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An autoregressive-ARCH model with possible exogeneous variables is treated. We estimate the conditional volatility of the model by applying feedforward networks to the residuals and prove consistency and asymptotic normality for the estimates under the rate of feedforward networks complexity. Recurrent neural networks estimates of GARCH and value-at-risk is studied. We prove consistency and asymptotic normality for the recurrent neural networks ARMA estimator under the rate of recurrent networks complexity. We also overcome the estimation problem in stochastic variance models in discrete time by feedforward networks and the introduction of a new distributions on the innovations. We use the method to calculate market risk such as expected shortfall and Value-at risk. We tested this distribution together with other new distributions on the GARCH family models against other common distributions on the financial market such as Normal Inverse Gaussian, normal and the Student's t- distributions. As an application of the models, some German stocks are studied and the different approaches are compared together with the most common method of GARCH(1,1) fit.

In the thesis the task of channel estimation in beyond 3G service area based mobile radio air interfaces is considered. A system concept named Joint Transmission and Detection Integrated Network (JOINT) forms the target platform for the investigations. A single service area of JOINT is considered, in which a number of mobile terminals is supported by a number of radio access points, which are connected to a central unit responsible for the signal processing. The modulation scheme of JOINT is OFDM. Pilot-aided channel estimation is considered, which has to be performed only in the uplink of JOINT, because the duplexing scheme TDD is applied. In this way, the complexity of the mobile terminals is reduced, because they do not need a channel estimator. Based on the signals received by the access points, the central unit estimates the channel transfer functions jointly for all mobile terminals. This is done by resorting to the a priori knowledge of the radiated pilot signals and by applying the technique of joint channel estimation, which is developed in the thesis. The quality of the gained estimates is judged by the degradation of their signal-to-noise ratio as compared to the signal-to-noise ratio of the respective estimates gained in the case of a single mobile terminal radiating its pilots. In the case of single-element receive antennas at the access points, said degradation depends solely on the structure of the applied pilots. In the thesis it is shown how by a proper design of the pilots the SNR degradation can be minimized. Besides using appropriate pilots, the performance of joint channel estimation can be further improved by the inclusion of additional a-priori information in the estimation process. An example of such additional information would be the knowledge of the directional properties of the radio channels. This knowledge can be gained if multi-element antennas are applied at the access points. Further, a-priori channel state information in the form of the power delay profiles of the radio channels can be included in the estimation process by the application of the minimum mean square error estimation principle for joint channel estimation. After having intensively studied the problem of joint channel estimation in JOINT, the thesis rounds itself by considering the impact of the unavoidable channel estimation errors on the performance of data estimation in JOINT. For the case of small channel estimation errors occurring due to the presence of noise at the access points, the performance of joint detection in the uplink and of joint transmission in the downlink of JOINT are investigated based on simulations. For the uplink, which utilizes joint detection, it is shown to which degree the bit error probability increases due to channel estimation errors. For the downlink, which utilizes joint transmission, channel estimation errors lead to an increase of the required transmit power, which can be quantified by the simulation results.

The thesis is focused on modelling and simulation of a Joint Transmission and Detection Integrated Network (JOINT), a novel air interface concept for B3G mobile radio systems. Besides the utilization of the OFDM transmission technique, which is a promising candidate for future mobile radio systems, and of the duplexing scheme time division duplexing (TDD), the subdivision of the geographical domain to be supported by mobile radio communications into service areas (SAs) is a highlighted concept of JOINT. A SA consists of neighboring sub-areas, which correspond to the cells of conventional cellular systems. The signals in a SA are jointly processed in a Central Unit (CU) in each SA. The CU performs joint channel estimation (JCE) and joint detection (JD) in the form of the receive-zero-forcing (RxZF) Filter for the uplink (UL) transmission and joint transmission (JT) in the form of the transmit-zero-forcing (TxZF) Filter for the downlink (DL) transmission. By these algorithms intra-SA multiple access interference (MAI) can be eliminated within the limits of the used model so that unbiased data estimates are obtained, and most of the computational effort is moved from mobile terminals (MTs) to the CU so that the MTs can do with low complexity. A simulation chain of JOINT has been established in the software MLDesigner by the author based on time discrete equivalent lowpass modelling. In this simulation chain, all key functionalities of JOINT are implemented. The simulation chain is designed for link level investigations. A number of channel models are implemented both for the single-SA scenario and the multiple-SA scenario so that the system performance of JOINT can be comprehensively studied. It is shown that in JOINT a duality or a symmetry of the MAI elimination in the UL and in the DL exists. Therefore, the typical noise enhancement going along with the MAI elimination by JD and JT, respectively, is the same in both links. In the simulations also the impact of channel estimation errors on the system performance is studied. In the multiple-SA scenario, due to the existence of the inter-SA MAI, which cannot be suppressed by the algorithms of JD and JT, the system performance in terms of the average bit error rate (BER) and the BER statistics degrades. A collection of simulation results show the potential of JOINT with respect to the improvement of the system performance and the enhancement of the spectrum e±ciency as compared to conventional cellular systems.

