge, our memory as well as our emotions. They create public spheres and public opinions and give rise to media realities. Media shape our socialisation and our communality. They transform economy, politics, science, religion and law. “What we know about our society, even about our world we are living in, we know via the mass media.” (Luhmann 1996:9; my translation) Accordingly, “the media” have become a paramount subject of interdisciplinary discourses in the last decades all over the world. All these developments have become topics of scienti?c analyses as well as parts of media programmes. Since decades, various academic disciplines focused on an other-observation (“Fremdbeobachtung”) of the media from an external state, whereas the media increasingly tend to observe themselves as well as one another in order to transform this self-observation into parts of their respective programmes. The other-observation is carried out either by scholars of communication- and/or media theory or by philosophers; but whereas the former are organised in academic disciplines, no established discipline entitled “media philosophy” exists until today. Instead, the various approaches to philosophical analyses of media are heterogeneous and lack a solid theoretical basis as well as a disciplinary organisation. Some scholars even hold the view that media are not even within the province of philosophers. Some people deeply regret this deadlock regarding not only topics and discourses but also future jobs and positions for scholars of a discipline “media philosophy” to come. Others welcome this stalemate which gives room to creative solutions of thematic as well as of organisational matters. Let us have a short look at some of the foreseeable options. One of the actual media philosophical approaches concentrates its efforts on a reformulation of traditional philosophical topics in the framework of media ef?ciencies. The list of such topics is rather long and covers nearly all famous crucial subjects of philosophical discourses, reaching from reality, truth, culture, society, education or politics to time, space, emotion, subject or entertainment. This kind of rethinking or reformulating philosophical topics concentrates upon the question how—in the co-evolution of media systems and society—our daily experiences as well as our theoretical modellings of these topics have changed on the historical way from writing to the Internet

The Financial Crisis and the Regulation of Credit Rating Agencies : A European Banking Perspective

Credit rating agencies (CRAs) bear some responsibility for the financial crisis that started in 2007 and remains ongoing. This is acknowledged by policymakers, market participants, and by the agencies themselves. It soon became clear that, given the depth of the crisis, CRAs would not be able to satisfy policymakers by eliminating flaws in their rating methods and improving corporate governance. Although the CRAs were more or less unregulated before the outbreak of the financial crisis, after the crisis started, politicians became increasingly vocal in demanding regulation. Initially, these demands were confined to a more binding form of self-regulation. But as the crisis progressed, the calls for state regulation grew ever louder. It became apparent after the November 2008 G-20 summit in Washington that state regulation could no longer be avoided. In Europe, the course had been set in this direction even before then. Since European policymakers saw the crisis as evidence that the Anglo-Saxon approach to the financial markets had failed, they believed they were now strongly placed to have a decisive influence on shaping a new international financial order. It is remarkable to note the shift in European policy from a self-regulatory approach, which was comparatively liberal in international terms, to quite rigorous state regulation of CRAs. Both the European Commission and the European Parliament drew up far-reaching plans. Although European policymakers knew that only globally consistent regulation would be appropriate for a new world financial order, their initial draft legislation was geared more toward stand-alone European regulation. While the final version of the European Union Regulation on Credit Rating Agencies focuses firmly on the European arena, the key point for all market participants is that this is unlikely to have an adverse effect on the global ratings market. It must nevertheless be recognized that the scope of the selected regulatory approach is extremely narrow. Certainly, it has the potential to improve the corporate governance of CRAs and prevent conflicts of interests. But it can do nothing to address the repeated calls for greater competition or for CRAs to be made liable for their ratings.credit rating agencies, financial crisis, financial regulation, European Regulation

Collective behavior of colloids due to critical Casimir interactions

If colloidal solute particles are suspended in a solvent close to its critical point, they act as cavities in a fluctuating medium and thereby restrict and modify the fluctuation spectrum in a way which depends on their relative configuration. As a result effective, so-called critical Casimir forces (CCFs) emerge between the colloids. The range and the amplitude of CCFs depend sensitively on the temperature and the composition of the solvent as well as on the boundary conditions of the order parameter of the solvent at the particle surfaces. These remarkable, moreover universal features of the CCFs provide the possibility for an active control over the assembly of colloids. This has triggered a recent surge of experimental and theoretical interest in these phenomena. We present an overview of current research activities in this area. Various experiments demonstrate the occurrence of thermally reversible self-assembly or aggregation or even equilibrium phase transitions of colloids in the mixed phase below the lower consolute points of binary solvents. We discuss the status of the theoretical description of these phenomena, in particular the validity of a description in terms of effective, one-component colloidal systems and the necessity of a full treatment of a ternary solvent-colloid mixture. We suggest perspectives on the directions towards which future research in this field might develop.Comment: review, 88 pages, 19 figure