Time series data analyses in space physics

Techniques of time series data analyses developed over the past decades are reviewed. We discuss the theoretical principles and mathematical descriptions of these analytical techniques that have been developed by scientists with different backgrounds and perspectives. These principles not only provide the guidelines to evaluate each particular technique but also point to directions for the development of new methods. Most time series analyses can be divided into three categories: discontinuity analysis, wave analysis and correlation analysis. Techniques for analyzing one-dimensional discontinuities have been well-developed and tested. The errors and ambiguities of discontinuity analyses are reasonably well, but not as widely, understood. Techniques for wave analyses have been developed for certain wave properties and are still under further active development. Problems in using these techniques are recognized to a certain extent. Because of the complicity of the waves in space and the limitation of probing, there are significant needs for the development of new methods. Although simple techniques for two-satellite correlation analyses have been developed and tested for some time, techniques for multiple satellites are in an embryonic stage. We expect to see significant advances in the development of new techniques and new concepts. We believe, however, that the problems in this area have not been fully appreciated.