In conventional radio communication systems, the system design generally starts from the transmitter (Tx), i.e. the signal processing algorithm in the transmitter is a priori selected, and then the signal processing algorithm in the receiver is a posteriori determined to obtain the corresponding data estimate. Therefore, in these conventional communication systems, the transmitter can be considered the master and the receiver can be considered the slave. Consequently, such systems can be termed transmitter (Tx) oriented. In the case of Tx orientation, the a priori selected transmitter algorithm can be chosen with a view to arrive at particularly simple transmitter implementations. This advantage has to be countervailed by a higher implementation complexity of the a posteriori determined receiver algorithm. Opposed to the conventional scheme of Tx orientation, the design of communication systems can alternatively start from the receiver (Rx). Then, the signal processing algorithm in the receiver is a priori determined, and the transmitter algorithm results a posteriori. Such an unconventional approach to system design can be termed receiver (Rx) oriented. In the case of Rx orientation, the receiver algorithm can be a priori selected in such a way that the receiver complexity is minimum, and the a posteriori determined transmitter has to tolerate more implementation complexity. In practical communication systems the implementation complexity corresponds to the weight, volume, cost etc of the equipment. Therefore, the complexity is an important aspect which should be taken into account, when building practical communication systems. In mobile radio communication systems, the complexity of the mobile terminals (MTs) should be as low as possible, whereas more complicated implementations can be tolerated in the base station (BS). Having in mind the above mentioned complexity features of the rationales Tx orientation and Rx orientation, this means that in the uplink (UL), i.e. in the radio link from the MT to the BS, the quasi natural choice would be Tx orientation, which leads to low cost transmitters at the MTs, whereas in the downlink (DL), i.e. in the radio link from the BS to the MTs, the rationale Rx orientation would be the favorite alternative, because this results in simple receivers at the MTs. Mobile radio downlinks with the rationale Rx orientation are considered in the thesis. Modern mobile radio communication systems are cellular systems, in which both the intracell and intercell interferences exist. These interferences are the limiting factors for the performance of mobile radio systems. The intracell interference can be eliminated or at least reduced by joint signal processing with consideration of all the signals in the considered cell. However such joint signal processing is not feasible for the elimination of intercell interference in practical systems. Knowing that the detrimental effect of intercell interference grows with its average energy, the transmit energy radiated from the transmitter should be as low as possible to keep the intercell interference low. Low transmit energy is required also with respect to the growing electro-phobia of the public. The transmit energy reduction for multi-user mobile radio downlinks by the rationale Rx orientation is dealt with in the thesis. Among the questions still open in this research area, two questions of major importance are considered here. MIMO is an important feature with respect to the transmit power reduction of mobile radio systems. Therefore, first questionconcerns the linear Rx oriented transmission schemes combined with MIMO antenna structures. The investigations of the MIMO benefit on the linear Rx oriented transmission schemes are studied in the thesis. Utilization of unconventional multiply connected quantization schemes at the receiver has also great potential to reduce the transmit energy. Therefore, the second question considers the designing of non-linear Rx oriented transmission schemes combined with multiply connected quantization schemes.

Competing Neural Networks as Models for Non Stationary Financial Time Series -Changepoint Analysis-
(2005)

The problem of structural changes (variations) play a central role in many scientific fields. One of the most current debates is about climatic changes. Further, politicians, environmentalists, scientists, etc. are involved in this debate and almost everyone is concerned with the consequences of climatic changes. However, in this thesis we will not move into the latter direction, i.e. the study of climatic changes. Instead, we consider models for analyzing changes in the dynamics of observed time series assuming these changes are driven by a non-observable stochastic process. To this end, we consider a first order stationary Markov Chain as hidden process and define the Generalized Mixture of AR-ARCH model(GMAR-ARCH) which is an extension of the classical ARCH model to suit to model with dynamical changes. For this model we provide sufficient conditions that ensure its geometric ergodic property. Further, we define a conditional likelihood given the hidden process and a pseudo conditional likelihood in turn. For the pseudo conditional likelihood we assume that at each time instant the autoregressive and volatility functions can be suitably approximated by given Feedfoward Networks. Under this setting the consistency of the parameter estimates is derived and versions of the well-known Expectation Maximization algorithm and Viterbi Algorithm are designed to solve the problem numerically. Moreover, considering the volatility functions to be constants, we establish the consistency of the autoregressive functions estimates given some parametric classes of functions in general and some classes of single layer Feedfoward Networks in particular. Beside this hidden Markov Driven model, we define as alternative a Weighted Least Squares for estimating the time of change and the autoregressive functions. For the latter formulation, we consider a mixture of independent nonlinear autoregressive processes and assume once more that the autoregressive functions can be approximated by given single layer Feedfoward Networks. We derive the consistency and asymptotic normality of the parameter estimates. Further, we prove the convergence of Backpropagation for this setting under some regularity assumptions. Last but not least, we consider a Mixture of Nonlinear autoregressive processes with only one abrupt unknown changepoint and design a statistical test that can validate such changes.

