Exploring local dependence

This paper discusses two graphical methods for the investigation of local association of two continuous random variables. Often, scalar dependence measures, such as correlation, cannot reflect the complex dependence structure of two variables. However, dependence graphs have the potential to assess a far richer class of bivariate dependence structures. The two graphical methods discussed in this article are the chi-plot and the local dependence map. After the introduction of these methods they are applied to different data sets. These data sets contain simulated data and daily stock return series. With these examples the application possibilities of the two local dependence graphs are shown.