Non-Gaussian time series, nonlinear dependence and financial markets

Key features in the statistical characterization of financial markets are nonlinearity and non-Gaussianity. These are compounded by nonstationarity and volatility of ARCH/GARCH type. In the project these problems are addressed in the three sub-projects: i) Local Gaussian Correlation: The ordinary correlation coefficient is extended such that local dependence in volatile financial markets can be measured in a more consistent and coherent manner. ii) Nonlinear cointegration: The cointegration concept has not been much used in financial markets, but recently the method of testing used in this context has been developed to such a stage that it could be applied to situations as in i). iii) Integer-valued time series: We explore autoregressive integer time s eries which are counterparts of ARCH/GARCH models. The integer time series could for example describe the number of transactions in a moving time window in a high frequency market. Funding of this project through travel grants would make it possible to s trengthen each sub-project and to increase interaction between them thus achieving synergy effects. The main participants will be Dag Tjøstheim, Hans Skaug, and Geir Drage Berentsen from the University of Bergen, Bård Støve from the Norwegian Business Sch ool, Jiti Gao, University of Adelaide and Kostas Fokianos, University of Cyprus. I have already established cooperation with these partners, and if funded Jiti Gao, Degui Li and Kostas Fokianos will visit the University of Bergen. Moreover, Jiti Gao is w illing to act as a host for Geir Drage Berentsen for a 3 month stay of his in Australia. There is also a link between these projects and the work on volatility by Hans Skaug and Tore Kleppe. This work is already funded by the Finansmarkedrådet. Finally, funding of this project will contribute to strengthen the research activity and the recruiting to the statistics group in finance and insurance mathematics. This is a high priority of the institute.