Dynamic dependence networks: Financial time series forecasting and portfolio decisions (with discussion)

We discuss Bayesian forecasting of increasingly high-dimensional time series, a key area of application of stochastic dynamic models in the financial industry and allied areas of business. Novel state-space models characterizing sparse patterns of dependence among multiple time series extend existing multivariate volatility models to enable scaling to higher numbers of individual time series. The theory of these "dynamic dependence network" models shows how the individual series can be "decoupled" for sequential analysis, and then "recoupled" for applied forecasting and decision analysis. Decoupling allows fast, efficient analysis of each of the series in individual univariate models that are linked-- for later recoupling-- through a theoretical multivariate volatility structure defined by a sparse underlying graphical model. Computational advances are especially significant in connection with model uncertainty about the sparsity patterns among series that define this graphical model; Bayesian model averaging using discounting of historical information builds substantially on this computational advance. An extensive, detailed case study showcases the use of these models, and the improvements in forecasting and financial portfolio investment decisions that are achievable. Using a long series of daily international currency, stock indices and commodity prices, the case study includes evaluations of multi-day forecasts and Bayesian portfolio analysis with a variety of practical utility functions, as well as comparisons against commodity trading advisor benchmarks.Comment: 31 pages, 9 figures, 3 table

Phase field simulation of dendritic microstructure in additively manufactured titanium alloy

Additive manufacturing (AM) processes for metals, such as selective laser sintering and electron beam melting, involve rapid solidification process. The microstructure of the fabricated material and its properties strongly depend on the solidification. Therefore, in order to control and optimize the AM process, it is important to understand the microstructure evolution. In this work, using Ti-6Al-4V as a model system, the phase field method is applied to simulate the microstructure evolution in additively manufactured metals. First, the fundamental governing equations are presented. Then the effects of various processing related parameters, including local temperature gradient, scan speed and cooling rate, on dendrites’ morphology and growth velocity are studied. The simulated results show that the dendritic arms grow along the direction of the heat flow. Higher temperature gradient, scan speed and cooling rate will result in small dendritic arm spacing and higher growth velocity. The simulated dendritic morphology and arm spacings are in good agreement with experimental data and theoretical predictions

An automata-based automatic verification environment

With the continuing growth of computer systems including safety-critical computer control systems, the need for reliable tools to help construct, analyze, and verify such systems also continues to grow. The basic motivation of this work is to build such a formal verification environment for computer-based systems. An example of such a tool is the Design Oriented Verification and Evaluation (DOVE) created by Australian Defense Science and Technology Organization. One of the advantages of DOVE is that it combines ease of use provided by a graphical user interface for describing specifications in the form of extended state machines with the rigor of proving linear temporal logic properties in a robust theorem prover, Isabelle which was developed at Cambridge University, UK, and TU Munich, Germany. A different class of examples is that of model checkers, such as SPIN and SMV. In this work, we describe our technique to increase the utility of DOVE by extending it with the capability to build systems by specifying components. This added utility is demonstrated with a concrete example from a real project to study aspects of the control unit for an infusion pump being built at the Walter Reid Army Institute of Research. Secondly, we provide a formulation of linear temporal logic (LTL) in the theorem prover Isabelle. Next, we present a formalization of a variation of the algorithm for translating LTL into Büchi automata. The original translation algorithm is presented in Gerth et al and is the basis of model checkers such as SPIN. We also provide a formal proof of the termination and correctness of this algorithm. All definitions and proofs have been done fully formally within the generic theorem prover Isabelle, which guarantees the rigor of our work and the reliability of the results obtained. Finally, we introduce the automata theoretic framework for automatic verification as our future works