RelMDD-A Library for Manipulating Relations Based on MDDs

Relation algebras is one of the state-of-the-art means used by mathematicians and computer scientists for solving very complex problems. As a result, a computer algebra system for relation algebras called RelView has been developed at Kiel University. RelView works within the standard model of relation algebras. On the other hand, relation algebras do have other models which may have different properties. For example, in the standard model we always have L;L=L (the composition of two (heterogeneous) universal relations yields a universal relation). This is not true in some non-standard models. Therefore, any example in RelView will always satisfy this property even though it is not true in general. On the other hand, it has been shown that every relation algebra with relational sums and subobjects can be seen as matrix algebra similar to the correspondence of binary relations between sets and Boolean matrices. The aim of my research is to develop a new system that works with both standard and non-standard models for arbitrary relations using multiple-valued decision diagrams (MDDs). This system will implement relations as matrix algebras. The proposed structure is a library written in C which can be imported by other languages such as Java or Haskell.

Macroeconomic News Effects and Foreign Exchange Jumps

This thesis investigates how macroeconomic news announcements affect jumps and cojumps in foreign exchange markets, especially under different business cycles. We use 5-min interval from high frequency data on Euro/Dollar, Pound/Dollar and Yen/Dollar from Nov. 1, 2004 to Feb. 28, 2015. The jump detection method was proposed by Andersen et al. (2007c), Lee & Mykland (2008) and then modified by Boudt et al. (2011a) for robustness. Then we apply the two-regime smooth transition regression model of Teräsvirta (1994) to explore news effects under different business cycles. We find that scheduled news related to employment, real activity, forward expectations, monetary policy, current account, price and consumption influences forex jumps, but only FOMC Rate Decisions has consistent effects on cojumps. Speeches given by major central bank officials near a crisis also significantly affect jumps and cojumps. However, the impacts of some macroeconomic news are not the same under different economic states.