title: Appropriate time scales for nonlinear analyses of deterministic jump systems.
abstract: In the real world, there are many phenomena that are derived from deterministic systems but which fluctuate with nonuniform time intervals. This paper discusses the appropriate time scales that can be applied to such systems to analyze their properties. The financial markets are an example of such systems wherein price movements fluctuate with nonuniform time intervals. However, it is common to apply uniform time scales such as 1-min data and 1-h data to study price movements. This paper examines the validity of such time scales by using surrogate data tests to ascertain whether the deterministic properties of the original system can be identified from uniform sampled data. The results show that uniform time samplings are often inappropriate for nonlinear analyses. However, for other systems such as neural spikes and Internet traffic packets, which produce similar outputs, uniform time samplings are quite effective in extracting the system properties. Nevertheless, uniform samplings often generate overlapping data, which can cause false rejections of surrogate data tests.
authors.affiliation: Department of Intelligent Systems Engineering, College of Engineering, Ibaraki University, 4-12-1 Nakanarusawa-cho, Hitachi, Ibaraki 316-8511, Japan.
authors.forename: Tomoya
authors.initials: T
authors.lastname: Suzuki