This thesis investigates the constrained form of the spherical Minimax location problem and the spherical Weber location problem. Specifically, we consider the problem of locating a new facility on the surface of the unit sphere in the presence of convex spherical polygonal restricted regions and forbidden regions such that the maximum weighted distance from the new facility on the surface of the unit sphere to m existing facilities is minimized and the sum of the weighted distance from the new facility on the surface of the unit sphere to m existing facilities is minimized. It is assumed that a forbidden region is an area on the surface of the unit sphere where travel and facility location are not permitted and that distance is measured using the great circle arc distance. We represent a polynomial time algorithm for the spherical Minimax location problem for the special case where all the existing facilities are located on the surface of a hemisphere. Further, we have developed algorithms for spherical Weber location problem using barrier distance on a hemisphere as well as on the unit sphere.

The present thesis deals with a novel approach to increase the resource usage in digital communications. In digital communication systems, each information bearing data symbol is associated to a waveform which is transmitted over a physical medium. The time or frequency separations among the waveforms associated to the information data have always been chosen to avoid or limit the interference among them. By doing so, n the presence of a distortionless ideal channel, a single receive waveform is affected as little as possible by the presence of the other waveforms. The conditions necessary to meet the absence of any interference among the waveforms are well known and consist of a relationship between the minimum time separation among the waveforms and their bandwidth occupation or, equivalently, the minimum frequency separation and their time occupation. These conditions are referred to as Nyquist assumptions. The key idea of this work is to relax the Nyquist assumptions and to transmit with a time and/or frequency separation between the waveforms smaller than the minimum required to avoid interference. The reduction of the time and/or frequency separation generates not only an increment of the resource usage, but also a degradation in the quality of the received data. Therefore, to maintain a certain quality in the received signal, we have to increase the amount of transmitted power. We investigate the trade-off between the increment of the resource usage and the correspondent performance degradation in three different cases. The first case is the single carrier case in which all waveforms have the same spectrum, but have different temporal locations. The second one is the multi carrier case in which each waveform has its distinct spectrum and occupies all the available time. Finally, the hybrid case when each waveform has its unique time and frequency location. These different cases are framed within the general system modelling developed in the thesis so that they can be easily compared. We evaluate the potential of the key idea of the thesis by choosing a set of four possible waveforms with different characteristics. By doing so, we study the influence of the waveform characteristics in the three system configurations. We propose an interpretation of the results by modifying the well-known Shannon capacity formula and by explicitly expressing its dependency on the increment of resource usage and on the performance degradation. The results are very promising. We show that both in the case of a single carrier system with a time limited waveform and in the case of a multi-carrier system with a frequency limited waveform, the reduction of the time or frequency separation, respectively, has a positive effect on the channel capacity. The latter, depending on the actual SNR, can double or increase even more significantly.

In traditional portfolio optimization under the threat of a crash the investment horizon or time to maturity is neglected. Developing the so-called crash hedging strategies (which are portfolio strategies which make an investor indifferent to the occurrence of an uncertain (down) jumps of the price of the risky asset) the time to maturity turns out to be essential. The crash hedging strategies are derived as solutions of non-linear differential equations which itself are consequences of an equilibrium strategy. Hereby the situation of changing market coefficients after a possible crash is considered for the case of logarithmic utility as well as for the case of general utility functions. A benefit-cost analysis of the crash hedging strategy is done as well as a comparison of the crash hedging strategy with the optimal portfolio strategies given in traditional crash models. Moreover, it will be shown that the crash hedging strategies optimize the worst-case bound for the expected utility from final wealth subject to some restrictions. Another application is to model crash hedging strategies in situations where both the number and the height of the crash are uncertain but bounded. Taking the additional information of the probability of a possible crash happening into account leads to the development of the q-quantile crash hedging strategy.

