Relaxed quaternionic Gabor expansions at critical density

Shifted and modulated Gaussian functions play a vital role in the representation of signals. We extend the theory into a quaternionic setting, using two exponential kernels with two complex numbers. As a final result, we show that every continuous and quaternion-valued signal f in the Wiener space can be expanded into a unique l2 series on a lattice at critical density 1, provided one more point is added in the middle of a cell. We call that a relaxed Gabor expansion

FDZ annual report 2007

"Following the two evaluations by the German Council for Social and Economic Data in 2006 and by the German Council of Science and Humanities in 2007, the Research Data Centre (FDZ) of the Federal Employment Agency at the Institute for Employment Research plans to report on its activities regularly in future. We are beginning with this FDZ Annual Report 2007, which is intended to summarise the main events of the past 12 or 24 months in a few pages. The Annual Report also serves to provide transparency for our users, who after all justify the existence of the FDZ. This Report is divided into the following chapters: 'General Function', 'Basic Information', 'The Service-Oriented FDZ', 'The International FDZ' and, as an apt conclusion, 'Research at the FDZ'. Parts of the appendices (for Example Publications or Presentations in German) are not translated into English." (Text excerpt, IAB-Doku) ((en)) Additional Information Here you can find the German version of the report.Forschungsdatenzentrum - Bericht, Bundesagentur für Arbeit, IAB, amtliche Statistik, Datenzugang, Datenschutz, Arbeitsmarkt- und Berufsforschung, IAB-Beschäftigtenstichprobe, IAB-Betriebspanel, IAB-Betriebs-Historik-Panel, IAB-Linked-Employer-Employee-Datensatz, Integrierte Erwerbsbiografien, Datenaufbereitung, Datenausgabe

Diversification in Firm Valuation: A Multivariate Copula Approach

We introduce a new discounted cash flow model which adopts the diversification effect of multi-business firms. We face two challenges: One is examining how different diversification extents can affect the firm value due to risk reduction, and the other is modeling segment-specific cash flows and discount rates to reflect the differences in risk and growth characteristics across the different businesses that a firm operates in. Since the co-movement of business segments depends on the state of the economy, we use a multivariate copula approach taking the state-varying dependence of business segments explicitly into account. A high level of a firm's diversification determined by a low dependence between the firm's business segments leads to a lower probability of firm default which results in a higher firm value through reduced bankruptcy costs. We demonstrate this effect by comparing the values of three U.S. firms when modeling independence, dependence with copulas, and perfect dependence between businesses.diversification, firm valuation, dependence modeling, multi-business firm, bankruptcy costs, default probability, copulas, Monte Carlo simulation, discounted cash flow model

Asset market linkages in crisis periods

We characterize asset return linkages during periods of stress by an extremal dependence measure. Contrary to correlation analysis, this non-parametric measure is not predisposed towards the normal distribution and can account for non-linear relationships. Our estimates for the G-5 countries suggest that simultaneous crashes in stock markets are about two times more likely than in bond markets. Moreover, stock-bond contagion is about as frequent as flight to quality from stocks into bonds. Extreme cross-border linkages are surprisingly similar to national linkages, illustrating a potential downside to international financial integration JEL Classification: G1, F3, C49Bivariate Extreme Value Analysis, Extreme Co-movements, Flight to Quality

Banking System Stability: A Cross-Atlantic Perspective

This paper derives indicators of the severity and structure of banking system risk from asymptotic interdependencies between banks%u2019 equity prices. We use new tools available from multivariate extreme value theory to estimate individual banks%u2019 exposure to each other (%u201Ccontagion risk%u201D) and to systematic risk. Moreover, by applying structural break tests to those measures we study whether capital markets indicate changes in the importance of systemic risk over time. Using data for the United States and the euro area, we can also compare banking system stability between the two largest economies in the world. Finally, for Europe we assess the relative importance of cross-border bank spillovers as compared to domestic bank spillovers. The results suggest, inter alia, that systemic risk in the US is higher than in the euro area, mainly as cross-border risks are still relatively mild in Europe. On both sides of the Atlantic systemic risk has increased during the 1990s.