Complex Correlation Approach for High Frequency Financial Data

We propose a novel approach that allows to calculate Hilbert transform based complex correlation for unevenly spaced data. This method is especially suitable for high frequency trading data, which are of a particular interest in finance. Its most important feature is the ability to take into account lead-lag relations on different scales, without knowing them in advance. We also present results obtained with this approach while working on Tokyo Stock Exchange intraday quotations. We show that individual sectors and subsectors tend to form important market components which may follow each other with small but significant delays. These components may be recognized by analysing eigenvectors of complex correlation matrix for Nikkei 225 stocks. Interestingly, sectorial components are also found in eigenvectors corresponding to the bulk eigenvalues, traditionally treated as noise

Discrete-Time Nonlinear Attitude Tracking Control of Spacecraft

Recent space programs require agile and large-angle attitude maneuvers for applications in various fields such as observational astronomy. To achieve agility and large-angle attitude maneuvers, it will be required to design an attitude control system that takes into account nonlinear motion because agile and large-angle rotational motion of a spacecraft in such missions represents a nonlinear system. Considerable research has been done about the nonlinear attitude tracking control of spacecraft, and these methods involve a continuous-time control framework. However, since a computer, which is a digital device, is employed as a spacecraft controller, the control method should have discrete-time control or sampled-data control framework. This chapter considers discrete-time nonlinear attitude tracking control problem of spacecraft. To this end, a Euler approximation system with respect to tracking error is first derived. Then, we design a discrete-time nonlinear attitude tracking controller so that the closed-loop system consisting of the Euler approximation system becomes input-to-state stable (ISS). Furthermore, the exact discrete-time system with a derived controller is indicated semiglobal practical asymptotic (SPA) stable. Finally, the effectiveness of proposed control method is verified by numerical simulations