Fragmentation of tropical rain forests is pervasive and results in various modifications in the ecosystem functioning such as … It has long been noticed that the colony densities of a dominant herbivore in the neotropics - leaf-cutting ant (LCA) - increase in fragmentation-related habitats like forest edges and small fragments, however the reasons for this increase are not clear. The aim of the study was to test the hypothesis that bottom-up control of LCA populations is less effective in fragmented compared to continuous forests and thus explains the increase in LCA colony densities in these habitats. In order to test for less effective bottom-up control, I proposed four working hypotheses. I hypothesized that LCA colonies in fragmented habitats (1) find more palatable vegetation due to low plant defences, (2) forage on few dominant species resulting in a narrow diet breadth, (3) possess small foraging areas and (4) increase herbivory rate at the colony level. The study was conducted in the remnants of the Atlantic rainforest in NE Brazil. Two fragmentation-related forest habitats were included: the edge and a 3500-ha continuous forest and the interior of the 50-ha forest fragment. The interior of the continuous forest served as a control habitat for the study. All working hypotheses can be generally accepted. The results indicate that the abundance of LCA host plant species in the habitats created by forest fragmentation along with weaker chemical defense of those species (especially the lack of terpenoids) allow ants to forage predominantly on palatable species and thus reduce foraging costs on other species. This is supported by narrower ant diet breadth in these habitats. Similarly, small foraging areas in edge habitats and in small forest fragments indicate that there ants do not have to go far to find the suitable host species and thus they save foraging costs. Increased LCA herbivory rates indicate that the damages (i.e., amount of harvested foliage) caused by LCA are more important in fragmentation-related habitats which are more vulnerable to LCA herbivory due to the high availability of palatable plants and a low total amount of foliage (LAI). (1) Few plant defences, (2) narrower ant diet breadth, (3) reduced colony foraging areas, and (4) increased herbivory rates, clearly indicate a weaker bottom-up control for LCA in fragmented habitats. Weak bottom-up control in the fragmentation-related habitats decreases the foraging costs of a LCA colony in these habitats and the colonies might use the surplus of energy resulting from reduced foraging costs to increase the colony growth, the reproduction and turnover. If correct, this explains why fragmented habitats support more LCA colonies at a given time compared to continuous forest habitats. Further studies are urgently needed to estimate LCA colony growth and turnover rates. There are indices that edge effects of forest fragmentation might be more responsible in regulating LCA populations than area or isolation effects. This emphasizes the need to conserve big forest fragments not to fall below a critical size and retain their regular shape. Weak bottom-up control of LCA populations has various consequences on forested ecosystems. I suggest a loop between forest fragmentation and LCA population dynamics: the increased LCA colony densities, along with lower bottom-up control increase LCA herbivory pressure on the forest and thus inevitably amplify the deleterious effects of fragmentation. These effects include direct consequences of leaf removal by ants and various indirect effects on ecosystem functioning. This study contributes to our understanding of how primary fragmentation effects, via the alteration of trophic interactions, may translate into higher order effects on ecosystem functions.

Inappropriate speed is the most common reason for road traffic accidents world wide. Thus, a necessity for speed management exists. The so-called SUNflower states Sweden, the United Kingdom and the Netherlands - each spending strong effort in traffic safety policies - have great success in reducing mean road speeds and speed variances through speed management. However, the effect is still insufficient for gaining real traffic safety. Thus, there is a discussion to make use of technical in-vehicle devices. One of these technologies called Intelligent Speed Adaptation (ISA) reduces vehicle speeds. This is done either by warning the driver that he is speeding, or activating the accelerator pedal with a counterforce, or reducing the gasoline supply to the motor. The three ways of reducing the speed are called version 1-3. The EC-project for research on speed adaptation policies on European roads (PROSPER) deals with strategic proposals for the implementation of the different ISA-versions. This thesis includes selected results of PROSPER. In this thesis two empiric surveys were done in order to give an overview about the basic conditions (e.g. social, economic, technical aspects) for an ISA implementation in Germany. On one hand, a stakeholder analysis and questionnaire using the Delphi-method has been accomplished in two rounds. On the other hand, a questionnaire with speed offenders has been accomplished, too, in two rounds. In addition, the author created an expert pool consisting of 23 experts representing the most important fields of science and practice in which ISA is involved. The author made phone or personal interviews with most of the experts. 12 experts also produced a detailed publication on their professional point of view towards ISA. The two surveys and the professional comments on ISA led to four possible implementation scenarios for ISA in Germany. However, due to a strong political opposition against ISA it is also thinkable that ISA is not implemented or the implementation process starts after 2015 (i.e. outside the aimed period of time). The scenarios are as follows: A) Implementation of version 1 by market forces with governmental subventions. B) Implementation of version 2 by market forces supported by traffic safety institutions and image-making processes. C) Implementation of a modified version 3 by law for speed offenders instead of cancellation of the driving licence. D) Implementation of various versions in Germany because of a broad implementation of ISA in the SUNflower states. X) Non-implementation of ISA leads to the necessity of alternative speed management measures. The author prefers scenario B because - ceteris paribus - it seems to be the most likely way to implement the technology. As soon as ISA reaches technical maturity, the implementation process has to be accomplished in three steps. 1) Marketing and image making 2) Margin introduction 3) Market penetration This implementation process for ISA by market forces could effect a percentage of at least 15% of all vehicles equipped with ISA before the year 2015.