  With the development of data-monitoring techniques in various fields of
science, multivariate functional data are often observed. Consequently, an
increasing number of methods have appeared to extend the general summary
statistics of multivariate functional data. However, trajectory functional
data, as an important sub-type, have not been studied very well. This article
proposes two informative exploratory tools, the trajectory functional boxplot,
and the modified simplicial band depth (MSBD) versus Wiggliness of Directional
Outlyingness (WO) plot, to visualize the centrality of trajectory functional
data. The newly defined WO index effectively measures the shape variation of
curves and hence serves as a detector for shape outliers; additionally, MSBD
provides a center-outward ranking result and works as a detector for magnitude
outliers. Using the two measures, the functional boxplot of the trajectory
reveals center-outward patterns and potential outliers using the raw curves,
whereas the MSBD-WO plot illustrates such patterns and outliers in a space
spanned by MSBD and WO. The proposed methods are validated on hurricane path
data and migration trace data recorded from two types of birds.
