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In this note we consider the autoregressive moving average recurrent neural network ARMA-NN(1, 1) process. We show that in contrast to the pure autoregressive process simple ARMA-NN processes exist which are not irreducible. We prove that the controllability of the linear part of the process is sufficient for irreducibility. For the irreducible process essentially the shortcut weight corresponding to the autoregressive part determines whether the overall process is ergodic and stationary. / Series: Working Papers SFB "Adaptive Information Systems and Modelling in Economics and Management Science"

The Internet sees an ongoing transformation process from a single best-effort service network into a multi-service network. In addition to traditional applications like e-mail,WWW-traffic, or file transfer, future generation networks (FGNs) will carry services with real-time constraints and stringent availability and reliability requirements like Voice over IP (VoIP), video conferencing, virtual private networks (VPNs) for finance, other real-time business applications, tele-medicine, or tele-robotics. Hence, quality of service (QoS) guarantees and resilience to failures are crucial characteristics of an FGN architecture. At the same time, network operations must be efficient. This necessitates sophisticated mechanisms for the provisioning and the control of future communication infrastructures. In this work we investigate such echanisms for resilient FGNs. There are many aspects of the provisioning and control of resilient FGNs such as traffic matrix estimation, traffic characterization, traffic forecasting, mechanisms for QoS enforcement also during failure cases, resilient routing, or calability concerns for future routing and addressing mechanisms. In this work we focus on three important aspects for which performance analysis can deliver substantial insights: load balancing for multipath Internet routing, fast resilience concepts, and advanced dimensioning techniques for resilient networks. Routing in modern communication networks is often based on multipath structures, e.g., equal-cost multipath routing (ECMP) in IP networks, to facilitate traffic engineering and resiliency. When multipath routing is applied, load balancing algorithms distribute the traffic over available paths towards the destination according to pre-configured distribution values. State-of-the-art load balancing algorithms operate either on the packet or the flow level. Packet level mechanisms achieve highly accurate traffic distributions, but are known to have negative effects on the performance of transport protocols and should not be applied. Flow level mechanisms avoid performance degradations, but at the expense of reduced accuracy. These inaccuracies may have unpredictable effects on link capacity requirements and complicate resource management. Thus, it is important to exactly understand the accuracy and dynamics of load balancing algorithms in order to be able to exercise better network control. Knowing about their weaknesses, it is also important to look for alternatives and to assess their applicability in different networking scenarios. This is the first aspect of this work. Component failures are inevitable during the operation of communication networks and lead to routing disruptions if no special precautions are taken. In case of a failure, the robust shortest-path routing of the Internet reconverges after some time to a state where all nodes are again reachable – provided physical connectivity still exists. But stringent availability and reliability criteria of new services make a fast reaction to failures obligatory for resilient FGNs. This led to the development of fast reroute (FRR) concepts for MPLS and IP routing. The operations of MPLS-FRR have already been standardized. Still, the standards leave some degrees of freedom for the resilient path layout and it is important to understand the tradeoffs between different options for the path layout to efficiently provision resilient FGNs. In contrast, the standardization for IP-FRR is an ongoing process. The applicability and possible combinations of different concepts still are open issues. IP-FRR also facilitates a comprehensive resilience framework for IP routing covering all steps of the failure recovery cycle. These points constitute another aspect of this work. Finally, communication networks are usually over-provisioned, i.e., they have much more capacity installed than actually required during normal operation. This is a precaution for various challenges such as network element failures. An alternative to this capacity overprovisioning (CO) approach is admission control (AC). AC blocks new flows in case of imminent overload due to unanticipated events to protect the QoS for already admitted flows. On the one hand, CO is generally viewed as a simple mechanism, AC as a more complex mechanism that complicates the network control plane and raises interoperability issues. On the other hand, AC appears more cost-efficient than CO. To obtain advanced provisioning methods for resilient FGNs, it is important to find suitable models for irregular events, such as failures and different sources of overload, and to incorporate them into capacity dimensioning methods. This allows for a fair comparison between CO and AC in various situations and yields a better understanding of the strengths and weaknesses of both concepts. Such an advanced capacity dimensioning method for resilient FGNs represents the third aspect of this work. / Das Internet befindet sich gegenwärtig in einem Transformationsprozess von einem Netz mit einer einzigen best-effort Dienstklasse hin zu einem Mehr-Dienste-Netz. Zusätzlich zu herkömmlichen Anwendungen wie E-Mail, WWW oder Datenübertragung werden zukünftige Netze Dienste mit Echtzeitbedürfnissen und strikten Anforderungen an Verfügbarkeit und Zuverlässigkeit wie Voice over IP (VoIP), Videokonferenzdienste, Virtual Private Networks (VPNs) für Finanzanwendungen und andere Geschäftsanwendungen mit Echtzeitanforderungen, Tele-Medizin oder Telerobotik tragen. Daher sind die Gewährleistung von Dienstgüte und Ausfallsicherheit wesentliche Merkmale zukünftiger Netzarchitekturen. Gleichzeitig muss der Netzbetrieb effizient sein. Dies zieht den Bedarf an ausgefeilten Mechanismen für die Dimensionierung und Kontrolle ausfallsicherer Kommunikationsstrukturen nach sich. In dieser Arbeit werden solche Mechanismen, nämlich Lastaufteilung, Konzepte zur schnellen Reaktion im Fehlerfall und intelligente Ansätze zur Netzdimensionierung, untersucht.

One of the central goals in finance is to find better models for pricing and hedging financial derivatives such as call and put options. We present a semi-nonparametric approach to risk-neutral density extraction from option prices which is based on an extension of the concept of mixture density networks. The central idea is to model the shape of the risk-neutral density in a flexible, non-linear way as a function of the time horizon. Thereby, stylized facts such as negative skewness and excess kurtosis are captured. The approach is applied to a very large set of intraday options data on the FTSE 100 recorded at LIFFE. It is shown to yield significantly better results in terms of out-of-sample pricing in comparison to the basic Black-Scholes model and to an extended model adjusting the skewness and kurtosis terms. From the perspective of risk management, the extracted risk-neutral densities provide valuable information about market expectations. (author's abstract) / Series: Report Series SFB "Adaptive Information Systems and Modelling in Economics and Management Science"