Informationskriterien und Volatility Clustering

Ein wichtiges Problem in der statistischen Analyse ist die Auswahl eines passenden Mo-dells. Im Kontext linearer ARIMA-Modelle kann gezeigt werden, dass - die Gültigkeit bestimmter Regularitätsbedingungen vorausgesetzt - die Minimierung des Schwarz-Kriteriums zu einer konsistenten Wahl der Anzahl der Parameter in einem Modell führt, wohingegen die Schätzung der Parameterzahl mit Hilfe des Akaike-Kriteriums tendenziell zu große Modelle liefert. Ziel dieser Analyse ist es, mit Hilfe von Monte-Carlo-Experimenten die Eigenschaften des Akaike- und des Schwarz-Informationskriteriums zu untersuchen, wenn der datengenerierende Prozess GARCH-Störungen aufweist. -- An important problem in statistical practise is the selection of a suitable statistical model. In the context of linear ARIMA-models it can be shown that - the validity of certain regu-larity conditions presupposed - the minimization from Black-criterion leads to a consistent choice of the parameters in a model whereas the estimation of the parameter number with the Akaike-criterion tendentious leads to too large models. Goal of this analysis is to examine with Monte Carlo experiments the characteristics of the Akaike- and of the Black-criterion if the data generating process exhibits GARCH-effects.

Ein übergeordnetes Variationsprinzip für den Fehlerabgleich der Finite-Element-Methode

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Untersuchung der Stabilität der Schätzung von Betafaktoren des CAPM - Ein Vergleich der KQ- mit robusten Methoden

Auf Tagesdaten mit der Methode der Kleinsten Quadrate geschätzte Betafaktoren des CAPM weisen bekanntlich eine starke zeitliche Instabilität auf, was ihre Brauchbarkeit für die kurzfristige Anlageentscheidung schmälert. Es soll deshalb untersucht werden, was die Ursachen dieser zeitlichen Instabilität sind, und ob es alternative Schätzverfahren gibt, die zu stabileren Betafaktoren führen. Als Ursache für die zeitliche Instabilität werden insbesondere Ausreißer in den Residuen vermutet. Alternative Schätzverfahren liefern die sog. robusten M- und GMSchätzer, die einen Schutz vor Ausreißern bieten. Da die Residuenverteilung zudem keine Normalverteilung sondern ausgesprochen leptokurtisch ist, versprechen diese zusätzlich eine größere asymptotische Effizienz als die KQ-Schätzung --

PDE-restringierte Optimierung in Anwendungen der spanenden Trockenbearbeitung

Nowadays industrial manufacturing is highly widespread while the demand of high-precision manufacturing is increasing constantly. In such processes, it is common to apply coolants to reduce the thermal stress of workpieces and tools as well as to guarantee the functional performance of the final parts. Nonetheless, there are several reasons like cost reduction and ecological benefits for omitting coolants or to use minimum quantity lubrication (MQL). In order to satisfy the quality standards in dry machining, compensation strategies of shape deviations are necessary. Due to the increasing digitalization of process chains (Industry 4.0), modern sensors and the usage of high-performance computing, nonlinear optimization is more convenient than ever before. In this context, a prediction model is required by which the machining can be optimized. In this work a hybrid approach is used to model thermo-elastic effects as well as geometrical deviations caused by a change of the residual stress state. Physical correlations of the modeling which are not investigated yet can be synthesized by empirical regression with a wide variety of data. The first part of this elaboration is the determination of heat fluxes in milling and drilling which cana t be measured directly. One goal is to utilize nonlinear optimization to solve parameter identification problems. The second part is the minimization of shape deviations in dry milling processes by means of the hybrid model. To achieve this, different milling strategies are compared and machining parameters are optimized with nonlinear optimization techniques, while an efficient machining process is sought at the same time. The mathematical majority of this work covers the PDE-constrained optimization. Still a challenging topic in this field is the treatment of complex problems involving high computational costs. It is still advisable to increase the efficiency of the optimization methods whereby the accuracy of the underlying model can be improved. One promising approach is the Simultaneous Analysis and Design (SAND) where a discretized PDE act as constraints of the optimization. This approach gives importance to exploiting the system structure of the optimization problem. Another common method is the Nested Analysis and Design (NAND). Theoretical considerations suggest that the SAND approach favored in this work has computational benefits for treating nonlinear PDEs. Beside the successful application of the SAND approach in dry machining one goal is to provide evidence of its computational efficiency

Die Berücksichtigung von Unsicherheit und Flexibilität in der Investitionsplanung – dargestellt am Beispiel einer Vertragsinvestition für Roggen

Investment decisions are, as a rule, characterized by uncertainty, irreversibility and flexibility. Simple net present value calculations will not account for these features. In many situations even flexible investment planning with decision trees, which represents the most advanced method of traditional investment appraisal, does not have the capacity to solve practical decision problems adequately. One handicap is a realistic and manageable representation of stochastic variables. It has long been known that stochastic simulation procedures offer a nearly unlimited capacity to represent distributions and stochastic processes. However, a standard simulation will not allow for the consideration of flexibility. The problem is that with a simple forward moving simulation of stochastic paths it is not clear at potential investment dates whether waiting or investing represents the optimal strategy. In this paper we show how stochastic simulation procedures can be integrated successfully into a backward recursive programming approach. The resulting modus operandi can be called “Bounded Recursive Stochastic Simulation†(BRSS). We use this efficient combination of simulation and dynamic programming to answer the question whether farmers should buy sales contracts which guarantee fixed prices for rye in the future. The results of the model affirm the importance of uncertainty and flexibility for investment decisions. They also show that the actual conditions offered by the wholesale buyer are not economically attractive for farmers, unless they are extremely risk averse. Thus, model results coincide with the empirical evidence that farmers do not enter these contracts.investment, uncertainty, flexibility, stochastic simulation, dynamic programming, sales contracts with fixed prices, Farm Management, Research Methods/ Statistical Methods, Risk and Uncertainty,